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The interrelationships of oxygen intake capacity, strength, body composition and physical working capacity. Miki, Kenneth Koji 1969

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THE INTERRELATIONSHIPS OF OXYGEN INTAKE CAPACITY, STRENGTH, BODY COMPOSITION AND PHYSICAL WORKING CAPACITY Dy KENNETH KOJI MIKI B . P . E . , U n i v e r s i t y of B r i t i s h Co lumbia , 196? A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF PHYSICAL EDUCATION i n the Schoo l of P h y s i c a l E d u c a t i o n and R e c r e a t i o n We a c cep t t h i s t h e s i s as conforming t o the r e q u i r e d s t anda rd THE UNIVERSITY OF BRITISH COLUMBIA Augus t , 1969 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and S t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d b y t h e Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g or, pub 1 i c a t i o n o f t h i s t h e s , i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada ABSTRACT The purpose of t h i s study was to determine the i n t e r r e -l a t i o n s h i p s between oxygen intake c a p a c i t y , s t r e n g t h , body composition and p h y s i c a l working c a p a c i t y , as measured by the Sjos t r a n d PWC170 t e s t . The s u b s i d i a r y problems were: 1. to determine what s t a t i s t i c a l procedure, i . e . , zero order c o r r e l a t i o n s , f i r s t order p a r t i a l c o r r e l a -t i o n s , twenty-second order p a r t i a l c o r r e l a t i o n s or stepwise m u l t i p l e r e g r e s s i o n a n a l y s i s , gave the gr e a t e s t i n s i g h t i n t o the p h y s i o l o g i c a l r e l a t i o n -ships between the v a r i a b l e s s e l e c t e d f o r t h i s study, 2. to determine the form i n which the v a r i a b l e s i n v e s -t i g a t e d have the most meaning b i o l o g i c a l l y , i . e . , as raw scores, as scores d i v i d e d by body weight, or as scores d i v i d e d by f a t f r e e weight, and 3. t o determine the accuracy of c a l c u l a t i n g PWC170 by g r a p h i c a l e s t i m a t i o n of the best f i t t i n g s t r a i g h t l i n e as compared w i t h the computer c a l c u l a t e d values obtained by the l e a s t squares r e g r e s s i o n method. F i f t y - f o u r subjects from the School of P h y s i c a l Educa-t i o n and Recreation a t the U n i v e r s i t y of B r i t i s h Columbia p a r t i c i p a t e d i n t h i s study. The Sjostrand PWC170 t e s t was conducted to es t imate p h y s i c a l work ing c a p a c i t y , and an " a l l ou t " r i d e on the b i c y c l e ergometer was a d m i n i s t e r e d to d e t e r -mine maximum oxygen in take v a l u e s . Body d e n s i t y was determined by the h y d r o s t a t i c we igh ing t e c h n i q u e , and body f a t was c a l c u -l a t e d by the f o rmu l a d e r i v e d by Keys and B rozek . A comprehensive s t r e n g t h t e s t was a l s o conducted on a l l the s u b j e c t s . The s t a t i s t i c a l a n a l y s i s of the da t a were ob ta ined through the Computing Center a t the U n i v e r s i t y of B r i t i s h Columbia (Program - T r i a n g u l a r R e g r e s s i o n Package ) . A ze ro o rde r c o r r e l a t i o n a n a l y s i s was conducted to a s s e s s the a c c u r -acy of the g r a p h i c method i n the c a l c u l a t i o n of PWC170 s c o r e s . A ze ro o rde r c o r r e l a t i o n a n a l y s i s was a l s o conducted to i n v e s -t i g a t e the i n t e r r e l a t i o n s h i p s between a l l the v a r i a b l e s when no v a r i a b l e s were he l d c o n s t a n t . Two f i r s t o rde r c o r r e l a t i o n a n a l y s i s were conducted t o i n v e s t i g a t e the i n t e r r e l a t i o n s h i p s between a l l the v a r i a b l e s when body s i z e was h e l d c o n s t a n t , i . e . , body weight and f a t f r e e we igh t , r e s p e c t i v e l y . A twenty-second o rde r c o r r e l a t i o n ma t r i x was ob ta ined to i n v e s t i g a t e the i n t e r r e l a t i o n s h i p between two v a r i a b l e s when a l l o thers were he l d c o n s t a n t . Three s tepwise m u l t i p l e r e g r e s s i o n a n a l y s i s were conducted to determine the i n t e r r e l a t i o n s h i p s between each of the dependent v a r i a b l e s (PWC170 kpm P e r min ; PWC170 kpm per min pe r kg body we igh t ; PWC170 k P m P e r m l n P e r k S f a t f r e e weight ) w i th two or more of the independent v a r i a b l e s . i v Within the l i m i t a t i o n s of the study, i t was concluded that the conventional graphic technique appeared to be an accurate method to estimate the best f i t t i n g straight l i n e i n the c a l c u l a t i o n of the PWC170 scores. The re s u l t s obtained i n t h i s study appeared to support the use of performance scores divided by f a t free weight as the most b i o l o g i c a l l y meaningful way to express performance capa-c i t y data. This appeared to be the preferred method f o r comparisons of indiv i d u a l s ' "true" a b i l i t i e s or capacities without regard to differences i n body size or body f a t . Consequently, the procedure appeared to be very appropriate f o r use i n normative tables. The f i r s t order p a r t i a l correlations of non-ratio variables with f a t free weight held constant appeared to be the best s t a t i s t i c a l procedure i n providing Insight into physiolo-g i c a l relationships between oxygen intake capacity, strength and physical working capacity (PWC170 kpm per min). The zero order c o r r e l a t i o n analysis, f i r s t order p a r t i a l c o r r e l a t i o n analysis and stepwise multiple regression analysis showed the following apparent relationships to exist between the variables explored i n t h i s study: i ) Fat free weight appeared to be the common factor i n the relationships between many of the variables i n t h i s study, i i ) Oxygen intake i n l i t e r s per min was s i g n i f i c a n t l y V r e l a t e d to p h y s i c a l work ing c a p a c i t y (PWC^ -po k P m per min) i n ze ro o rde r and f i r s t o rde r c o r r e l a -t i o n a n a l y s i s ( s i g n i f i c a n t a t the G.01 l e v e l of c o n f i d e n c e ) . In the s tepwise m u l t i p l e r e g r e s s i o n a n a l y s i s , oxygen i n t ake i n l i t e r s per minute d i d not c o n t r i b u t e to the p r e d i c t i o n of P W C 1 7 0 kpm per m in , but i t would have been the bes t s i n g l e p r e d i c t o r i n the absence of f a t f r e e we igh t . Oxygen i n t ake i n ml per min pe r kg body weight was the bes t p r e d i c t o r of P W C 1 7 0 kpm per min per kg body we igh t . I t was a l s o the bes t p r e d i c t o r of P W C 1 7 0 kpm pe r min pe r kg f a t f r e e we igh t , but t h i s appeared to be due to the s m a l l e r d i s p e r -s i o n s of oxygen i n t ake i n ml pe r min per kg f a t f r e e we igh t . i i i ) S t r eng th of the r i g h t l e g ex tenso r muscles c o r r e -l a t e d s i g n i f i c a n t l y w i t h PWC170 kpm per min i n ze ro o rde r and f i r s t o rde r c o r r e l a t i o n a n a l y s i s ( s i g n i f i c a n t a t the 0.05 l e v e l of c o n f i d e n c e ) . T h i s v a r i a b l e made a s m a l l c o n t r i b u t i o n t o >the p r e d i c t i o n of p h y s i c a l work ing c a p a c i t y i n . a l l t h r ee s tepwise m u l t i p l e r e g r e s s i o n a n a l y s i s , i v ) Body d e n s i t y c o r r e l a t e d s i g n i f i c a n t l y w i th PWC170 kpm pe r min pe r kg body weight i n ze ro o rde r c o r r e l a t i o n a n a l y s i s and w i th FWC170 kpm per min when body weight was s t a t i s t i c a l l y h e l d constant ( s i g n i f i c a n t a t the 0.01 l e v e l of c o n f i d e n c e ) . I t c o n t r i b u t e d t o the p r e d i c t i o n of F W C 1 7 0 kpm per min per kg body weight only s l i g h t l y l e s s than oxygen i n t a k e ml per min per kg body weight. Thus, i t appeared t h a t i n t h i s study, l e a n e r s u b j e c t s appeared to a t t a i n h i g h e r PWC170 kpm per min per kg body weight s c o r e s . ACKNOWLEDGEMENTS The author wishes to express h i s s i n c e r e a p p r e c i a t i o n t o Dr. S. Brown f o r h i s guidance, co-o p e r a t i o n a.nd c o n s i d e r a t i o n throughout the study, and to Mr. A. Bakogeorge, Miss A. E e d l i c h and to Dr. R. Hlndmarch, f o r s e r v i n g as committee members. The author f u r t h e r wishes t o thank Miss R. S t a d f e l d f o r her t e c h n i c a l a s s i s t a n c e i n t e s t i n g and i n computing the raw d a t a . DEDICATION To Dr. S.R. Brown, P r o f e s s o r , School of P h y s i c a l Education and Recreation, U n i v e r s i t y of B r i t i s h Columbia: "A student's v i c t o r y i s the teacher's g l o r y . " G i l b e r t of A u r i l l a c , c i r c a 1200 A.D. TABLE OF CONTENTS CHAPTER PAGE I. STATEMENT OF THE PROBLEM 1 I n t r o d u c t i o n to the Problem 1 The Problem 2 S u b s i d i a r y Problems 2 J u s t i f i c a t i o n of the Problem 3 D e f i n i t i o n of Terms 7 L i m i t a t i o n s 8 Assumpt ion 8 D e l i m i t a t i o n s 8 Refe rences 10 I I . REVIEW OF LITERATURE 12 I n t r o d u c t i o n - The S Jos t rand PWC170 Tes t 12 The P h y s i o l o g i c a l B a s i s of the PWC170 Tes t . . . . 13 The R e l a t i o n s h i p Between PWC170 and Maximum Oxygen Intake 20 The R e l a t i o n s h i p Between PWC170 and S t r eng th 25 The R e l a t i o n s h i p Between PWC170 and Body S i z e . . 28 A n a l y s i s of the S t a t i s t i c a l Methodology i n the I n t e r r e l a t i o n s h i p of Maximum Oxygen In take , S t r e n g t h , Body S i z e and PWC170 31 Re fe rences 3^ X CHAPTER PAGE I I I . METHODOLOGY 39 I n t r o d u c t i o n 39 E s t i m a t i o n of P h y s i c a l Work Capacity 39 E s t i m a t i o n of Maximum Oxygen Intake 43 E s t i m a t i o n of Body Density 46 E s t i m a t i o n of Muscular Strength 48 S t a t i s t i c a l Methodology 49 References 52 IV. RESULTS 55 Observations on the Subjects 55 Sample Data . . 56 Comparison Between Manual and Computer Methods f o r C a l c u l a t i n g the PWC170 Values 57 Zero Order C o r r e l a t i o n A n a l y s i s 59 Normality of the D i s t r i b u t i o n of Scores 67 F i r s t Order C o r r e l a t i o n A n a l y s i s 74 Twenty-Second Order C o r r e l a t i o n A n a l y s i s 77 Stepwise M u l t i p l e Regression A n a l y s i s 79 References 92 V. DISCUSSION 93 Observations on the Subjects 93 The Sample Data Compared w i t h Data from Other Studies 93 x i CHAPTER PAGE Comparison Between Manual and Computer Methods for Calculating the PWC170 Values . . . 104 Zero Order Correlation Analysis 1 0 5 Normality of the Distribution of Scores 114 Firs t Order Correlation Analysis 1 1 5 Twenty-Second Order Correlation Analysis 1 1 9 Stepwise Multiple Regression Analysis 1 1 9 References 1 2 ? VI. SUMMARY AND CONCLUSIONS 1 3 1 Summary 1 3 1 Conclusions 1 3 3 References 140 BIBLIOGRAPHY l 4 l APPENDICES A. STATISTICAL TREATMENT 148 B. SAMPLE DATA SHEETS 1 5 6 C. RAW SCORES AND CORRELATION MATRICES 1 6 4 LIST OF TABLES TABLE PAGE I. Comparat ive D e s c r i p t i v e S t a t i s t i c s of the Two Groups of Sub jec t s 55 I I . Means and Standard D e v i a t i o n s of A l l the V a r i a b l e s 57 I I I . Compar ison Between the Manual and Computer Methods f o r C a l c u l a t i n g PWC170 58 IV. Zero Order C o e f f i c i e n t s of C o r r e l a t i o n Between the Dependent V a r i a b l e PWC170 kpm per min and the Independent V a r i a b l e s (X4 .... X24) 60 V . Zero Order C o e f f i c i e n t s of C o r r e l a t i o n Between the Dependent V a r i a b l e PWC170 kpm per min pe r kg Body Weight and the Independent V a r i a b l e s (X4 . . . . X2i+) 62 V I . Zero Order C o e f f i c i e n t s of C o r r e l a t i o n Between the Dependent V a r i a b l e PWC170 kpm per min per kg Fa t F ree Weight and the Independent V a r i a b l e s (X4 .... X2l^) 64 V I I . Zero Order C o e f f i c i e n t s of C o r r e l a t i o n Between the Independent V a r i a b l e Body Weight and Other Independent V a r i a b l e s (X5 .... X24) . . . . 65 V I I I . Zero Order C o e f f i c i e n t s of C o r r e l a t i o n Between the Independent V a r i a b l e Fa t F ree Weight and Other Independent V a r i a b l e s (X£ . . . . X24) . . . . 67 x l i i TABLE PAGE IX. F i r s t Order Coefficients of Correlation Between Dependent Variable PWC170 kpm per min and Other Independent Variables with Body Weight Held Constant 75 X. F i r s t Order Coefficients of Correlation Between Dependent Variable PWC170 kpm per min and Other Independent Variables with Fat Free Weight Held Constant 76 XI. Twenty-Second Order Coefficients of Correlation Between Dependent Variable PWC170 kpm per min and Each Independent Variable with A l l Other Variables Held Constant 78 XII. Stepwise Multiple Regression Analysis with PWC170 kpm per min as the Dependent Variable . . 80 XIII. Variance of the Multiple Regression of the Dependent Variable PWC170 kpm per min 83 XIV. Stepwise Multiple Regression Analysis with PWC170 kpm per min per kg Body Weight as the Dependent Variable 85 XV. Variance of the Multiple Regression of the Dependent Variable P W C 1 7 0 kpm per min per kg Body Weight 87 XVI. Stepwise Multiple Regression Analysis with PWC170 kpm per min per kg Fat Free Weight as the Dependent Variable 89 xiv TABLE PAGE XVII. Variance of the Multiple Regression of the Dependent Variable PWC170 kpm per min per kg Fat Free Weight 91 XVIII. A Comparison of Investigations Determining Body Composition and Physical Working Capacity 9k XIX. Comparative Body Composition and Maximum Oxygen Intake Data of Several Investigations 100 XX. A Comparison of Investigations Determining Maximum Oxygen Intake and Physical Working Capacity 105 LIST OF FIGURES FIGURE PAGE 1-24 H is tograms of A l l the V a r i a b l e s Inc luded i n the Study (X i X24) 68 CHAPTER I STATEMENT OF THE PROBLEM I n t r o d u c t i o n to the Problem P h y s i c a l work c a p a c i t y , o r the a b i l i t y t o pe r fo rm heavy work a t h i g h i n t e n s i t i e s w i thout f a t i g u e , i s becoming an i n c r e a s i n g l y p o p u l a r concept i n the measurement of f u n c t i o n a l p h y s i o l o g i c a l c a p a c i t i e s of i n d i v i d u a l s . The Research Committee of the Canadian A s s o c i a t i o n f o r H e a l t h , P h y s i c a l E d u c a t i o n and R e c r e a t i o n has r e c e n t l y s t a t e d : The l i m i t a t i o n s of performance items as measures of p h y s i c a l f i t n e s s a r e , of c o u r s e , w e l l known and i n an e f f o r t to eva lua te f i t n e s s i n a more o b j e c t i v e and r e f i n e d manner on a n a t i o n a l s c a l e , the Research Committee vo ted to a d m i n i s t e r an i n t e r n a t i o n a l l y a c cep ted t e s t of work c a p a c i t y t o Canadian c h i l d r e n . (1:13) The work c a p a c i t y t e s t a c cep ted by the Research Committee was the m o d i f i e d S j o s t r a n d PWCiyo t e s t . The t e s t i s based on the r e a d i l y demonstrab le l i n e a r r e l a t i o n s h i p between s teady s t a t e p u l s e f r e q u e n c i e s and the work l o a d p roduc ing these pu l s e f r e q u e n c i e s (2,3 .4 ,5 )• I t i s conducted on a b i c y c l e ergometer and the s u b j e c t ' s s co re i s the work produced a t a s teady s t a t e hea r t r a t e of 170 beats pe r m inu te . S j o s t r a n d (6:14-3) has s t a t e d tha t t h i s v a l u e , work a t p u l s e r a t e 1?0, i s h i g h l y c o r r e l a t e d w i th c a r d i o v a s c u l a r and r e s p i r a -t o r y f u n c t i o n s such as s t r o k e volume, hea r t volume hemoglobin c o n c e n t r a t i o n and d i f f u s i o n c a p a c i t y of the l u n g s . These q u a l i t i e s and such advantages as low cos t of equipment, the 2 ease of t r a n s p o r t i n g equipment, the requ i rement of on l y sub-maximal energy expend i tu re on the p a r t of the s u b j e c t , and the s i m p l i c i t y of the t e s t i n g procedure has promoted the acceptance and use of the S j o s t r a n d PWC170 t e s t . P h y s i c a l work ing c a p a c i t y cannot , however, be r e l a t e d to a s i n g l e f u n c t i o n such as the oxygen fo rwa rd ing c a p a c i t y of the c a r d i o v a s c u l a r system but i s r a t h e r , d i r e c t l y or i n d i r e c t l y , dependent upon a number of f u n c t i o n s . S j o s t r a n d (6) and the Committee f o r the I n t e r n a t i o n a l B i o l o g i c a l Programme (7) have proposed the measurement of anae rob i c as w e l l as a e r o b i c c a p a -c i t i e s , muscu la r s t r e n g t h , and an th ropomet r i c measures such as body weight and s k i n f o l d t h i c k n e s s e s . A l l these f u n c t i o n s a r e i n t e r r e l a t e d but the t rue r e l a t i o n s h i p s have not been adequa te l y i n v e s t i g a t e d . The Problem The purpose of t h i s s tudy was t o determine the i n t e r r e -l a t i o n s h i p s of oxygen Intake c a p a c i t y , s t r e n g t h , body compos i t i on and p h y s i c a l work ing c a p a c i t y as measured by the S j o s t r a n d PWC170 t e s t . S u b s i d i a r y Problems The s u b s i d i a r y problems were: 1. t o determine which s t a t i s t i c a l p rocedu re , i . e . , ze ro o rde r c o r r e l a t i o n s , f i r s t o rde r p a r t i a l c o r r e l a -t i o n s , twenty-second o rde r p a r t i a l c o r r e l a t i o n s or s t e p w i s e m u l t i p l e r e g r e s s i o n a n a l y s i s , gave the g r e a t e s t i n s i g h t i n t o t h e t r u e p h y s i o l o g i c a l r e l a -t i o n s h i p s between the v a r i a b l e s s e l e c t e d f o r t h i s s t u d y , 2. t o d e t e r m i n e i n w h i c h form th e v a r i a b l e s i n v e s t i g a -t e d have the most b i o l o g i c a l meaning, i . e . , as raw s c o r e s , as s c o r e s d i v i d e d by body w e i g h t , o r as s c o r e s d i v i d e d by f a t f r e e w e i g h t and, 3* t o d e t e r m i n e th e a c c u r a c y of e s t i m a t i n g g r a p h i c a l l y t h e b e s t f i t t i n g s t r a i g h t l i n e i n t h e c a l c u l a t i o n of PWC170 a s compared w i t h computer c a l c u l a t e d v a l u e s o b t a i n e d by t h e l e a s t squares r e g r e s s i o n method. J u s t i f i c a t i o n of t h e Problem A l t h o u g h p h y s i c a l w o r k i n g c a p a c i t y as d e t e r m i n e d by the S j o s t r a n d t e s t appears t o be p r i m a r i l y dependent on c a r d i o -v a s c u l a r and r e s p i r a t o r y c a p a c i t i e s ( 2 , 3 , 4 , 5 ) . i t would seem l o g i c a l t h a t s i n c e e x t e r n a l work i s a c c o m p l i s h e d by m u s c u l a r c o n t r a c t i o n s , a s t r o n g e r i n d i v i d u a l would be a b l e t o p e r f o r m heavy p h y s i c a l work w i t h g r e a t e r ease t h a n a weak i n d i v i d u a l ( 8 ) . F u r t h e r m o r e , a l t h o u g h the r e l a t i v e i n f l u e n c e of s t r e n g t h on performance d e c r e a s e s p r o p o r t i o n a t e l y w i t h I n c r e a s e s i n work ti m e a t l i g h t e r l o a d s , a r e l a t i o n s h i p s h o u l d e x i s t between s t r e n g t h and t h e S j o s t r a n d t e s t where the s u b j e c t ' s h e a r t r a t e i s i n c r e a s e d to a near maximal 170 beats per m inu te . Body compos i t i on a l s o appears to be an important c o n s i -d e r a t i o n i n any assessment of p h y s i c a l work c a p a c i t y . Wllmore (9:209) s t a t e d t h a t : T h i s i s t rue f o r the b i c y c l e ergometer because of the s i g n i f i c a n t p o s i t i v e i n f l u e n c e of body weight on p e r f o r m -ance , i . e . , the l a r g e r i n d i v i d u a l has the p o t e n t i a l to pe r fo rm a g r e a t e r amount of work than the s m a l l e r man because of the advantage g i v en to him by h i s body s i z e . L a r g e r s u b j e c t s would have a p r o p o r t i o n a t e l y g r e a t e r oxygen t r a n s p o r t c a p a c i t y due to l a r g e r d imens ions of l u n g s , h e a r t , and b lood v e s s e l s w i t h c o r r e s p o n d i n g lower hea r t r a t e f o r a g i v e n oxygen i n t a k e . A s t a t i s t i c a l r e l a t i o n s h i p between the S j o s t r and t e s t and body weight has r e c e n t l y been r epo r t ed i n the l i t e r a t u r e (1,10,11,12). A r e l a t i o n s h i p between maximum oxygen i n t ake and body weight has a l s o been demonstrated (13t 14,15)• In o rde r t o remove the e f f e c t of body s i z e i n a s s e s s -ments i n d i v i d u a l d i f f e r e n c e s i n work c a p a c i t y parameters have been expressed as PWC170 kpm per min per kg body weight (1,10, 11,12,16) o r maximum oxygen in take per min per kg body weight (13,14,15). The use of body weight has , however, s e v e r a l d i sadvan tages i n making compar isons between i n d i v i d u a l s and between g roups . Body weight i n c l u d e s ad ipose t i s s u e , the amount of which d i f f e r s c o n s i d e r a b l y among i n d i v i d u a l s and a l though f a t t y a c i d s are me tabo l i z ed i n muscu lar c o n t r a c t i o n s , i t does not s i g n i f i c a n t l y c o n t r i b u t e to work output a t h i g h 5 i n t e n s i t i e s . Moreover , i t i s l a b i l e t i s s u e which may d i m i n i s h w i t h t r a i n i n g o r r e d u c t i o n of c a l o r i c i n t a k e . Thus , i n d i v i d u a l d i f f e r e n c e s i n r e l a t i v e a d i p o s i t y or changes i n ad ipose t i s s u e p r o p o r t i o n s can c r e a t e d i f f i c u l t i e s or even c o n f u s i o n In the i n t e r p r e t a t i o n of work c a p a c i t y measurements. F a t f r e e weight (body weight - ad ipose t i s s u e ) has been employed i n r e c e n t s t u d i e s (9,13,14,15) and appears to be a more b i o l o g i c a l l y mean ing fu l r e f e r e n c e than body we igh t . Wilmore (21) ob t a i ned a h i g h e r c o r r e l a t i o n between endurance work and f a t f r e e weight than between endurance and body we igh t . The p resen t s tudy pu rpo r t ed to i n v e s t i g a t e the e f f e c t of bo th body weight and f a t f r e e weight upon p h y s i c a l work c a p a c i t y as measured by the S j o s t r a n d PWC170 t e s t . The type of s t a t i s t i c a l p rocedure used i s an impor tant c o n s i d e r a t i o n i n an a n a l y s i s of r e l a t i o n s h i p s between p h y s i o l o -g i c a l pa ramete r s . Most b i o l o g i c a l s t u d i e s have employed l i n e a r or z e ro o rde r c o r r e l a t i o n s . However, ze ro o rde r c o r r e l a t i o n s a r e s u s c e p t i b l e to m i s i n t e r p r e t a t i o n due t o spu r i ous e f f e c t s . T h i s i s l i k e l y where the c o r r e l a t i o n between two se t s o f s co res may be due i n p a r t t o f a c t o r s o the r than those which determine the performance i n the t e s t s themse l ves . The u s u a l e f f e c t i s a " b o o s t i n g " or i n f l a t i o n of the c o r r e l a t i o n c o e f f i c i e n t . The l i n e a r r e l a t i o n s h i p between p h y s i c a l work c a p a c i t y and o the r measures such as oxygen i n t ake or s t r e n g t h may be i n f l a t e d due to the i n f l u e n c e of body s i z e on bo th v a r i a b l e s . 6 Some s t u d i e s (1,16) have a t tempted t o c o n t r o l the e f f e c t of body s i z e by d i v i d i n g bo th v a r i a b l e s by body we igh t , i . e . PWC170 kpm per min and maximum oxygen Intake ml per min ^h ls body weight body weight p rocedu re , however, may a l s o induce spu r i ous e f f e c t s i n t o the c o r r e l a t i o n due to a common f a c t o r (body weight ) employed as a denominator i n the r a t i o s . A more l o g i c a l p rocedure may be to s t a t i s t i c a l l y p a r t i a l the e f f e c t of body s i z e to o b t a i n a t r u e r p h y s i o l o g i c a l r e l a t i o n s h i p between o the r v a r i a b l e s . Very few s t u d i e s have at tempted to e s t a b l i s h p h y s i o l o -g i c a l r e l a t i o n s h i p s between more than two v a r i a b l e s . In o rde r to g a i n g r e a t e r i n s i g h t i n t o v a r i a b l e s which c o n t r i b u t e to p h y s i c a l work ing c a p a c i t y , a s tepwise m u l t i p l e r e g r e s s i o n a n a l y s i s i s v e r y u s e f u l . T h i s s t a t i s t i c a l p rocedure was employed i n t h i s s t u d y . An a n a l y s i s o f the p h y s i o l o g i c a l v a r i a b l e s which c o n t r i -bute to p h y s i c a l work ing c a p a c i t y , as w e l l as an i n v e s t i g a t i o n of the r e l a t i v e v a l ue of the s t a t i s t i c a l p rocedures used i n such a n a l y s i s may enhance unde rs t and ing i n the a r e a of s tudy of man's c a p a c i t y to per form work. Such i n f o r m a t i o n may be employed i n s o l v i n g problems l n the assessment of work c a p a c i t y t e s t s , i n the p r e d i c t i o n of p h y s i c a l work c a p a c i t y and i n the methodology of improv ing an i n d i v i d u a l ' s work ing c a p a c i t y , i . e . , th rough the t r a i n i n g of p h y s i c a l q u a l i t i e s i d e n t i f i e d l n t h i s s tudy as b e i n g impor t an t . 7 D e f i n i t i o n of Terms P h y s i c a l Working Capac i t y (PWC170). In t h i s s t udy , the term p h y s i c a l work ing c a p a c i t y was l i m i t e d to Boyd ' s (17) d e s c r i p t i o n : the work l o a d r e q u i r e d to produce a hea r t r a t e of 170 beats pe r minute on the b i c y c l e ergometer a t a s teady s t a t e . Steady S t a t e . The p h y s i o l o g i c a l c o n d i t i o n a t which the hea r t r a t e d i d not va r y more than two beats pe r minute w h i l e pe r fo rm ing a s p e c i f i c t a sk on the b i c y c l e e rgometer . Maximum Oxygen Intake (Max V02 ) » Maximum oxygen i n t ake r e f e r r e d to the l a r g e s t volume of oxygen i n t ake i n l i t e r s pe r minute d u r i n g the l a s t f o u r minutes of an exhausted r i d e on the b i c y c l e e rgometer . Muscu la r S t r e n g t h . Th i s f a c t o r was d e f i n e d by F l e i shman (18) as s t a t i c s t r e n g t h where the i n d i v i d u a l exe r t s maximum f o r c e over a b r i e f p e r i o d and the f o r c e i s exe r t ed c o n t i n u o u s l y up to t h i s maximum. K i l opond ( kp ) . One k i l o p o n d i s the f o r c e a c t i n g on a mass of one k i l o g r a m a t normal a c c e l e r a t i o n of g r a v i t y . K i l opond Meter (kpm). One k i l o p o n d meter i s the u n i t work per formed by a f o r c e of one k i l o p o n d moving i t s p o i n t o f a p p l i c a t i o n one meter i n the d i r e c t i o n of the f o r c e ( 1 9 ) » 8 Work L o a d . Th i s term means the c a l i b r a t e d f r l c t i o n a l f o r c e a p p l i e d to a f r i c t i o n b e l t which the sub j e c t must o v e r -come to con t inue p e d a l l i n g a t a s p e c i f i e d r a t e (20). Fa t F ree Body Weight . The f a t f r e e body weight i s equa l t o the t o t a l body weight minus the weight of the f a t p o r t i o n of ad ipose t i s s u e . The term l e a n body mass was i n t e r p r e t e d as a synonym of f a t f r e e body we igh t . L i m i t a t i o n s 1. The s u b j e c t s of the s tudy were not r e p r e s e n t a t i v e of a random sample . 2. I n t e r l n d l v l d u a l d i f f e r e n c e s l n s k i l l and exper i ence i n r i d i n g the b i c y c l e ergometer were not de t e rm ined . Assumpt ion 1. The hea r t r a t e s r e co rded i n the l a s t q u a r t e r o f each minute were r e p r e s e n t a t i v e of the mean hea r t r a t e pe r m inu te . D e l i m i t a t i o n s 1. The s tudy was c o n f i n e d t o an i n v e s t i g a t i o n i n t o the i n t e r r e l a t i o n s h i p s of s t r e n g t h , maximum oxygen In take , body compos i t i on and p h y s i c a l work c a p a c i t y of young men. 2. The s tudy was not des igned to i n c l u d e a l l the 9 v a r i a b l e s of work ing c a p a c i t y nor the range of p o s s i b l e measurements of c a r d i o v a s c u l a r and r e s p i r a t o r y c o n d i t i o n s . REFERENCES 1. Howe l l , M .L . , Macnab, R.B. , The P h y s i c a l Working C a p a c i t y of Canadian C h i l d r e n , The Canadian A s s o c i a t i o n f o r H e a l t h , P h y s i c a l E d u c a t i o n and R e c r e a t i o n , 1968. 2. A s t r a n d , P .O . , "Human P h y s i c a l F i t n e s s w i t h S p e c i a l Re ference to Age and S e x , " P h y s i o l o g i c a l Reviews, Volume 36, 1956, pp . 326-372. 3. Lundgren , N .P . , "The P h y s i o l o g i c a l E f f e c t s of Time Schedule Work on Lumber Workers , " A c t a P h y s i o l o g i c a  S c a n d i n a v i c a . Volume 13, ( Supp l . 4 1 ) , 1946. 4 . S chne ide r , E . C . , " A Study of Responses t o Work on a B i c y c l e E rgomete r , " Amer i can J o u r n a l of P h y s i o l o g y , Volume 96, 1931, PP- 353-364. 5. Wahlund, H . , " D e t e r m i n a t i o n of P h y s i c a l Working C a p a c i t y , " A c t a Medica S c a n d i n a v i c a , Volume 132, ( Supp l . 215 ) , 1948, p p . 5-78. 6. S j o s t r a n d , T . , " T e s t i n g of the P h y s i c a l Working C a p a c i t y -D e f i n i t i o n , H i s t o r y and A p p l i c a t i o n , " F o r v a r s m e d l c l n , Volume 3. 196?, p p . 141-145. ? . Weiner , J . S . , I n t e r n a t i o n a l B i o l o g i c a l Programme, S p e c i a l Committee f o r the I n t e r n a t i o n a l B i o l o g i c a l Programme, London, 1965. 8. T u t t l e , W.W., S c h o t t e l i u s , B .A . , Textbook of P h y s i o l o g y , C V . Mosby C o . , S t . L o u i s , I9ZJ". 9. Wi lmore, J . H . , "Maximal Oxygen Intake and I t s R e l a t i o n s h i p to Endurance Capac i t y on a B i c y c l e E rgomete r , " Research Q u a r t e r l y . Volume 40, 1969, p p . 203-210. 10 . Cumming, G .R . , Cummlng, P .M . , "Working C a p a c i t y of Normal C h i l d r e n Tes ted on the B i c y c l e E rgomete r , " Canadian  M e d i c a l A s s o c i a t i o n J o u r n a l , Volume 21 , 196£~i 1807-1814. 1 1 . Holmgren, A . , A s t r a n d , P .O . , "Dx, and the Dimensions and F u n c t i o n a l C a p a c i t i e s of the Oxygen T r anspo r t Systems i n Humans," J o u r n a l o f A p p l i e d P h y s i o l o g y , Volume 21, 1966, pp . 1463-1470. 11 12 . Adams, F . H . , L l n d e , L . M . , Miyake, H . t "The P h y s i c a l Work C a p a c i t y of Normal Schoo l C h i l d r e n , ( C a l i f o r n i a ) , " P e d i a t r i c s . Volume 18, 1961, pp . 55-64. 13* Coyne, L . L . , "The R e l a t i o n s h i p of Maximal Oxygen Intake t o Body Compos i t i on and T o t a l Body Weight i n A c t i v e M a l e s , " Unpub l i shed M a s t e r ' s T h e s i s , U n i v e r s i t y o f A l b e r t a , 1963. 14. B u s k i r k , E . , T a y l o r , H . , "Maximum Oxygen Uptake and I t s R e l a t i o n t o Body Compos i t i on w i th S p e c i a l Re ference to Ch ron i c P h y s i c a l A c t i v i t y and O b e s i t y , " J o u r n a l of  A p p l i e d P h y s i o l o g y , Volume 11 , 1957. p p . 72-76. 1 5 . Welch, B . E . , R iendeau, R.P. , C r i s p , C . E . , I s e n s t e i n , R .S . , " R e l a t i o n of Maximum Oxygen Consumption to V a r i o u s Components of Body C o m p o s i t i o n , " J o u r n a l of A p p l i e d  P h y s i o l o g y , Volume 12, 1958. pp . 395-398. 1 6 . D e V r i e s , H .A . , K l a f s , C , " P r e d i c t i o n of Maximal Oxygen Intake from Submaximal T e s t s , " J ou rna l of Spor ts  Med i c ine and P h y s i c a l F i t n e s s , Volume 5, 1965, p p . 207-214. 1 7 . Boyd, W.R., "A Phase P lane A n a l y s i s of P h y s i c a l Working C a p a c i t y , " Unpub l i shed M a s t e r ' s T h e s i s , U n i v e r s i t y o f B r i t i s h Co lumbia , 1967• 18. F l e i s h m a n , E .A . , The S t r u c t u r e and Measurement of P h y s i c a l F i t n e s s , P r e n t i c e - H a l l I n c . , New J e r s e y , 1964. 19. C a r r o l l , P . J . , "Hear t Rate Response to B i c y c l e Ergometer E x e r c i s e as a F u n c t i o n of P h y s i c a l F i t n e s s , " Research  Un i t Report 6-M 1967. U n i v e r s i t y of A l b e r t a , 1967-20 . Zahar , W.E.R. , " R e l i a b i l i t y and Improvement w i t h Repeated Performance of the S j o s t r and Work Capac i t y T e s t , " Unpub l i shed M a s t e r ' s T h e s i s , U n i v e r s i t y o f A l b e r t a , 1965. CHAPTER II REVIEW OF LITERATURE I n t r o d u c t i o n - The S j o s t r a n d PWC170 Tes t The submaximal S j o s t r a n d PWC170 t e s t i n v e s t i g a t e s the work l o a d accomp l i shed on the b i c y c l e ergometer a t a hea r t r a t e of 170 bea ts pe r minute and i s based on a l i n e a r r e l a t i o n s h i p between p u l s e r a t e and the i n t e n s i t y of work (1,2,3,4,5.6,7,8). S j o s t r a n d (7) deve loped the i n i t i a l submaximal work c a p a c i t y t e s t i n 1942 by u s i n g a b i c y c l e ergometer and th ree s u c c e s -s i v e l y i n c r e a s i n g work l oads t o t e s t the r e s p i r a t o r y c o n d i t i o n of sme l t e r wo rke r s . Wahlund (8), u s i n g the b a s i c t echn ique proposed by S j o s t r a n d (7). conc luded tha t i t was p o s s i b l e to es t ima te the l i m i t of c a r d i a c output by s t u d y i n g the i n d i v i d u a l s u b j e c t s ' pu l s e c u r v e . The maximum hea r t r a t e a t which work may be per formed adequa te l y was s e t a t 170 beats pe r m inu te . I f t h i s hea r t r a t e was not r ea ched , i t was proposed tha t use be made of the l i n e a r r e l a t i o n s h i p between work l o a d and hea r t r a t e to i n t e r p o l a t e or e x t r a p o l a t e the work l o a d which can be accomp l i shed a t a hea r t r a t e of 170 beats per m inu te . Th i s concept became known as P h y s i c a l Work C a p a c i t y and i s u s u a l l y a b b r e v i a t e d t o PWCi70» In 1949 K j e l l b e r g et a l . (9) sugges ted a f u r t h e r m o d i f i -c a t i o n by s h o r t e n i n g the work p e r i o d from 6.5 minutes t o 6 minu te s . Wahlund's (8) t e chn ique of i n t e r p o l a t i n g or 13 e x t r a p o l a t i n g the pu l s e curve to 170 bea ts per minute was a l s o s u p p o r t e d . Bengtsson (3) i n c o r p o r a t e d the method of a d j u s t i n g the work l oads so tha t the hea r t r a t e would approx imate 125 t o 130, 140 to 150 and 170 beats pe r m inu te . A l s o , the concept of s teady s t a t e was i n c o r p o r a t e d i n t o the PWC170 t e s t a t t h i s t i m e . In r e c e n t y e a r s , the PWC170 t e s t has been employed e x t e n s i v e l y to a s s e s s p h y s i c a l work c a p a c i t y of i n d i v i d u a l s . A l s o , the r e l a t i o n s h i p of p h y s i c a l work c a p a c i t y w i t h o the r p h y s i o l o g i c a l parameters has been i n v e s t i g a t e d . The a fo rement ioned a spec t s have been rev iewed under the f o l l o w i n g subhead ings : 1. The P h y s i o l o g i c a l Bas i s of the PWC170 T e s t ; 2. The R e l a t i o n s h i p Between the PWC170 Tes t and Maximum Oxygen In take ; 3. The R e l a t i o n s h i p Between the PWC170 Tes t and S t r e n g t h ; k. The R e l a t i o n s h i p Between the PWC170 Tes t and Body S i z e ; and 5. The A n a l y s i s o f the S t a t i s t i c a l R e l a t i o n s h i p Between Maximum Oxygen In take , S t r e n g t h , Body S i z e and PWC170. The P h y s i o l o g i c a l B a s i s o f the PWC170 Test The S j o s t r a n d PWC170 t e s t i n v e s t i g a t e s the work 14 accompl i shed a t a hea r t r a t e of 170 bea ts pe r m inu t e . S j o s t r a n d has s t a t e d tha t (10 :143 ) : The v a l u e , work a t p u l s e r a t e 170, has proved to be h i g h l y c o r r e l a t e d t o the s t roke volume of the h e a r t , t o t a l hea r t vo lume, b l ood volume or t o t a l amount of Hemoglobin, and the d i f f u s i o n c a p a c i t y of the l u n g s . Consequent l y , the work a t p u l s e r a t e 170 i s c o r r e l a t e d t o s e r i e s of f u n c t i o n a l and ana tomica l measures which may be expected to have a d i r e c t i n f l u e n c e upon the p h y s i c a l ivorking c a p a c i t y during e x e r c i s e demanding a. high oxygen i n t a k e . S t roke Volume. Ca rd i a c output i s determined by bo th hea r t r a t e and s t r oke volume d u r i n g the r e s t i n g s t a t e . In the a c t i v e s t a t e c a r d i a c output i s b e l i e v e d to be s o l e l y augmented by hea r t r a t e s . However, i n the p a s t , t he re has been some d i s p u t e as to whether o r not the hea r t r a t e i s a c c u r a t e l y i n d i c a t i v e of c a r d i a c o u t p u t . S t a r l i n g ' s Law was i n t e r p r e t e d to mean tha t the p r i n c i p l e mechanism r e g u l a t i n g s t r o k e volume of the v e n t r i c l e s was dependent upon the degree of d i a s t o l i c d i s t e n t i o n . Wright (11) r e p o r t e d tha t the l a r g e r the i n f l o w i n t o the h e a r t , the l a r g e r the output w i thout a change i n hea r t r a t e . Rushmer (12 :340 ) , on the o the r hand, has s t a t e d t h a t : . . . x-rays show tha t i n c r e a s e d s t r oke volume i s not a lways accompanied by d i a s t o l i c d i s t e n t i o n . G rea t e r s t r oke volume i s a t t a i n e d by a more complete e j e c t i o n . Fu r the rmore , an a n a l y s i s of t en s t u d i e s (13) r e v e a l e d tha t d u r i n g heavy p h y s i c a l work, the re d i d not appear to be a p r o g r e s s i v e i n c r e a s e l n s t r o k e volume a s s o c i a t e d w i t h g r e a t e r oxygen d e l i v e r y o r l e v e l s of p h y s i c a l e x e r t i o n . S a l t i n (14) conc luded tha t d u r i n g l i g h t work, both s t r o k e volume and hea r t 15 r a t e c o n t r i b u t e d to c a r d i a c output i n c r e a s e . A t l oads over 40 pe rcen t a e r o b i c c a p a c i t y , s t r o k e volume became l i m i t i n g and hea r t r a t e was the s o l e c o n t r i b u t o r i n augmenting c a r d i a c o u t p u t . A t 40 pe r cen t a e r o b i c c a p a c i t y , the hea r t r a t e was about 120 bea ts pe r m inu te . • We l l t r a i n e d a t h l e t e s may a ch i e ve maximal c a r d i a c o u t -puts w e l l above 30 l i t e r s pe r minute d u r i n g e x e r c i s e compared to about 20 l i t e r s f o r sedenta ry s u b j e c t s . Anderson (15:122) has s t a t e d , "The b e t t e r e f f i c i e n c y of the hea r t as a pump which comes w i t h t r a i n i n g i s man i f e s t ed i n the w e l l known i n c r e a s e of s t r o k e volume and a co r r e spond ing r e d u c t i o n of hea r t r a t e . " The r e s t i n g s t r o k e volume was found to be about 105 ml In w e l l t r a i n e d a t h l e t e s compared t o 60 to 70 ml i n non-a th l e t e s ( 15 :122 ) . DeVr l es (16) a l s o l ends h i s suppor t to the p r e p o n -derance of ev idence t h a t i n d i c a t e s t ha t the i n c r e a s e d c a r d i a c output i n a t h l e t e s i s l a r g e l y due to an i n c r e a s e i n s t r o k e vo lume. I f t h i s i s assumed to be t r ue (the ev idence s t r o n g l y i n d i c a t e s t h a t i t i s ) then d i f f e r e n c e s i n s t r o k e volume - o the r t h i n g s b e i n g equa l such as body s i z e and sex - a re r e l a t e d to d i f f e r e n c e s i n t r a i n i n g . Thus, s i n c e the c i r c u l a t o r y response ( c a r d i a c output ) i s p r o p o r t i o n a l to work i n t e n s i t y , the hea r t r a t e f o r t r a i n e d persons w i l l be lower than f o r u n t r a i n e d a t any g i v e n r a t e of work. C o n v e r s e l y , a t any g i v e n hea r t r a t e a t r a i n e d pe r son w i l l be a b l e to s u s t a i n a h i g h e r i n t e n s i t y of 16 work than an u n t r a i n e d p e r s o n . S j o s t r a n d (17:14) has s t a t e d t h a t " . . . the g r e a t e r the maximum s t r oke vo lume, the g r e a t e r the .stroke volume a t any g i v e n c a r d i a c ou tpu t . . . . " Due to the p r a c t i c a l comp lex i t y i n the measurement of s t r o k e volume, r e s e a r c h i n v o l v i n g t h i s parameter i n r e l a t i o n to p h y s i c a l work c a p a c i t y i s l i m i t e d . Bevegard (18) r e p o r t e d a c o r r e l a t i o n c o e f f i c i e n t of 0.84 between PWC170 and s t r oke volume f o r 27 young male s u b j e c t s . Holmgren et a l . ( 1 9 ) ob ta ined a c o r r e l a t i o n c o e f f i c i e n t of 0.649 f o r the same v a r i a b l e s . Holmgren et a l . ( 2 0 ) conc luded , a f t e r i n v e s t i g a t i n g 87 young men, t ha t an Increase i n P W C 1 7 0 of 29 kpm per minute cor responded t o an i n c r e a s e of 2 0 ml i n s t r oke vo lume. Thus, ev idence appears to suppor t the P W C 1 7 0 t e s t as a measure of c a r d i a c e f f i c i e n c y . Hear t S i z e and Hear t Volume• The weights of a t h l e t e s ' hea r t s have been r e p o r t e d as w e l l above the average of the sedenta ry p o p u l a t i o n ( 1 5 ) . DeVr i es (16:76) has s t a t e d t h a t : A l t hough l i t t l e da ta i s a v a i l a b l e f o r man s i c the impor tant f a c t t o be noted i s tha t a change l n hea r t s i z e would be a normal p h y s i o l o g i c a l r e a c t i o n i n a l l r e s p e c t s s i m i l a r to the p h y s i o l o g i c a l hyper t rophy of s k e l e t a l muscle as a r e s u l t of t r a i n i n g . There i s a g r e a t e r amount of a v a i l a b l e da t a p e r t a i n i n g to hea r t volume and work c a p a c i t y than the re i s f o r hea r t weight and work c a p a c i t y . Anderson (15) r e p o r t e d tha t 15 percen t i n c r e a s e s i n hea r t volume were ob ta ined d u r i n g the 17 course of 5 weeks s t renuous t r a i n i n g . The e a r l y works of K j e l l b e r g e t a l . (21), i n 1950, i n d i c a t e d tha t i n c r e a s e s i n hea r t volume cor responded t o i n c r e a s e s i n c a p a c i t y to work. The same au tho r s (22) r e p o r t e d a c o r r e l a t i o n c o e f f i c i e n t of 0.96 between hea r t volume and PWCi-po* Holmgren et a l . (19) ob ta ined a c o r r e l a t i o n c o e f f i c i e n t of 0.829 f o r the same v a r i a b l e s . H e l l s t r o m (23) i n v e s t i g a t e d 88 young c o n s c r i p t s and r e p o r t e d an i n c r e a s e i n the mean PWC170 s co res f rom 1273 t o 1502 kpm per minute i n a th ree month t r a i n i n g p e r i o d . Du r ing the same t ime , hea r t volume i n c r e a s e d f rom 947 ml t o 1078 m l . The c o r r e l a t i o n c o e f f i c i e n t o f 0.55 was, however, somewhat lower than tha t ob ta ined i n the p rev i ous s t u d i e s . L i n r o t h (24) r e p o r t e d t h a t a c o r r e l a t i o n of 0.49 was ob ta ined which appears t o be i n agreement w i th the f i n d i n g s of H e l l s t r o m (23). I t would appear t ha t a l t hough the c o r r e l a t i o n c o e f f i c i e n t s ob ta ined i n d i f f e r e n t s t u d i e s have a c o n s i d e r a b l e range i n v a l ue they a re a l l p o s i t i v e . I t seems, t h e r e f o r e , t ha t an i n c r e a s e i n hea r t volume may be regarded as an a d a p t a t i o n of the hea r t t o i n c r e a s e d demands as man i f e s t ed i n h i g h e r PWC170 sco res (25). B lood Volume and T o t a l Hemoglobin . DeVr ies (16) r e p o r t e d t ha t b l ood volume was found to be 10 t o 19 pe r cen t h i ghe r a f t e r t r a i n i n g than b e f o r e . Anderson (15) ob ta ined a va l ue of 5*7 l i t e r s o f b l ood f o r sedenta ry sub j e c t s and 7.5 18 l i t e r s f o r a t h l e t e s . K j e l l b e r g e t a l . (9,21,22,26), Holmgren et a l . (20,25) and Bevegard (18) a l s o r e p o r t e d s i m i l a r r e s u l t s . Holmgren e t a l . (19) ob ta ined a c o r r e l a t i o n of 0.886 between PWC170 s co res and b l ood volume when 20 young men were t e s t e d . Thus , i t would seem tha t b l ood volume v a r i e s p r o p o r t i o n a l l y w i th the amount of p h y s i c a l a c t i v i t y . Inc reased b l ood volume would then be a c o n s i d e r a b l e advantage i n heavy e z e r c l s e f o r the purpose of heat d i s s i p a t i o n and to h e l p a s su re an adequate venous r e t u r n t o the h e a r t . The obv ious i m p l i c a t i o n of an i n c r e a s e i n b l o o d volume i s an i n c r e a s e d amount of hemoglobin which would enhance the oxygen fo rwa rd ing c a p a c i t y . K j e l l b e r g et a l . (21) ob ta ined a c o r r e l a t i o n c o e f f i c i e n t o f 0.90 between t o t a l hemoglobin and hea r t vo lume. H e l l s t r o m (23) found t h a t In w e i g h t l l f t e r s the t o t a l hemoglobin t o body weight r a t i o was 11.4 wh i l e the r a t i o i n midd le d i s t a n c e runners was 1 3 . 2 . Hence, i t would seem t h a t i n c r e a s e d t o t a l hemoglobin count would promote g r e a t e r c a p a c i t y to work. K j e l l b e r g e t a l . (26) ob ta ined a c o r r e l a t i o n c o e f f i c i e n t of 0.82 f o r 87 s u b j e c t s and 0.90 f o r 136 s u b j e c t s when PWC170 was compared w i th t o t a l hemog lob in . L i n r o t h (24) r e p o r t e d a c o r r e l a t i o n of O.98 between t o t a l hemoglobin and PWCi7Q. Holmgren et a l . (19) ob ta ined a v a l u e of 0.91 between the a fo rement ioned v a r i a b l e s . I t appears tha t p h y s i c a l l y t r a i n e d sub j e c t s have a c o n s i d e r a b l y l a r g e r amount of hemoglobin as compared to u n t r a i n e d s u b j e c t s . 19 Moreover , the amount of i n c r e a s e of hemoglobin appears to vary-a c c o r d i n g t o the i n t e n s i t y of t r a i n i n g . These i n c r e a s e s seem to p a r a l l e l i n c r e a s e d b lood volume so tha t no i n c r e a s e s i n hemoglobin c o n c e n t r a t i o n (hemoglobin per u n i t b l o o d volume) seems t o occur (16:181) . T h i s i s i n c o n s i s t e n t w i th the r e s u l t r e p o r t e d by Holmgren et a l . (19) where the c o r r e l a t i o n c o e f f i -c i e n t between PWC170 and hemoglobin c o n c e n t r a t i o n was 0 . 6 1 2 . An i n t e r e s t i n g s tudy by G u l l b r l n g et a l . ( 2 7 ) r e p o r t e d t ha t the e f f e c t of b l e e d i n g of 10 pe r cen t of b l ood volume r e s u l t e d i n an i n c r e a s e i n p u l s e r a t e d u r i n g e x e r c i s e and a d e c l i n e i n the S j o s t r a n d PWC170 t e s t s c o r e . As the b lood volume i n c r e a s e d In subsequent days , the work c a p a c i t y i n c r e a s e d and p u l s e r a t e d e c r e a s e d . Consequent l y , i t appears tha t s t r oke vo lume, hea r t vo lume, b l ood volume, and t o t a l hemoglobin a re d i r e c t l y r e l a t e d i n l i n e a r f a s h i o n to the r a t e of work accomp l i shed a t a hea r t r a t e of 170 bea ts pe r minute on the b i c y c l e e rgometer . D i f f u s i o n Capac i t y of the Lungs . Bes ides c a r d i o v a s c u l a r f u n c t i o n s , pulmonary f a c t o r s may be important t o p h y s i c a l work c a p a c i t y . DeVr i es (16:138) s t a t e d t h a t , B T h e r e i s ev idence tha t h i g h l y t r a i n e d i n d i v i d u a l s demonstrate b e t t e r pulmonary d i f f u s i o n under maximal and submaximal work r a t e s than do non-a t h l e t e s . " Holmgren et a l . (19) i n v e s t i g a t e d the r e l a t i o n s h i p between the d i f f u s i o n c a p a c i t y f o r carbon d i o x i d e i n the lungs 20 of 38 s u b j e c t s and t h e i r r e s p e c t i v e PWC170 s co re s and r e p o r t e d a c o r r e l a t i o n c o e f f i c i e n t of 0.922. The R e l a t i o n s h i p Between PWC170 and Maximum Oxygen Intake Maximum oxygen i n t ake has. been e x t e n s i v e l y i n v e s t i g a t e d as a measure of the c a r d i o v a s c u l a r and r e s p i r a t o r y c a p a c i t i e s t o take up and d e l i v e r oxygen t o the work ing t i s s u e . Holmgren (28) c a t e g o r i z e d the p r e r e q u i s i t e s of an e f f i c i e n t oxygen t r a n s p o r t system as f o l l o w s : A . D imens iona l f a c t o r s : 1. s i z e of l u n g s , 2. s i z e of d i f f u s i o n s u r f a c e , 3- s i z e of c a p i l l a r y beds , 4 . s i z e of v a s c u l a r sys tem, 5. s i z e of h e a r t , 6. hea r t vo lume, 7. b l o o d vo lume, 8. t o t a l hemog lob in . F u n c t i o n a l c a p a c i t i e s : 1. d i f f u s i o n c a p a c i t y , 2. maximum c a r d i a c ou tpu t , 3- s t r oke vo lume. S j o s t r a n d (10:143) has s t a t e d tha t maximum oxygen i n t ake i s : . . . a measure of the volume of oxygen t aken up by tha t amount of b l o o d which i s pumped out of the r i g h t v e n t r i c l e i n t o the pulmonary c i r c u l a t i o n a t every p u l s e b e a t . I t i s easy to unders tand tha t t h i s volume of oxygen i s determined 21 by the amount of r educed , un loaded hemoglobin pumped to the lungs pe r p u l s e b e a t . T h i s , i n t u r n , i s determined by the s t r o k e volume of the r i g h t v e n t r i c l e , the hemoglobin c o n c e n t r a t i o n , and how much oxygen the b lood has g i v e n o f f i n the p e r i p h e r y . The l a t t e r i s determined p r i m a r i l y by how much of the c a r d i a c output passes th rough the a c t i v e musc les i n which the oxygen uptake i s the h i g h e s t . In o the r words, maximum oxygen Intake may be c o n s i d e r e d a good s i n g l e measure of the e f f i c i e n c y of the oxygen t r a n s p o r t system as d e s c r i b e d by Holmgren (28) and S j o s t r a n d (10). Moreover , a l i n e a r r e l a t i o n s h i p between oxygen i n t ake and work i n t e n s i t y or hea r t r a t e has been demonstra ted (29,30,31,32,33,34,35). Cumming et a l . (5:204) s t a t e d t h a t , " . . . the v a l i d i t y of the pu l s e r a t e method f o r de t e rm in i ng work c a p a c i t y i s con f i rmed by oxygen i n t ake t e s t s . " Q u a l i f i c a t i o n s of the term maximum oxygen i n t ake and i t s r e l a t i o n s h i p w i th p h y s i c a l work c a p a c i t y appea r , however, to be n e c e s s a r y . The a c t u a l v a l ue of maximum oxygen Intake f o r a g i v e n i n d i v i d u a l depends on the na tu re of the p h y s i c a l a c t i v i t y i n which the i n d i v i d u a l i s engaged when the measure i s t a k e n . I t i s , t h e r e f o r e , maximal - not i n the a b s o l u t e sense - but r e l a t i v e to a g i v e n se t of c o n d i t i o n s , c a r e f u l l y d e f i n e d . F o r example, Rowel l (36) conc luded t h a t , i n the n o n - b i c y c l i n g Amer ican p o p u l a t i o n , the h i g h e s t maximum oxygen i n t ake a t t a i n -a b l e on the b i c y c l e ergometer was c o n s i s t e n t l y below va lues ob ta ined on the t r e a d m i l l . The t r e a d m i l l v a l u e s exceeded peak oxygen i n t ake v a l u e s on the b i c y c l e ergometer by 4 to 23 pe rcen t o r 600 c u b i c cen t ime te r s per m inu te . T a y l o r et a l . (31) 22 ob ta ined an i n c r e a s e of 200 c u b i c cen t ime te r s pe r minute i n maximum oxygen i n t ake v a l u e s when arm work on an ergometer was conducted i n a d d i t i o n to l e g work r e q u i r e d by the t r e a d m i l l r u n . Consequen t l y , i t appears tha t an important de te rminant of maximum oxygen Intake i s . t h e mass of muscles employed i n pe r fo rm ing the p h y s i c a l t a s k . Both submaximal and maximal methods have been i n common use f o r d e t e r m i n i n g maximum oxygen i n t a k e . The popu l a r sub-maximal A s t r a n d t e s t has " . . . a tendency f o r the maximum oxygen i n t a k e of u n t r a i n e d i n d i v i d u a l s to be underes t imated and tha t of w e l l t r a i n e d to be o v e r e s t i m a t e d , " ( 37 :36 ) . DeVr i es et a l . (38) have r e p o r t e d , however, a c o r r e l a t i o n c o e f f i c i e n t of 0.736 between the As t r and t e s t and a maximal t e s t f o r 16 young normal men. N e v e r t h e l e s s , owing to d i f f e r e n t p h y s i o l o g i -c a l m a n i f e s t a t i o n s i n submaximal and maximal work, the p r e d i c t e d v a l ues may not be s i m i l a r to ob ta ined v a l u e s . Both age and t r a i n i n g appear to i n f l u e n c e maximum oxygen i n t ake v a l u e s . A s t r a n d (39) noted tha t maximum hea r t r a t e s and oxygen i n t ake v a l u e s d e c l i n e d from the age of 30 to 70 y e a r s . M i t c h e l l e t a l . (40) r e p o r t e d a s i g n i f i c a n t d e c l i n e i n f o u r age g roups : 20 to 29 y e a r s ; 30 to 39 y e a r s ; 40 t o 49 y e a r s ; and 50 years and o v e r . The average v a l ues i n l i t e r s per minute f o r the r e s p e c t i v e age groups were: 3«15» 2 .88 ; 2 .79 ; and 2.13« These r e s u l t s were comparable w i t h Rob inson ' s (41). B u s k i r k e t a l . (42) ob ta ined a mean v a l ue of 3.44 l i t e r s 23 pe r minute f o r sedenta ry s u b j e c t s f rom 18 to 29 yea rs o l d . M i t c h e l l et a l . (39) t e s t e d sedenta ry 2G t o 29 year o lds and r e p o r t e d a mean v a l u e of 3.37 l i t e r s per m inu te . Maximum oxygen i n t ake v a l u e s have J l s o been determined f o r w e l l t r a i n e d i n d i v i d u a l s . A s t r a n d (30).I B u s k i r k et a l . ( 4 l ) , S lon lm et a l . (43) and Coyne (44) i n v e s t i g a t e d young t r a i n e d men i n the same age range of 20 t o 29 years and r e p o r t e d the f o l l o w i n g mean v a l u e s : 4 .15 - 0-36; 4 .05 - 0 . 3 9 ; 3.95 - 0 .43 ; and 4.75 - 0.70 l i t e r s pe r minute , r e s p e c t i v e l y . S i nce t r a i n i n g enhances the e f f i c i e n c y of the oxygen t r a n s p o r t system (maximum oxygen in take ) th rough i n c r e a s e s i n p h y s i o l o g i c a l d i m e n s i o n a l and f u n c t i o n a l c a p a c i t i e s , p h y s i c a l work c a p a c i t y would a l s o be expected to i n c r e a s e . DeVr ies e t a l . (38) r e l a t e d the S j o s t r a n d PWC170 t e s t t o maximum oxygen i n t ake and ob t a i ned a c o r r e l a t i o n c o e f f i c i e n t of O.703. Holmgren e t a l . (19) ob ta ined a h i g h c o r r e l a t i o n c o e f f i c i e n t of 0.93 f o r the same v a r i a b l e s . The s t a t i s t i c a l r e l a t i o n s h i p between PWC170 and maximum oxygen i n t a k e , however, may not be expected to be h i g h i n tha t the l i n e a r r e l a t i o n s h i p between p u l s e r a t e and oxygen i n t ake which e x i s t s a t submaximal l e v e l s does not con t inue a t near maximal l e v e l s . Two q u i t e d i f f e r e n t reasons f o r t h i s have been o f f e r e d . Ba lke (45) and Nagle et a l . (46) noted tha t the r a t i o of oxygen consumed per hea r t b e a t , i . e . , oxygen p u l s e , decreased a t app rox ima te l y 180 bea ts pe r m inu te . Th i s was conc luded t o 2k i n d i c a t e the attainment of maximum aer o b i c c a p a c i t y because i n c r e a s i n g heart r a t e was not accompanied by a p r o p o r t i o n a l increase i n the d e l i v e r y of oxygen to the working t i s s u e s . I n other words, maximum oxygen intake was reached before maximum heart r a t e . But Wyndham (35) and M a r i t z (3*0 noted that heart r a t e reached i t s maximum a t s l i g h t l y lower work r a t e s than d i d oxygen i n t a k e . The higher oxygen intake occurred because of the g r e a t e r arterio-venous oxygen d i f f e r e n c e due to shunting of the blood from organs w i t h a lower e x t r a c t i o n of oxygen t o the working muscle. The l a t t e r s t u d i e s appear to be more accurate i n that the former s t u d i e s i m p l i e d that stroke volume decreases a t near maximal l e v e l s . The work of Rushmer (13). S a l t l n (Ik) and Sjostrand (17) have shown that maximum stroke volume was a t t a i n e d d u r i n g moderate work and that t h i s maximum was main-ta i n e d up to maximum heart r a t e . More simply, the s t a t i s t i c a l r e l a t i o n s h i p between PWC170 and maximum oxygen intake may not be high i n that the former i s a submaximal t e s t whereas the l a t t e r i s a maximal t e s t . T o r n v a l l (47) i n v e s t i g a t e d the r e l a t i o n s h i p of maximal work a t d i f f e r e n t durations w i t h maximum oxygen int a k e and PWCi70« Maximum oxygen i n t a k e c o r r e l a t e d 0.83 w i t h maximal work f o r 1 minute and 0.95 w i t h maximal work f o r 15 minutes. This appears to suggest that i n exhausting work l a s t i n g f o r very short periods of time, t h e - l a r g e energy demands of the muscles w i l l be met, only to a small extent, by the oxygen a v a i l a b l e ; 2 5 anae rob i c mechanisms have t o p rov i de the g r e a t e r p a r t of the energy s u p p l y . On the o ther hand, l ong t e s t t imes ( f o r example, 15 minutes ) a t s l i g h t l y lower i n t e n s i t i e s appear t o p l a c e g r e a t e r emphasis on a e r o b i c c a p a c i t i e s as i n d i c a t e d by a c o r r e l a t i o n c o e f f i c i e n t of 0 . 9 5 ' Moreover , work a t low i n t e n -s i t i e s which can be per formed f o r l ong d u r a t i o n s ( f o r example, 60 minutes ) i s dependent p r a c t i c a l l y on l y on the supp l y of chemica l energy f o r a e r o b i c work i n the a c t i v e musc l e s . Here , the supp l y of oxygen i s not a l i m i t i n g f a c t o r ( 10 :142 ) . The submaximal S j o s t r a n d PWC170 t e s t appears to be a s s o -c i a t e d more w i t h a 1 5 minute t e s t than w i th the 1 minute maximal t e s t . T o r n v a l l (47) compared the PWC170 t e s t t o the 15 minute maximal t e s t and a 1 minute maximal t e s t and r e p o r t e d v a l u e s of 0 . 4 9 and 0 . 3 1 , r e s p e c t i v e l y . Thus, i t appears t ha t a l t h o u g h the submaximal PWC170 i s r e l a t e d to maximum in t ake c a p a c i t y , as i n d i c a t e d by the r e l a t i o n s h i p of bo th v a r i a b l e s to the 15 minute maximal t e s t , the a s s o c i a t i o n i s not l a r g e . In o the r words , bo th the oxygen i n t ake t e s t and the 15 minute t e s t demand maximal e f f o r t but the S j o s t r a n d t e s t does not and , t h e r e f o r e , the p h y s i o l o g i c a l m a n i f e s t a t i o n s of the two types of work appear to be d i f f e r e n t . The R e l a t i o n s h i p Between PWC170 and S t r eng th There has been a consensus tha t the c a p a c i t y t o work f o r l o n g d u r a t i o n s a t h i g h i n t e n s i t y work l oads was p r i m a r i l y 26 dependent on the a b i l i t y of the c a r d i o v a s c u l a r and r e s p i r a t o r y systems to absorb and t r a n s p o r t oxygen to the work ing t i s s u e ( 1 4 , 3 4 , 4 0 ) . The q u a l i t y of the v a s c u l a r i z a t i o n of the muscle was a l s o c o n s i d e r e d of prime impor tance . On the o ther hand, v e r y l i t t l e r e s e a r c h has been conducted on the i n f l u e n c e of muscu lar s t r e n g t h on work c a p a c i t y . S i n ce e x t e r n a l work i s per formed by muscu la r c o n t r a c -t i o n s , the q u a l i t y of the muscle as a whole shou ld be an Impor-t an t a spec t of an i n d i v i d u a l ' s c a p a c i t y t o do work. I t would seem l o g i c a l t ha t the s t r o n g e r the muscle f i b e r s , l e s s f i b e r s would be needed to pe r fo rm a s p e c i f i c t a sk and consequen t l y , l e s s oxygen would be u t i l i z e d . Morehouse e t a l . ( 48:23) wrote : "The s t r e n g t h of the work ing muscles i s a l i m i t i n g f a c t o r i n endurance . A l o a d e a s i l y c a r r i e d by s t r o n g musc les may q u i c k l y exhaust weak o n e s . " S j o s t r a n d ( 1 0 : 1 4 2 ) s t a t e d : The d e t e r m i n a t i o n of muscu lar s t r e n g t h can be of v a l u e when judg ing an i n d i v i d u a l ' s a b i l i t y f o r c e r t a i n t a sks which need g rea t muscu lar s t r e n g t h . But as a s i n g l e i n v e s t i g a t i o n i t i s not s u f f i c i e n t to judge an I n d i v i d u a l ' s p h y s i c a l work c a p a c i t y . I t shou ld n e v e r t h e l e s s be mentioned tha t underdevelopment of muscles may be a l i m i t i n g f a c t o r on oxygen i n t ake d u r i n g work w i t h l a r g e muscle g roups , as on the b i c y c l e ergometer . H e l l s t r o m (23) i n v e s t i g a t e d the d i f f e r e n c e i n PWC170 sco res and s t r e n g t h between 4 8 w e l g h t l i f t e r s and 2 8 m idd le d i s t a n c e r u n n e r s . The mean age i n both groups was 2 6 y e a r s . The w e i g h t l i f t e r s were assumed to have pursued a form of a t h l e t i c s which Inc reased p r i n c i p a l l y the muscu la r s t r e n g t h , 2? and the runners a form which had augmented, i n p a r t i c u l a r , the p h y s i c a l work ing c a p a c i t y . The weight l i f t e r s o b v i o u s l y had h i g h e r s co res f o r push and p u l l s t r e n g t h and hand g r i p . The r u n n e r s ' PWC170 s co re of 1607 kpm per minute was h i g h e r than the PWC170 s c o r e of 1213 ob ta ined by the w e i g h t l i f t e r s . H e l l s t r o m (23:50) s t a t e d , " I t may be conc luded , t h e r e f o r e , t h a t e x e r c i s e p r i n c i p a l l y des igned to i n c r e a s e p h y s i c a l work c a p a -c i t y w i l l not n e c e s s a r i l y augment the muscu lar s t r e n g t h as determined i n the p resen t i n v e s t i g a t i o n . " The da t a and o b s e r v a t i o n s put f o r t h by H e l l s t r o m (23) does not appear to o f f e r any i n s i g h t i n t o the t rue r e l a t i o n s h i p between PWC170 and s t r e n g t h . Shou lder and g r i p s t r e n g t h would be expected to be h i g h e r amongst w e i g h t l i f t e r s as PWC170 sco re would be expected to be h i g h e r amongst r u n n e r s . Pe rhaps , i f some parameters o f l e g s t r e n g t h such as knee e x t e n s i o n was i n c l u d e d i n t o the s tudy , the au thor would no t have found a l a r g e d i f f e r e n c e between the two groups i n t h i s measure. More i n f o r m a t i v e d a t a was p resen ted by A h l b o r g (49) who i n v e s t i g a t e d the r e l a t i o n s h i p between a 6 minute maximum t e s t , a 100 minute maximum t e s t , s t r e n g t h measures and PWG170* The 6 minute maximum work t e s t c o r r e l a t e d h i g h e r w i th PWC170 (0.72) than the 100 minute maximum t e s t ( 0 . 6 1 ) . A s i m i l a r o rde r of r e s u l t s was ob ta ined f o r s t r e n g t h i tems where knee s t r e n g t h c o r r e l a t e d O.32 w i th the 6 minute t e s t and O.30 w i th the 100 minute t e s t . T o t a l l e g p ress c o r r e l a t e d 0.29 and 0.19» 28 r e s p e c t i v e l y . Thus , i t would appear t ha t s t r e n g t h i s not h i g h l y r e l a t e d to work on the b i c y c l e ergometer a t a hea r t r a t e of 170 bea ts pe r minute but such r e l a t i o n s h i p as does e x i s t seems to be dependent on the type of work. B r i e f heavy work appears t o r e q u i r e more s t r e n g t h than l i g h t e r work done f o r l o n g e r d u r a t i o n s . T o r n v a l l (47) i n v e s t i g a t e d the a fo rement ioned r e l a t i o n -s h i p l n 27 young a t h l e t e s . C o r r e l a t i o n a n a l y s i s was conducted between s t r e n g t h and maximal work f o r 6 m inu tes , maximal work f o r 10 m inu tes , maximal work f o r 15 minutes and PWCi-po* The c o r r e l a t i o n c o e f f i c i e n t s were 0 .69 . 0 .68 , 0 .65 . and 0.46, r e s p e c t i v e l y . The c o r r e l a t i o n c o e f f i c i e n t of 0.46 between s t r e n g t h and PWC170 appears to be r a t h e r h i g h i n v iew of the f i n d i n g s r e p o r t e d by A h l b o r g (49). There i s , however, a s i m i -l a r i t y between the two s t u d i e s i n tha t a r e l a t i o n s h i p i s e s t a b l i s h e d where the c o n t r i b u t i o n of s t r e n g t h t o p h y s i c a l work c a p a c i t y d e c l i n e s as the d u r a t i o n of the t e s t i n c r e a s e s . The R e l a t i o n s h i p Between PWC17Q and Body S i z e In any a n a l y s i s of the a b i l i t y to pe r fo rm work, c o n s i -d e r a t i o n must be g i v e n to i n d i v i d u a l d i f f e r e n c e s i n body c o m p o s i t i o n . B u s k i r k e t a l . (42), Welch et a l . (50) and Von Dobe ln (51) have i n d i c a t e d tha t d u r i n g heavy work, f a t i s i n e r t and n o n c o n t r i b u t o r y . In o the r words, ca rbohydra te metabol i sm appears to be the main source o f energy d u r i n g heavy work and 2 9 the c o n t r i b u t i o n of f a t t y a c i d metabo l i sm becomes l i m i t i n g . T h e r e f o r e , i n work t a sks where the body mass i s l i f t e d , such as runn ing o r d u r i n g a s t ep t e s t , an i n c r ea se i n weight due to f a t r e p r e s e n t s an i n c r e a s e d burden and w i l l , t h u s , i n c r e a s e the energy r equ i r emen t . C o n v e r s e l y , i f the body weight i s s u p p o r -t e d , as when work i s per formed on the b i c y c l e ergometer , the energy c o s t of work f o r normal i n d i v i d u a l s shou ld be l a r g e l y independent of the amount of f a t p resen t ( 8 , 3 0 ) . On the o the r hand, Dempsey et a l . (52) found tha t the performance of obese i n d i v i d u a l s on the b i c y c l e ergometer was s i g n i f i c a n t l y below tha t of young men of normal we igh t . How-eve r , the excess a d i p o s i t y p robab l y c o n t r i b u t e d to mechan i ca l i n e f f i c i e n c y r a t h e r than c a r d i o v a s c u l a r or r e s p i r a t o r y l i m i t a -t i o n s . A l though the energy cos t of work on the b i c y c l e e r g o -meter i s independent f rom the amount of f a t p r e s e n t , the suppor t of the body weight would o f f e r an advantage to l a r g e r s u b j e c t s . A h l b o r g ( 4 - 9 : 1 9 7 ) s t a t e d t h a t , "The r eason f o r t h i s must be tha t t a l l e r and h e a v i e r s u b j e c t s have a l a r g e r s k e l e t a l d imens ion and l a r g e r hea r t vo lume, a l t hough s t a t i s t i c a l d i f f e r -ences i n these r e s p e c t s do not a lways e x i s t between g r o u p s . " Research d a t a p e r t a i n i n g t o the S j o s t r a n d PWC170 t e s t appeared to I nd i c a t e a s i g n i f i c a n t r e l a t i o n s h i p between body weight and PWCi^O' Cumming et a l . (4) reported a c o r r e l a t i o n c o e f f i c i e n t of 0 . 8 9 7 f o r boys and O . 6 9 6 f o r g i r l s when weight 30 and work ing c a p a c i t y were compared. Adams et a l . (2) ob ta ined a c o r r e l a t i o n c o e f f i c i e n t of 0 . 8 1 f o r boys and 0 . 7 7 f o r g i r l s when comparing l o g r i t h m l c weight to p h y s i c a l work c a p a c i t y . Holmgren et a l . (19) r e p o r t e d a c o r r e l a t i o n c o e f f i c i e n t of 0 . 7 6 2 between body weight and PWC170. B u s k i r k et a l . (42) and Welch et a l . (50) ob ta ined c o r -r e l a t i o n c o e f f i c i e n t s of O . 6 3 and 0 . 5 9 . r e s p e c t i v e l y , between body weight and maximum oxygen i n t a k e . B u s k i r k et a l . (42) , Welch et a l . (50) and Von Dobeln (51) ob ta ined c o r r e l a t i o n c o e f f i c i e n t s of 0 . 8 5 . O .65 and 0 . 7 2 , r e s p e c t i v e l y , when maximum oxygen in take was compared to f a t f r e e we igh t . Thus , the i n f l u e n c e of body s i z e may induce spu r i ous e f f e c t s i f the r e l a t i o n s h i p between P W C 1 7 0 and o the r f a c t o r s a r e i n v e s t i g a t e d . I t f o l l o w s , t h e n , t ha t i f the P W C 1 7 0 t e s t i s to i n d i c a t e p h y s i o l o g i c a l e f f i c i e n c y to per form work o r r e l a -t i v e " p h y s i c a l f i t n e s s " the i n f l u e n c e of body s i z e must be c o n t r o l l e d . DeVr i es et a l . (38) compared P W C 1 7 0 kpm pe r mm per kg body weight and maximum oxygen i n t ake pe r kg body weight and ob ta ined a c o r r e l a t i o n c o e f f i c i e n t of O . 8 7 7 . A l t hough body weight has l o n g been used i n these r a t i o v a r i a b l e s , the re has been a t r end i n r e c e n t years to use f a t f r e e we igh t . Any two sub j e c t s may have the same f a t f r e e weight but d i f f e r g r e a t l y i n a d i p o s i t y and t h e r e f o r e , body weight w i l l d i f f e r . The t i s s u e of b i o l o g i c a l i n t e r e s t i n the r a t i o measured i s , however, the a c t i v e f r a c t i o n of body weight so t ha t the use of 31 f a t f r e e weight i s p r e f e r r e d . A n a l y s i s o f the S t a t i s t i c a l Methodology i n the I n t e r r e l a t i o n - s h i p s of Maximum Oxygen In take , S t r e n g t h , Body S i z e and PWC170 The d i f f i c u l t i e s i n employ ing ze ro o rder c o r r e l a t i o n s i n i n v e s t i g a t i o n s of p h y s i c a l work c a p a c i t y , maximum oxygen i n t ake and s t r e n g t h has been d i s c u s s e d . Perhaps the most b i o l o g i c a l l y mean ing fu l e x p r e s s i o n of an i n d i v i d u a l ' s p h y s i c a l work c a p a c i t y would be "PWC170 kpm per minute per kg f a t f r e e w e i g h t . " However, a l t h o u g h t h i s p rocedure i s most mean ing fu l when used i n normat ive t a b l e s , when i t Is employed f o r s t a t i s t i c a l r e l a -t i o n s h i p s , some problems a re encoun te red . In ze ro o rde r c o r r e l a t i o n s , the c o r r e l a t i o n c o e f f i c i e n t or the s i z e of the r e l a t i o n s h i p between the two v a r i a b l e s Is dependent on the d e v i a t i o n of each sco re f rom the mean (53)* Macnab (54:750) has s t a t e d t h a t , " P r e d i c t i o n s based on a e r o b i c c a p a c i t y a re q u i t e a c c u r a t e i n heterogeneous samples but poor i n homogeneous s a m p l e s . " In r ega rd to the PWC170 t e s t , Howel l e t a l . (32:39) conc luded t h a t , " . . . equa t ing s u b j e c t s f o r s i z e by d i v i d i n g t h e i r s co res by t h e i r weight..may not be e n t i r e l y s a t i s f a c t o r y . . . . " because the homogeneity of the sample i s i n c r e a s e d and the c o r r e l a t i o n c o e f f i c i e n t d e c r e a s e d . A l though no da t a was a v a i l a b l e f rom the above s tudy f o r s co res d i v i d e d by f a t f r e e we igh t , i t i s most l i k e l y t h a t the same i n c r e a s e i n homogeneity would have o c c u r r e d . 32 The d i s t r i b u t i o n a t t a i n e d when a score i s d i v i d e d by-body weight or f a t f r e e weight has not been adequa te l y i n v e s -t i g a t e d . Hays (55:510) has i m p l i e d t ha t un l e s s the d i s t r i b u t i o n s of the two v a r i a b l e s c o r r e l a t e d a re s i m i l a r i n fo rm, the c o r r e l a t i o n c o e f f i c i e n t w i l l be low. On the o the r hand, c o r r e l a t i o n of i n d i c e s or r a t i o s such as PWC170 kpm per minute per kg body weight (or pe r kg f a t f r e e weight ) may induce s p u r i o u s e f f e c t s Into the c o r r e l a t i o n due to a common f a c t o r (body weight ) employed as a denominator i n bo th r a t i o s ( 56 :162 ) . In t h i s c ase , the c o r r e l a t i o n c o e f f i c i e n t may be h i g h e r than e x p e c t e d . P o s s i b l y a more i n f o r m a t i v e as w e l l as a more a c c u r a t e p rocedure would be to use a p a r t i a l c o r r e l a t i o n t echn ique where the i n t e r f e r i n g v a r i a b l e i s h e l d c o n s t a n t . R e c e n t l y , Wilmore (57) used p a r t i a l c o r r e l a t i o n s to i n v e s t i g a t e the r e l a t i o n s h i p between endurance c a p a c i t y and maximum oxygen i n t a k e . When work output was compared to maximum oxygen Intake w i t h body s i z e not p a r t i a l l e d , the c o r r e l a t i o n c o e f f i c i e n t was O.836. When body weight was h e l d cons tan t the above r e l a t i o n s h i p was reduced to 0.787 and when f a t f r e e weight was f a c t o r e d ou t , the c o r r e l a t i o n c o e f f i c i e n t was reduced f u r t h e r to 0.693- Th i s p rocedure appears to be more a p p r o p r i a t e i n t h a t i t does not s u f f e r f rom the p o s s i b i l i t y of d i s t o r t i n g d i s t r i b u t i o n s o r i n d u c i n g s p u r i o u s e f f e c t s . A l t hough p a r t i a l c o r r e l a t i o n i s u s e f u l i n an a n a l y s i s i n 33 which the effects of some variable or variables are to be eliminated, " . . . i t s chief value l i e s in the fact that i t enables us to set up a multiple regression equation of two or more variables by which we can predict another variable or criterion" (53'404). The multiple regression analysis was used in this study to investigate the interrelationships of the selected variables. REFERENCES 1. Adams, H.A., Bengtsson, E.B., Birwan, H., Wegellus, C , "The P h y s i c a l Working Capacity of Normal School C h i l d r e n (Sweden)," P e d i a t r i c s , Volume 28, 1961, pp. 243-257. 2. Adams, F.H., Linde, L.M., Miyake, H., "The P h y s i c a l Working Capacity of Normal School C h i l d r e n , ( C a l i f o r n i a ) , " P e d i a t r i c s , Volume 28, 1961, pp. 55-64. 3. Bengtsson, E., "The Working Capacity of Small C h i l d r e n Evaluated by Submaximal E x e r c i s e on the B i c y c l e Ergometer and Compared w i t h A d u l t s , " Acta Medlca  Scandinavica, Volume 154, 1956, pp. 91-109. 4 . Cumming, G.R., Cumming, P.M., "Working Capacity of Normal C h i l d r e n Tested on the B i c y c l e Ergometer," Canadian  Medical A s s o c i a t i o n J o u r n a l , Volume 21, 1966, pp. 1807-1814. 5. Cumming, G.R., Danzinger, R., " B i c y c l e Ergometer Studies i n C h i l d r e n , " P e d i a t r i c s , Volume 32, 1963, pp. 202-208. 6. Cumming, G.R., "Current Levels of F i t n e s s , " Canadian Medical A s s o c i a t i o n J o u r n a l . Volume 96, 1967. p. 868. 7. S j o s t r a n d , T., "Changes i n R e s p i r a t o r y Organs of Workmen at an Ore Smelting Works," Acta Medica Scandinavica, Volume 128, (Suppl. 196) , 1947, pp. 687-699-8. Wahlund, H., "Determination of P h y s i c a l Working Capacity," Acta Medlca Scandinavica, Volume 132, (Suppl. 215) , 1948. 9. K j e l l b e r g , S.R., Rudhe, U . , S j o s t r a n d , T., "The Amount of Hemoglobin i n R e l a t i o n to the Pulse Rate and Heart Volume During Work," Acta P h y s i o l o g i c a Scandinavica, Volume 19, 1950, pp. 152-169. 10. S j o s t r a n d , T., " T e s t i n g of P h y s i c a l Work Capacity: D e f i n i t i o n , H i s t o r y , and A p p l i c a t i o n , " Forvarsmedlcln, Volume 3, 1967, pp. 141-144. 1 1 . Wright, Samson, A p p l i e d Physiology, Oxford U n i v e r s i t y Press, Toronto, 1952. 35 12. Ruch, T., F u l t o n , J . , Medical Physiology and B i o p h y s i c s , W.B. Saunders Company, London, I960. 13. Rushmer, R.F., "Cardiac C o n t r o l , " Physiology Review, Volume 39. 1959. pp. 41-68. 14. S a l t i n , B., "Aerobic Work Capacity and C i r c u l a t i o n a t Ex e r c i s e i n Man," Acta P h y s i o l o g l c a Scandinavica, Volume 62, (Suppl. 230 ) , 1964. 15. F a l l s , H.B., E d i t o r , E x e r c i s e Physiology, Academic Press, London, 1968, Anderson, L.K., "Cardiovascular System i n E x e r c i s e , " pp. 79-127. 16. DeVries, H.A., E x e r c i s e Physiology, W.C. Brown Company, Iowa, 1968. 17 . S j o s t r a n d , T., "Regulatory Mechanisms R e l a t i n g to Blood Volume," Minnesota Medicine, Volume 37, 1954, pp. 10-18. 18 . Bevegard, S., "Studies on the Regulation of the C i r c u l a -t i o n of Man," Acta P h y s i o l o g l c a Scandinavica, Volume 57. (Suppl. 200 ) , 1962-63-1 9 . Holmgren, A., Astrand, P.O., "DL and the Dimensions and F u n c t i o n a l C a p a c i t i e s of the Oxygen Transport Systems i n Humans," Journal of A p p l i e d Physiology, Volume 21 , 1966, pp. 1463-1470. 20 . Holmgren, A., Mossfeldt, F., Sjostrand, T., Strom, G., " E f f e c t of T r a i n i n g on Work Capacity, T o t a l Hemoglobin, Blood Volume, Heart Volume, and Pulse Rate i n Recom-bent and Upright P o s i t i o n s , " Acta P h y s i o l o g l c a Scan- d i n a v i c a . Volume 50 , I960, pp. 72-83. 2 1 . K j e l l b e r g , S.R., Rudhe, U., Sjostrand, T., "The Amount of Hemoglobin and Blood Volume i n R e l a t i o n to the Pulse Rate and Cardiac Volume During Rest," Acta  P h y s i o l o g l c a Scandinavica, Volume 19. 1950, pp. 136-145^ 22 . K j e l l b e r g , S.R., Rudhe, U., Sj o s t r a n d , T., "The R e l a t i o n of the Cardiac Volume to the Weight and Surface Area of the Body, the Blood Volume and the P h y s i c a l Capacity f o r Work," Acta R a d i o l o g l c a , Volume 31 , 1949, pp. 113-122. 36 23 . H e l l s t r o m , R., "Body B u i l d , Muscular Strength, and C e r t a i n C i r c u l a t o r y F actors i n M i l i t a r y Personnel," Acta  Medioa Scandinavica. (Suppl. 371 ) , 1961. 24. L i n r o t h , K., " P h y s i c a l Work Capacity i n Conscripts During M i l i t a r y S e r v i c e , " Acta Medlca Scandinavica, Volume 157, (Suppl. 324, 1957. 2 5 . Holmgren, A., S t r a n d e l l , T., "The R e l a t i o n s h i p Between Heart Volume, T o t a l Hemoglobin, and P h y s i c a l Working Capacity i n Former A t h l e t e s , " Acta Medioa Scandinavica, Volume 163. 1959. PP. 149-160. 2.6. K j e l l b e r g , S.R., Rudhe, U., Sjostrand, T., "Increase of the Amount of Hemoglobin and Blood Volume i n Connec-t i o n w i t h P h y s i c a l T r a i n i n g , " Acta P h y s i o l o g i c a  Scandinavica, Volume 19 , 1950, pp. 146-151. 27 . G u l l b r i n g , B., Holmgren, A., Sjostrand, T., S t r a n d e l l , T., "The E f f e c t of Blood Volume V a r i a t i o n s on the Pulse Rate i n Supine and Upright P o s i t i o n s and During E x e r c i s e , " Acta P h y s i o l o g i c a Scandinavica, Volume 50, I960, pp. 62-71. 28. Holmgren, A., " C a r d i o r e s p i r a t o r y Determinants of Cardiovascular F i t n e s s , " Canadian Medical A s s o c i a t i o n J o u r n a l , Volume 96, 1967, pp. 697-702. 2 9 . Astrand, P.O., Rhyming, I . , "A Nomogram f o r C a l c u l a t i o n of Aerobic Capacity from Pulse Rate During Submaximal Work," Journal of A p p l i e d Physiology, Volume 7, 195^» pp. 218-221. 30 . Astrand, P.O., "Human P h y s i c a l F i t n e s s w i t h S p e c i a l Reference to Age and Sex," P h y s i o l o g i c a l Reviews, Volume 36, 1956, p. 327. 31- T a y l o r , H.L., Bu s k i r k , E., Henschel, A., "Maximum Oxygen Intake as an Objective Measure of Cardio-Respiratory Performance," J o u r n a l of A p p l i e d Physiology, Volume 8, 1955, PP. 73-80. 32 . Howell, M.L., Macnab, R.B., The P h y s i c a l Work Capacity of  Canadian C h i l d r e n , Canadian A s s o c i a t i o n of Health, P h y s i c a l Education, and Recreation, 1968. 33* M a r i t z , J.S., "Maximum Oxygen Intake and Maximum Heart Rate," Ergonomics, Volume 4 , 1961, pp. 97-101. 37 34. Wyndham, C . H . , S t rydom, N .B . , M a r l t z , J . S . , M o r r i s o n , J . F . , P e t e r , J . , P o t z i e t e r , Z . , "Maximum Oxygen Intake and Maximum Heart Rate Dur ing Strenuous Work," J o u r n a l of A p p l i e d P h y s i o l o g y , Volume 14, 1959. PP. 927-936. 35* Wyndham, C . H . , "Submaximal Tes t s f o r E s t i m a t i n g Maximum Oxygen I n t a k e , " Canadian M e d i c a l A s s o c i a t i o n J o u r n a l , Volume 96, 1967, p p . 736-741. 36. R o w e l l , L . B . , "Commentary, " Canadian M e d i c a l A s s o c i a t i o n J o u r n a l , Volume 96, 1967. p. 735. 37. A s t r a n d , P .O . , Work Tes t s on the B i c y c l e Ergometer , Department of P h y s i o l o g y , Gymnast ika , C e n t r a l s t i t u e n t , S tockho lm, Sweden. 38. D e V r i e s , H .A . , K l a f s , C . E . , " P r e d i c t i o n of Maximal Oxygen Intake f rom Submaximal T e s t s , " J o u r n a l of Spor ts  Med i c ine and P h y s i c a l F i t n e s s , Volume 5, 1965. p p . 207-214. 39• A s t r a n d , P .O . , "Commentary, " Canadian M e d i c a l A s s o c i a t i o n  J o u r n a l , Volume 96, 1967, pp . 742-743. 40. M i t c h e l l , J . H . , S p r o u l e , B . J . , Chapman, C . B . , "The P h y s i o l o g i c a l Meaning of the Maximal Oxygen Uptake T e s t , " J o u r n a l of C l i n i c a l I n v e s t i g a t i o n , Volume 37. p. 538-54T: 41. Rob inson , S . , " Expe r imen t a l S tud i e s of P h y s i c a l F i t n e s s i n R e l a t i o n t o A g e , " A r b l e t p h y s l o l o g i c a . Volume 10, 1938, p. 251. 42. B u s k i r k , E . , T a y l o r , H . , "Maximum Oxygen Uptake and i t s R e l a t i o n to Body Compos i t i on w i t h S p e c i a l Re fe rence to Ch ron i c P h y s i c a l A c t i v i t y and O b e s i t y , " J ou rna l of  A p p l i e d P h y s i o l o g y , Volume 11, 1957. p p . 72-78. 43. S l o n i m , N .B . , G i l l e s p i e , D . G . , H a r o l d , W.H. , "Peak Oxygen Uptake of Hea l thy Young Men as Determined by a Treadmi l l Me thod , " J o u r n a l of A p p l i e d P h y s i o l o g y , Volume 10, 1957. p p . 401-404. 44. Coyne, L . L . , "The R e l a t i o n s h i p of Maximal Oxygen Intake to Body Compos i t i on and T o t a l Body Weight l n A c t i v e M a l e s , " Unpub l i shed Masters T h e s i s , U n i v e r s i t y o f A l b e r t a , 1963-38 45. B a l k e , B., Ware, C.W., "An Expe r imen ta l Study of P h y s i c a l F i t n e s s of A i r Fo r ce P e r s o n n e l , " Un i t ed S t a t es Armed  Fo r ce s M e d i c a l J o u r n a l , Volume 10, 1959. PP« 675-688. 46. Nag le , F . J . , B ed i c ke , T . G . , "The Use of the E x e r c i s e Heart Rate Responses as a Measure of C i r c u l o - R e s p i r a t o r y C a p a c i t y , " Research Q u a r t e r l y , Volume 3 4 , 1963. p p . 3 ^ - 3 9 . 47. T o r n v a l l , G . , "Assessment of P h y s i c a l C a p a c i t i e s , " A c t a P h y s i o l o g i c a S c a n d i n a v i c a , Volume 58, ( Supp l . 201) , 48. Morehouse, T . E . , M i l l e r , A . T . , P h y s i o l o g y of E x e r c i s e , S t . L o u i s , C V . Mosby, I963. 4 9 . A h l b o r g , B., " C a p a c i t y f o r P ro longed P h y s i c a l E x e r c i s e i n R e l a t i o n to Some An th ropomet r i c and Other D a t a , " F o r v a r s m e d l c l n , Volume 3 , ( Supp l . 1 ) , 1966, p p . 194-202. 5 0 . Welch, B . E . , R iendeau , R.P . , C r i s p , C . E . , I s e n s t e i n , R .S . , " R e l a t i o n ' o f Maximum to V a r i o u s Components of Body C o m p o s i t i o n , " J o u r n a l of A p p l i e d P h y s i o l o g y . Volume 12, 1958, pp . 395-398. 5 1 . Von Dobe ln , W., "Human Standard and Maximum M e t a b o l i c Rate i n R e l a t i o n to F a t F r ee Body M a s s , " A c t a P h y s i o l o g i c a  S c a n d i n a v i c a . Volume 3 7 , ( Supp l . 126) , 1956. 5 2 . Dempsey, J . A . , Redden, W., Rank in , J . , B a l k e , B., " A l v e o l a r - A r t e r i o l Gas Exchange Dur ing Muscu la r Work i n O b e s i t y , " J ou rna l of A p p l i e d P h y s i o l o g y . Volume 21 , 1966, pp . 1807-1814. 5 3 . G a r r e t t , H . E . , S t a t i s t i c s i n Psycho logy and E d u c a t i o n , Dav id McKay Company, I n c o r p o r a t e d , New York , 1966. 54. Macnab, R .B . , "Commentary, " The Canadian M e d i c a l A s s o c i a -t i o n J o u r n a l . Volume 9 6 , 1967, p. 750. 55. Hays, W.L . , S t a t i s t i c s , Ho l t R ineha r t and Winston, New York , 196*3^ 5 6 . McNemar, Q., P s y c h o l o g i c a l S t a t i s t i c s , John W i l son and Sons, New York , 1962. 57. Wi lmore, J . H . , "Maximal Oxygen Intake and I t s R e l a t i o n s h i p t o Endurance C a p a c i t y on a B i c y c l e E rgomete r , " Research Q u a r t e r l y , Volume 40 , I969, pp . 203-210. CHAPTER III METHODOLOGY Introduction F i f t y - f o u r subjects from the School of Physical Educa-t i o n and Recreation at the University of B r i t i s h Columbia underwent a series of tests; the r e s u l t s of which were used to determine the i n t e r r e l a t i o n s h i p s of maximum oxygen Intake, strength, body siz e and physical work capacity. The Sjostrand PWC170 test was conducted to estimate physical work capacity and an " a l l out" r i d e on the bicycle ergometer was administered to determine maximum oxygen intake values. The subjects were weighed underwater to assess t h e i r f a t free weight and a comprehensive strength test was also conducted. The s t a t i s t i c a l analysis of the data was procured through the University of B r i t i s h Columbia Computing Center. Estimation of Physical Work Capacity The Sjostrand PWC170 Test. Physical work capacity has been defined as the work load necessary to produce a heart rate of 1 7 0 beats per minute at a steady state. The PWC170 test employed d i f f e r e n t and s u f f i c i e n t l y heavy loads to make possible the estimation of the maximum steady state l e v e l . Astrand ( 1 : 1 5 ) has stated that, "Generally, a f t e r 6 minutes of work at a s p e c i f i c work load, the lack of any further increase 40 i n hea r t r a t e i n d i c a t e s t h a t the d e s i r e d hea r t r a t e had been r e a c h e d . " Fu r the rmore , a work ing t ime of 18 minutes shou ld not exhaust the g l y cogen supp l y i n the l e g muscles ( 2 : 1 ? ) . P rocedure f o r E s t i m a t i n g PWC170. The procedure f o r e s t i m a t i n g p h y s i c a l work c a p a c i t y was the same method used by Boyd ( 3 ) . A l l the s u b j e c t s rode a Monark b i c y c l e ergometer a t th ree p r o g r e s s i v e l y i n c r e a s i n g work l oads des igned t o produce s teady s t a t e hea r t r a t e s f a l l i n g w i t h i n the i n t e r v a l s of 120 t o 130, 140 to 150 and 160 t o 1?0 beats per minute , r e s p e c t i v e l y ( 1 . 4 , 5 ) . The r a t e of work was 60 c y c l e s per minute and the s u b j e c t s were accompanied by a metronome. The s u b j e c t s worked f o r 6 minutes a t each l e v e l , i . e . , f o r a t o t a l of 18 minutes w i thout s t o p p i n g . The average hea r t r a t e of f i f t h and s i x t h minute a t each l e v e l was . cons ide r ed to conform to the r e q u i r e -ments of the s teady s t a t e i f the d i f f e r e n c e between the f i f t h and s i x t h minute r a t e s was l e s s than 2 beats per m inu te . I f i t was more than t h i s amount, the s u b j e c t con t i nued t o peda l a t the same l e v e l u n t i l s teady s t a t e was r e a c h e d . The hea r t r a t e s f o r the PWC170 t e s t were determined i n the f o l l o w i n g manner. Hear t r a t e s were r eco rded d u r i n g the l a s t q u a r t e r of each minute on an e l e c t r o c a r d i o g r a m (Sanborn 500 V i s o - C a r d i e t t e ) . Two Beckman b i o p o t e n t i a l s k i n e l e c t r o d e s were used i n t h i s p ro cedu re , one was p l a c e d on the upper sternum and the o the r on the f i f t h i n t e r c o s t a l space under the 41 l e f t n i p p l e . The e l e c t r o d e s were w i red to an ECG. Te l eme te r i ng T r a n s m i t t e r (Models 27-1 and 27-2) which were a t t a c h e d to a b e l t worn around the w a i s t . E l e c t r i c a l impulses were p i c k e d up on an ECG. Radio Te lemetry Rece i v e r (Models RC 27-1 and 27-2) which i n t u r n was connected to the e l e c t r o c a r d i o g r a m . The paper speed on the e l e c t r o c a r d i o g r a m was 25 mm per second and a S te inmeyer Pocket V e r n i e r C a l i p e r was used to measure 6 b e a t s . A t a b l e used by the CAHPER r e s e a r c h committee (5:60) was u t i l i z e d i n the p r e sen t s tudy t o conver t the c a l i p e r measurements i n t o hea r t bea ts pe r m inu te . The PWC170 t e s t was per formed t w i c e . The f i r s t t e s t se rved as a p r a c t i c e r i d e to f a m i l i a r i z e the s u b j e c t s w i t h the t e s t i n g procedure and t o a l l o w the t e s t a d m i n i s t r a t o r t o approxi -mate the work l o a d s neces sa r y to produce the r e q u i r e d hea r t r a t e s . The approximate h e i g h t of the sea t on the b i c y c l e ergometer was a l s o determined f o r each sub j e c t and r e co rded a t t h i s t i m e . Sub j ec t s were a l s o r eques ted to r e f r a i n f rom d r i n k i n g c o f f e e o r t e a and from smoking f o r a t l e a s t one hour b e f o r e the t e s t . I n v e s t i g a t o r s have i n d i c a t e d t h a t the i n j e s t i o n o f f o o d may i n f l u e n c e p h y s i o l o g i c a l parameters i n c l u d e d i n t h i s s t u d y . Lundgren (6) has demonstrated tha t a l a r g e meal w i l l i n c r e a s e maximum oxygen In take . T a y l o r e t a l . (7) have shown tha t a meal of 1000 c a l o r i e s i n c r e a s e d pu l s e r a t e f rom 132 to 144 beats pe r minute a t an oxygen i n t ake of two l i t e r s pe r minute and the e f f e c t had not d i s s i p a t e d 42 comp le te l y a f t e r one and one h a l f h o u r s . C a l c u l a t i o n of PWC170. The va lue of PWC170 was d e t e r -mined both by a manual method and by computer . In the manual method, a graph f o r each t r i a l was prepared w i t h s teady s t a t e hea r t r a t e p l o t t e d a g a i n s t work l o a d a t each of the three l e v e l s o f work. The bes t f i t t i n g s t r a i g h t l i n e was drawn through the th ree p o i n t s and the es t ima ted work co r r e spond ing t o a hea r t r a t e of 170 bea ts per minute was ob ta ined by i n t e r p o l a t i o n or e x t r a p o l a t i o n . The l i n e a r r e g r e s s i o n l i n e f o r s teady s t a t e hea r t r a t e s and work loads and the co r r e spond ing es t imated work c a p a c i t y were a l s o c a l c u l a t e d through the U n i v e r s i t y of B r i t i s h Columbia Computing C e n t e r . R e l i a b i l i t y of the S j o s t r a n d PWC170 T e s t . A l t hough many r e s e a r c h e r s have i m p l i e d tha t the S j o s t r a n d t e s t was r e l i a b l e , l i t t l e da t a i s a v a i l a b l e . Two s t u d i e s (8,9) have i n d i c a t e d tha t no s i g n i f i c a n t d i f f e r e n c e of PWC170 s co re s was found between a t e s t i n the s p r i n g and i n the f a l l , but no v a l u e s were c i t e d . Zahar (10) has conducted a ve r y comprehensive s tudy on the r e l i a b i l i t y of the S j o s t r and t e s t . The t e s t -r e t e s t t echn ique of 6 t r i a l s r e v e a l e d the lowest c o r r e l a t i o n of 0.809 between t r i a l s 1 and 4 . The h i g h e s t c o r r e l a t i o n was 0.947 between t r i a l s 5 and 6 . Perhaps the most p e r t i n e n t da t a to the s tudy was the r e l i a b i l i t y between the second and t h i r d t e s t , which was r e p o r t e d to be 0 .894. k3 E s t i m a t i o n of Maximum Oxygen Intake The " A l l Out " B i o y o l e Ergometer T e s t , When a t t empt i ng to measure maximum oxygen i n t a k e , i t i s necessa r y to e s t a b l i s h when maximum oxygen i n t ake o c c u r s . T a y l o r et a l . (7) r e p o r t e d t ha t oxygen i n t ake rose l i n e a r l y w i t h hea r t r a t e as work r a t e i n c r e a s e d and t h u s , when hea r t r a t e became a s y m p t o t i c , maximum oxygen i n t ake was r e a c h e d . A work ing t ime of l e s s than 5 minutes was suggested as be ing adequate to e l i c i t maximum oxygen I n t ake . However, Wyndham (11,12) and M a r i t z (13) have e s t a b l i s h e d tha t maximum oxygen i n t ake occurs a f t e r the hea r t r a t e became asympto t i c and recommended a t e s t t ime g r e a t e r than 5 m inu te s . T o r n v a l l (14) r e p o r t e d a c o r r e l a t i o n c o e f f i c i e n t of 0 .91 between a 3 minute maximal t e s t and maximum oxygen i n t a k e . A h i g h e r c o r r e l a t i o n c o e f f i c i e n t of 0.95 was ob ta ined between a 15 minute maximal t e s t and maximum oxygen i n t a k e . T o r n v a l l (14 :91) conc luded t h a t , " . . . a n incomple te c i r c u l a t o r y a d a p t a t i o n i n exhaus t i ng per formances of a s h o r t e r d u r a t i o n than 6 minutes may o c c u r . " Th i s l a t t e r approach f o r o b t a i n i n g maximum oxygen i n t ake was used i n the p resen t s t u d y . P rocedure f o r E s t i m a t i n g Maximum Oxygen I n t ake . The t e s t to measure maximum oxygen i n t ake r e q u i r e d a minimum of 7 minutes and took the f o l l o w i n g fo rm: kk Minutes Speed - km per hr Resistance - kp 1 20 2 2 20 2 3 20 2 k 25 2.5 or 3 5 30 2.5 or 3 6 35 2.5 or 3 7 ko 2.5 or 3 exhaustion ko 2.5 or 3 The i n i t i a l three minutes served as a p r e l i m i n a r y "warm-up." The subjects then began a progressive increase i n r a t e of p e d a l l i n g w i t h an increased r e s i s t a n c e as i n d i c a t e d on the c h a r t . The r e s i s t a n c e of 2.5 or 3 kiloponds was a r b i -t r a r i l y assigned to the subjects a f t e r an a n a l y s i s of t h e i r body weight and PWC170 scores. During the "warm-up" p e r i o d , a l l subjects were f i t t e d w i t h a nose c l i p and a Modified O t i s -McKerrow p l a s t i c v a lve (15:250) supported by a head band. At the beginning of the f o u r t h minute, the va l v e was connected t o a mixing chamber v i a a non-kinkable hose ( i n t e r i o r diameter -1.5 i n c h e s ) . The t e r m i n a l end of the mixing chamber was connected to a Parkinson-Cowan high p r e c i s i o n , low r e s i s t a n c e gas meter by a s i m i l a r hose. A report by D i l l (16) described i n d e t a i l the apparatus employed i n t h i s study. Beginning w i t h the f o u r t h minute, a 30 cubic centimeter sample of expired a i r was drawn i n t o a syringe during the l a s t 4 5 h a l f of the minute and the temperature of the gas was recorded. The volume of expired a i r was recorded from the gas meter a t the end of each minute. The heart r a t e was recorded i n the f a s h i o n as described f o r the PWC170 t e s t . The maximum oxygen intake t e s t continued u n t i l the subject was exhausted, i . e . , he was no longer a b l e to maintain r e q u i r e d p e d a l l i n g speed. In order t o standardize c o n d i t i o n s f o r the t e s t , a l l subjects were requested to r e f r a i n from e a t i n g , smoking and d r i n k i n g c offee or tea the morning of the t e s t . The e f f e c t of i n j e s t i o n of food on heart r a t e and maximum oxygen intake has been demonstrated by Lundgren ( 6 ) and Taylor et a l . ( 7 ) . C a l c u l a t i o n of Maximum Oxygen Intake. A l l gas samples were analyzed on the micro-Scholander apparatus as soon as pos-s i b l e a f t e r the t e r m i n a t i o n of the t e s t ( 1 6 : 5 ) ' A nomogram designed by D a r l i n g ( 1 5 ) was used to reduce the saturated gas volumes to 0 degree Centigrade dry and 7 6 0 mm hg. The r e s p i r a -t o r y q u o t ient and true oxygen values were c a l c u l a t e d by means of a nomogram constructed by D i l l ( 1 5 ) • Maximum oxygen int a k e was determined by the equation: True Oxygen x C o r r e c t i o n Volume = Oxygen Intake i n L i t e r s per Minute. R e l i a b i l i t y of Maximum Oxygen Intake Test. No r e l i a -b i l i t y values have been reported f o r the maximum oxygen Intake t e s t developed by D i l l ( 1 6 ) . However, r e l i a b i l i t y measures f o r 46 the more comp l i c a t ed t r e a d m i l l t e s t have been r e p o r t e d by-numerous i n v e s t i g a t o r s . T a y l o r e t a l . (7). B u s k i r k et a l . (17), and Coyne (18) ob ta ined r e l i a b i l i t y c o e f f i c i e n t s of 0.95. 0.98 and 0.926, r e s p e c t i v e l y . Thus , a h i g h r e l i a b i l i t y of the b i c y c l e ergometer t e s t might be expec t ed . E s t i m a t i o n of Body D e n s i t y The Underwater Weighing T e s t . The q u a n t i t y of a d i p o s e t i s s u e was es t imated by d e t e r m i n i n g the s p e c i f i c g r a v i t y of i n d i v i d u a l s by the method of underwater w e i g h i n g . T h i s p r o c e -dure u t i l i z e d the A r ch imed i an p r i n c i p l e : Body d e n s i t y = Weight i n a i r - Weight i n wa te r . S ince the s p e c i f i c g r a v i t y of ad ipose t i s s u e i s 0.94 (19) which i s l e s s than t h a t of water and s i n c e the s p e c i f i c g r a v i t y of a l l o the r t i s s u e s " a re g r e a t e r than 1.0, the nega t i v e weight o r buoyancy l n water must be p r o p o r t i o n a l to the amount of ad ipose t i s s u e p resen t (20). Procedure f o r E s t i m a t i n g Body D e n s i t y . The s u b j e c t s were weighed i n t h e i r swim s u i t s be fo re e n t e r i n g the wa te r . Three o r more v i t a l c a p a c i t y r e c o r d i n g s were taken on a Wet Sp i romete r w i th the sub j e c t s t and ing emerged so tha t the l e v e l of water was j u s t above the s h o u l d e r s . The l a r g e s t r e a d i n g was accep ted as the v i t a l c a p a c i t y when one o the r r e a d i n g d i d not d i f f e r by more than 0.3 l i t e r s . A l l s u b j e c t s were then f i t t e d 47 w i th a we ighted b e l t , a nose c l i p and a h a r n e s s . The u n d e r -water we igh ing was conducted on a C h a t t e l o n Autopsy s c a l e a f t e r the sub j e c t had exha led f u l l y and then i n h a l e d a measured q u a n t i t y of a i r f rom the Wet Sp i rome te r . Two e q u i v a l e n t we ights were a c cep t ed as the body weight i n wa te r . An at tempt was made to remove a l l bubbles of a i r f rom the s u r f a c e of the s k i n , the h a i r and f rom w i t h i n the swim s u i t s b e f o r e the w e i g h i n g s . A f t e r each t e s t , the temperature of the a i r and the water was r e c o r d e d . C a l c u l a t i o n of Body F a t . The e s t i m a t i o n of s p e c i f i c g r a v i t y v a l u e s were conducted i n the manner proposed by Yuhasz (21 ) . C o r r e c t i o n s f o r water and a i r temperatures were r e co rded and the r e s i d u a l l ung volume was taken t o be JO percen t of the v i t a l c a p a c i t y v a l u e . To conver t the s p e c i f i c g r a v i t y measurements to percentage of body f a t v a l u e s , a f o rmu la d e v i s e d by Keys and Brozek (22) was used : Percentage body f a t = 4.201 - 3.813 x UgL. R e l i a b i l i t y o f the Body D e n s i t y T e s t . Yuhasz (21) ob ta ined a r e l i a b i l i t y c o e f f i c i e n t of O.967 when t e s t s were conducted on the same day and 0.972 when the t e s t s were c o n -duc ted on c o n s e c u t i v e day s . Coyne (18) and Dempsey (23) have r e p o r t e d r e l i a b i l i t y c o e f f i c i e n t s f o r submerged we ights of 0.929 and 0 .983 , r e s p e c t i v e l y . 48 E s t i m a t i o n of Muscu la r S t r eng th S t r eng th T e s t s . The t e s t f o r muscu lar s t r e n g t h was c o n -duc ted i n the manner d e s c r i b e d i n the d e f i n i t i o n , i . e . , i t was des igned to measure a maximum f o r c e exe r t ed f o r a b r i e f t ime where the f o r c e was exe r ted c o n t i n u o u s l y up to the maximum. The f o r c e was exe r ted a g a i n s t e x t e r n a l ob j e c t s such as the dynamometer, r a t h e r than i n s u p p o r t i n g or p r o p e l l i n g the body ' s own we igh t . F l e i shman has s t a t e d t h a t , "The r e l a t i o n between body weight and performance of t h i s f a c t o r i s e s p e c i a l l y h i g h " (24:65)• Procedure f o r E s t i m a t i n g Muscu la r S t r e n g t h . The i tems of the t e s t were as f o l l o w s : Type 1. G r i p a) l e f t b) r i g h t 2. Push s t r e n g t h 3. P u l l s t r e n g t h 4. Leg s t r e n g t h 5. Back s t r e n g t h 6. Trunk e x t e n s i o n 7. Trunk f l e x i o n 8. Knee e x t e n s i o n a) l e f t b) r i g h t Instrument Manuometer Manuometer Manuometer Manuometer Dynamometer Dynamometer Tens iometer Tens iometer Tens iometer The procedure f o r t e s t i n g w i t h the manuometer and the dynamometer was conducted i n the manner d e s c r i b e d i n McCloy 49 (25:148-151). Before the gri p strength tests, a l l subjects were warned not to rest t h e i r elbows on t h e i r hips while execu-tin g the t e s t . For the leg strength tests, a bel t was employed to strap the bar to the waist. An angle of 120 degrees behind the knees was determined by a goniometer. The procedure f o r te s t i n g with the tensiometer was described by Clarke et a l . (26:73-96). Calculation of Muscular Strength. For a l l tests excep-t i n g the back and l e g dynamometer tests, a minimum of two t r i a l s and a maximum of four t r i a l s was conducted. When a v a r i a t i o n of less than 3 pounds i n the readings between successive t r i a l s occurred, the highest reading of the two scores was accepted as a maximum strength f o r a s p e c i f i c t e s t . For individuals with a larger v a r i a t i o n than 3 pounds a f t e r 4 t r i a l s , the mean of the two highest recordings was accepted. Only one t r i a l was conducted f o r the back and leg strength. R e l i a b i l i t y of the Strength Test. No r e l i a b i l i t y coef-f i c i e n t s were available f o r the s p e c i f i c instruments and procedure i n the dynamometer and manuometer tests used i n t h i s study. Clarke et a l . (26) obtained a r e l i a b i l i t y c o e f f i c i e n t of 0.90 f o r the tensiometer t e s t s . S t a t i s t i c a l Methodology The PWC170 values computed by both manual and computer 50 methods were c o r r e l a t e d t o assess the r e l a t i v e accuracy of the manual technique. The computer program - T r i a n g u l a r R e g r e s s i o n Package (TRIP) (27) - was u t i l i z e d i n t h i s and other a n a l y s e s through the U n i v e r s i t y of B r i t i s h Columbia Computing Center. The means and standard d e v i a t i o n s of a l l of the f o l l o -wing v a r i a b l e s i n c l u d e d i n t h i s study were c a l c u l a t e d : Dependent V a r i a b l e s : X i PWC170 kpm per min, X2 PWC170 kpm per min per kg body weight, X3 P W C 1 7 0 kpm per min per kg f a t f r e e weight. Independent V a r i a b l e s : X2j. Body weight (kg), X5 Pat f r e e weight (kg), X$ V i t a l c a p a c i t y ( l i t e r s ) , X7 Oxygen i n t a k e L P e r min, Xs Oxygen i n t a k e ml per min per kg body weight, X9 Oxygen i n t a k e ml per min per kg f a t f r e e weight, X10 Push s t r e n g t h ( l b s . ) , X n P u l l s t r e n g t h ( l b s . ) , X 1 2 Trunk f l e x i o n ( l b s . ) , X13 Trunk e x t e n s i o n ( l b s . ) , Xi4 Right knee e x t e n s i o n ( l b s . ) , X15 L e f t knee e x t e n s i o n ( l b s . ) , X 1 6 Average knee e x t e n s i o n ( l b s . ) , X17 Right g r i p ( l b s . ) , 51 X i 8 Left grip ( l b s . ) . X 1 9 Back strength ( l b s . ) , X20 Leg strength ( l b s . ) , X21 Total strength ( l b s . ) , X22 Total strength l b s . per kg body weight, X 2 3 Total strength l b s . per kg f a t free weight, X2^ Body density gm per cm3. Intercorrelation matrices were obtained through the Computing Center. The following analysis was conducted on the aforementioned matrices: 1. A zero order c o r r e l a t i o n matrix investigated the inte r r e l a t i o n s h i p s between a l l the variables when no variables were held constant, 2 . Two f i r s t order, or p a r t i a l correlations investiga-ted the int e r r e l a t i o n s h i p s between a l l the variables when body weight and f a t free weight were held constant, respectively, 3 . A twenty-second order matrix was included to inves-tigate the l i n e a r r e l a t i o n s h i p of two variables when a l l others were held constant. A multiple regression analysis was conducted on each of the dependent variables to investigate the i n t e r r e l a t i o n s h i p between physical work capacity and two or more of the indepen-dent variables. REFERENCES 1. A s t r a n d , P .O . , Work Tes t s on the B i c y c l e Ergometer , Dep t . of P h y s i o l o g y , Gymnast lka , C e n t r a l i n s t i t u e n t , S tockho lm, Sweden. 2. 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L . , "The R e l a t i o n s h i p of Maximal Oxygen Intake to Body Compos i t i on and T o t a l Body Weight l n A c t i v e M a l e s , " Unpub l i shed M a s t e r ' s T h e s i s , U n i v e r s i t y of A l b e r t a , 1963. 1 9 . Behnke, A . R . , F een , B .G . , Welham, W . C , "The S p e c i f i c G r a v i t y of Hea l thy Men ( O b e s i t y ) , " J o u r n a l of the  Amer i can M e d i c a l A s s o c i a t i o n , Volume 118, 1942, P P . 495-498. ; 5 20 . Behnke, A . R . , Welham, W . C , "The S p e c i f i c G r a v i t y of Hea l thy Men ( A t h l e t e s ) , " J o u r n a l of the Amer ican M e d i c a l A s s o c i a t i o n , Volume 118, 1942, pp . 498-500. 2 1 . Yuhasz , M. , "The E f f e c t s of Spor t s T r a i n i n g on Body Fa t i n Man w i t h P r e d i c t i o n of Opt ima l Body We igh t , " Unpub-l i s h e d D o c t o r a l D i s s e r t a t i o n , U n i v e r s i t y of I l l i n o i s , 1962. 22. Keys , A . , B rozek , J . , "Body F a t i n A d u l t Man , " P h y s i o l o g i - c a l Reviews, Volume 33, 1953, pp . 245-325. 54 2 3 . Dempsey, J . A . , Redden, W., Rank in , J . , B a l k e , B., " A l v e o l a r - A r t e r i a l Gas Exchange Dur ing Muscu la r Work i n O b e s i t y , " J ou rna l of A p p l i e d P h y s i o l o g y , Volume 21, 1966, p p . 1807-1814. 24 . F l e i s h m a n , E . A . , The S t r u c t u r e and Measurement of P h y s i c a l F i t n e s s , P r e n t i c e H a l l , New J e r s e y , 1964. 25« McCloy , C , Young, N . , Tes t and Measurement i n Hea l t h and P h y s i c a l E d u c a t i o n , App le ton-Cen tu ry C r o f t s , New York , 1942. 26 . C l a r k e , H . , C l a r k e , D . , Deve lopmenta l and Adapted P h y s i c a l E d u c a t i o n , P r e n t i c e H a l l , New J e r s e y , 1963* 2 7 . Dempster , J . H . , Gagne, A . E . , Hogan, R., U .B .C . TRIP ( T r i a n g u l a r R e g r e s s i o n Package ) , U n i v e r s i t y of B r i t i s h Columbia Computing Cen t e r , 1968. CHAPTER IV RESULTS Obse r va t i ons on the Sub jec t s The s u b j e c t s f o r t h i s s tudy c o n s i s t e d of s tudents e n r o l l e d i n a t e s t s and measurement course l n the Schoo l of P h y s i c a l E d u c a t i o n and R e c r e a t i o n a t the U n i v e r s i t y o f B r i t i s h Co lumbia . Twenty-four male undergraduates and th ree male graduate s tuden ts were t e s t e d d u r i n g the f a l l of 1966. Twenty-seven male undergraduates were t e s t e d i n the f a l l o f 1967. The t o t a l p o p u l a t i o n of the s tudy was f i f t y - f o u r (N=54). Comparat ive d a t a on age , body we igh t , f a t f r e e we igh t , body d e n s i t y and PWC170 k P m P e r m i n s co res have been p resen ted i n Tab le I. TABLE I COMPARATIVE DESCRIPTIVE STATISTICS OF THE TWO GROUPS OF SUBJECTS Year V a r i a b l e Mean S tandard Deviat ion Range 1966 1967 Age ( y r s . ) Age ( y r s . ) 22.00 22.88 1.20 1.51 20 20 - 24 - 25 1966 1967 Body Weight (kg) Body Weight (kg) 76.55 75-03 10.40 10.55 56.24 60.21 - 93.37 - 111.24 1966 1967 Fa t F r ee Wt. (kg) Fa t F r ee Wt. (kg) 69.14 68.74 7.34 8.90 51.46 52.25 81.28 95-44 1966 1967 Body Density (gm per cm3) Body Density (gm per cm 3) 1.077 1.079 0.0095 0.0131 1.054 1.047 1.091 1.095 1966 1967 PWC170 kpm pe r min PWC170 kpm pe r min 1120.0 1166.8 200.2 162.4 712.9 795.7 - 1564.0 - 1565.9 56 The subjects t e s t e d i n the f a l l of 1966 were i n the age range of 20 to 24 years, w i t h a mean age of 22.00 t 1.20 years. The mean body weight, f a t f r e e weight, body d e n s i t y and P W C 1 7 0 kpm per min score were: 76.55 t 10.40 kg, 69.14 t 7*34 kg, 1.077 t 0.0095 gm per cm3, and 1120 ± 200.2 kpm per min, r e s p e c t i v e l y . The subjects t e s t e d i n the f a l l of 1967 were i n the age range of 20 to 25 years, w i t h a mean age of 22.88- 1.51 years. Mean values f o r body weight, f a t f r e e weight, body d e n s i t y , and PWC170 kpm per min of t h i s group were 75.03+ 10.55 kg, 6 8 . 7 4 t 8.90 kg, 1.079 - 0.0131 gm per cm3, and 1166.8 t kpm per min, r e s p e c t i v e l y . Sample Data The means and standard d e v i a t i o n s of a l l the v a r i a b l e s f o r the t o t a l group (N=54) have been presented i n Table I I . Haw scores have been recorded i n Appendix C. 57 TABLE I I MEANS AND STANDARD DEVIATIONS OF ALL THE VARIABLES V a r i a b l e Mean Standard D e v i a t i o n XI PWC170 kpm per min 1143.0 186.8 X2 PWC170 kpm per min per kg body wt. 15.14 2.151 X3 PWC170 kpm per min per kg fat free wt. 16.58 2.005 X4 Body weight (kg) 7 5 - 9 6 10.71 X5 Fat f r e e weight (kg) 69.10 8.204 X 6 V i t a l c a p a c i t y ( L i t e r s ) 5.274 0.7641 X7 Oxygen intake L per min 3-774 0.5056 X8 Oxygen intake ml per min per kg body wt. 49*77 6.451 X9 Oxygen int a k e ml per min per kg fat free wt. 54.41 6.163 X10 Strength ( l b s ) Push 123.8 18.19 XII P u l l 97-11 13.82 X12 Trunk f l e x i o n 150.5 31.03 X 1 3 Trunk extension 174-5 42.69 X14 Knee extension r i g h t 277.6" 50.77 X 1 5 Knee extension l e f t 280.9 44.85 X16 Knee extension average 277.4 47.64 X17 Right g r i p 136.2 16.39 X18 L e f t g r i p 121.5 14.70 X19 Back 527.4 77.70 X20 Leg 1140.0 189.0 X21 T o t a l s t r e n g t h ( l b s ) 1925.0 262.5 X22 Strength per body weight l b s per kg 11.59 1.392 X23 Strength per f a t f r e e weight lbs per kg 12.68 1.370 X24 Body d e n s i t y (gm per cm3) 1.078 0.01141 Comparison Between Manual and Computer Methods f o r C a l c u l a t i n g  the PWC170 Values Both manual (graphic) and computer p l o t t i n g techniques were employed to estimate the best f i t t i n g s t r a i g h t l i n e i n the c a l c u l a t i o n of PWC170 v a l u e s . This was done to assess the 58 ac cu r a c y of the s i m p l e r manual t e c h n i q u e . The means, s t anda rd d e v i a t i o n , c o r r e l a t i o n c o e f f i c i e n t and the v a r i a n c e of the two techn iques have been p resen ted i n Tab le I I I . TABLE I I I COMPARISON BETWEEN THE MANUAL AND COMPUTER METHODS FOR CALCULATING P W C 1 7 0 Technique Mean S tandard D e v i a t i o n C o r r e l a t i o n C o e f f i c i e n t V a r i a n c e r2 x100 Manual 1145 184.6 0.9912** 98.24 Computer 1143 186.8 r > 0.348; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.01 l e v e l of c o n f i d e n c e . The e s t i m a t i o n s o f the l i n e a r r e g r e s s i o n l i n e f o r de t e rm in i ng PWC170 v a l ue s and the c o r r e l a t i o n c o e f f i c i e n t f o r the two methods were ob ta ined through the U n i v e r s i t y of B r i t i s h Columbia Computing Cen te r - TRIP Program (1). The raw sco res have been i n c l u d e d i n Appendix C. The mean PWC170 v a l ue f o r the manual method was 1145 - 184.6 kpm per min and the mean f o r the computer t e c h -n ique was 1143 1 186.8 kpm p e r m in . The c o e f f i c i e n t of c o r r e l a t i o n between the methods was 0.9912 which was s t a t i s t i -c a l l y s i g n i f i c a n t a t the 0.01 l e v e l o f c o n f i d e n c e . A v a r i a n c e , o r the c o e f f i c i e n t of d e t e r m i n a t i o n ( r | y ) of 0.9912 i n d i c a t e d tha t 98.24 pe r cen t of the v a r i a n c e of one v a r i a b l e was p r e d i c -59 t a b l e from the v a r i a n c e of the o the r v a r i a b l e (2:108). Va r i ance due t o e r r o r was I.76 p e r c e n t . Zero Order C o r r e l a t i o n A n a l y s i s A ze ro o rde r i n t e r c o r r e l a t l o n m a t r i x o f the twenty-four v a r i a b l e s i n v e s t i g a t e d i n t h i s s tudy was ob ta ined th rough the U n i v e r s i t y of B r i t i s h Columbia Computing Cente r and has been p resen ted i n Appendix C . The c o e f f i c i e n t s of c o r r e l a t i o n of the v a r i a b l e s most p e r t i n e n t to the a n a l y s i s of the da t a have been e x t r a c t e d f rom the a fo rement ioned i n t e r c o r r e l a t l o n ma t r i x and have been p re sen ted i n Tab les IV, V , V I , V I I and V I I I . V a r i a n c e s between the v a r i a b l e s were a l s o i n c l u d e d . Dependent V a r i a b l e PWC170 kpm per m i n . C o e f f i c i e n t s of c o r r e l a t i o n between the dependent v a r i a b l e PWC170 kpm per min and the independent v a r i a b l e s (Xij, . . . . X24) were i n c l u d e d i n Tab le IV. Body weight ( r = O.5233), f a t f r e e weight (r= 0.6293), v i t a l c a p a c i t y ( r = 0.4091), oxygen i n t ake i n l i t e r s pe r min ( r = 0.6225), r i g h t knee e x t e n s i o n ( r = 0.4632), l e f t knee e x t e n s i o n ( r = 0.3614) and knee e x t e n s i o n average ( r = 0.3959) were s i g n i f i c a n t l y c o r r e l a t e d w i t h the dependent v a r i a b l e PWC170 kpm per min a t the 0.01 l e v e l of c o n f i d e n c e . The c o r r e l a t i o n c o e f f i c i e n t s f o r push s t r e n g t h ( r = 0.3116), t runk f l e x i o n ( r = O.3035), t r unk e x t e n s i o n ( r = 0.3395). l e g s t r e n g t h ( r = 0.3373) and t o t a l s t r e n g t h 60 TABLE IV ZERO ORDER COEFFICIENTS OF CORRELATION BETWEEN THE DEPENDENT VARIABLE PWC 1 7 0 KPM PER MIN AND THE INDEPENDENT VARIABLES (X4 X24) Independent V a r i a b l e C o r r e l a t i o n Variance C o e f f i c i e n t r2 x 100 X4 Body weight (kg) 0 .5233** 27 .38 X5 Fat f r e e weight (kg) 0 .6293** 39.60 X6 V i t a l c a p a c i t y ( l i t e r s ) 0.4091** 16 .74 X7 Oxygen int a k e L per min 0 .6225** 38.75 X8 Oxygen intake ml per min per kg body wt. 0 .1025 1.05 X9 Oxygen intake ml per min per kg fat free wt. 0.0932 0 .87 X10 Strength ( l b s ) Push 0 .3116* 9.71 X l l P u l l 0.1927 3.71 XI2 Trunk F l e x i o n 0.3035 9.21 X13 Trunk extension 0 .3395* 11 .53 X l 4 Knee extension r i g h t 0.4632** 21.46 X15 Knee extension l e f t 0.3614** 13.06 X16 Knee extension average O .3959** 14.09 X17 Right g r i p 0.1240 1 .54 X18 L e f t g r i p 0.0982 O.96 X19 Back 0.2662 7.09 X20 Leg 0 .3373* 11 .38 X21 T o t a l s t r e n g t h ( l b s ) O.3338* 11.14 X22 Strength per body weight l b s per kg -0.2058 4.24 X23 Strength per f a t f r e e weight lbs per kg -0.2427 5.89 X24 Body d e n s i t y (gm per cm3) 0 .0798 0.64 df = 52 (N-2) * r > 0.268; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0 .05 l e v e l of confidence. ** r > 0.348; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.01 l e v e l of confidence. ( r = O.3338) were s i g n i f i c a n t a t the 0.05 l e v e l of confidence. The c o r r e l a t i o n c o e f f i c i e n t s obtained f o r the r e l a t i o n -ship of PWC170 kpm per min to a l l other independent v a r i a b l e s 61 i n c l u d e d i n t h i s s tudy were not s t a t i s t i c a l l y s i g n i f i c a n t . A l t h o u g h seven of the twenty-one independent v a r i a b l e s c o r r e l a t e d s i g n i f i c a n t l y a t the 0.01 l e v e l of c o n f i d e n c e , the h i g h e s t pe rcentages of v a r i a n c e ob ta ined were 39.60 and 38.75 f o r f a t f r e e weight and oxygen i n t ake i n l i t e r s per m in , r e s p e c t i v e l y . Dependent V a r i a b l e PWC170 kpm per min per kg Body  Weight . The c o e f f i c i e n t s of c o r r e l a t i o n of the dependent v a r i a b l e PWC170 kpm per min pe r kg body weight and the i n d e p e n -dent v a r i a b l e s (Xij. . . . . X24) were p resen ted i n Tab le V . Oxygen i n t a k e i n ml per min pe r kg body we igh t , oxygen i n t ake i n ml pe r min pe r kg f a t f r e e weight and body d e n s i t y y i e l d e d c o r r e l a t i o n c o e f f i c i e n t s of O.5617, 0.4199 and 0-5404, r e s p e c t i v e l y , which were s i g n i f i c a n t a t the 0.01 l e v e l of c o n f i d e n c e . Body weight c o r r e l a t e d n e g a t i v e l y ( r = 0.3091) w i th the dependent v a r i a b l e PWC170 kpm per min per kg body weight and was s i g n i f i c a n t a t the 0.05 l e v e l o f c o n f i d e n c e . A l l o the r Independent v a r i a b l e s y i e l d e d i n s i g n i f i c a n t c o r r e l a t i o n c o e f f i c i e n t s . The h i g h e s t percentages of v a r i a n c e were ob ta ined between dependent v a r i a b l e PWC170 kpm per min pe r kg body weight and oxygen i n t ake i n ml pe r kg body weight and body d e n s i t y . These v a l u e s were 31.55 pe r cen t and 29.20 p e r c e n t , r e s p e c t i v e l y . 62 TABLE V ZERO ORDER COEFFICIENTS OF CORRELATION BETWEEN THE DEPENDENT VARIABLE PWC170 KPM PER MIN PER KG BODY WEIGHT AND THE INDEPENDENT VARIABLES (X4 X24) Independent V a r i a b l e C o r r e l a t i o n V a r i a n c e C o e f f i c i e n t r2 x 100 X4 Body weight (kg) -0 .3091* 9.55 X5 Fa t f r e e weight (kg) -0.1216 1.48 X6 V i t a l c a p a c i t y ( l i t e r s ) 0.0117 0.14 X7 Oxygen Intake L pe r min 0.2239 5.01 X8 Oxygen i n t ake ml per min per kg body wt. 0 .5617** 31.55 X9 Oxygen intake ml per min per kg fat free wt. 0 .4199** 17.63 X10 S t r e n g t h ( l b s ) Push -0.2144 4.60 XI1 P u l l -0.1360 I.85 X12 Trunk f l e x i o n -0.0717 0.51 X13 Trunk e x t e n s i o n -0.1867 3.49 X l 4 Knee e x t e n s i o n r i g h t 0.1678 2.82 -X15 Knee e x t e n s i o n l e f t O.0398 0.16 Xl6 Knee e x t e n s i o n average 0.1422 2.02 XI? R ight g r i p -0.1295 1.68 X18 L e f t g r i p -0.1975 3.90 X19 Back -0.1425 2.03 X20 Leg -0.0965 0.93 X21 T o t a l s t r e n g t h ( l b s ) -0.1325 1.76 X22 S t r eng th p e r body weight l b s per kg 0.1696 2.88 X23 Strength per fat free weight lbs pe r kg -0.0528 0.28 X24 Body d e n s i t y (gm per cm3) 0 .5404** 29.20 d f = 52 (N-2) * r ^ 0 .268 ; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.05 l e v e l of c o n f i d e n c e . * * r > 0 .348; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.01 l e v e l of c o n f i d e n c e . 63 Dependent V a r i a b l e PWC170 kpm per min per kg Fat Free  Weight. The c o e f f i c i e n t s of c o r r e l a t i o n between the dependent v a r i a b l e PWC170 kpm per min per kg f a t f r e e weight and the independent v a r i a b l e s (X4 .... Xzk) and t h e i r r e s p e c t i v e percentages of var i a n c e were shown i n Table V I . Oxygen i n t a k e i n ml per kg body weight ( r = 0.4277) and oxygen intake i n ml per kg f a t f r e e weight ( r = 0.4117) c o r r e -l a t e d s i g n i f i c a n t l y w i t h the dependent v a r i a b l e PWC170 kpm per min per kg f a t f r e e weight at the 0.01 l e v e l of confidence. The a n a l y s i s revealed t h a t no other independent v a r i a b l e had a s t a t i s t i c a l l y s i g n i f i c a n t r e l a t i o n s h i p with the dependent v a r i a b l e . 64 TABLE VI ZEHO ORDER COEFF IC I ENTS OF CORRELATION BETWEEN THE DEPENDENT V A R I A B L E P W C 3 7 0 KPM PER MIN PER KG F A T F R E E WEIGHT AND THE INDEPENDENT VAR IABLES (X4 X24) Independent V a r i a b l e C o r r e l a t i o n C o e f f i c i e n t Variance r2 x 100 x4 Body weight (kg) -0.1481 2.19 X5 Fat f r e e weight (kg) -0.0872 0.76 X6 V i t a l c a p a c i t y ( l i t e r s ) 0.0775 0.60 X7 Oxygen int a k e L per min 0.2398 5-75 X8 Oxygen intake ml per min per kg body wt. 0 .4277** 0.4117 18.29 X9 Oxygen intake ml per min per kg fat free wt. 16.95 XIO Strength ( l b s ) Push -0.1439 2.07 X l l P u l l -0.1225 1.50 X12 Trunk f l e x i o n -0.0276 0.76 X13 Trunk extension -0.1156 1.34 X l 4 Knee extension r i g h t 0.1997 3.99 X 1 5 Knee extension l e f t O.0736 5.42 X 1 6 Knee extension average O.I672 2.79 XI? Right g r i p -0.1977 3.91 X18 L e f t g r i p -0.1851 3.43 X19 Back -0.0975 0.95 X20 Leg -0.0762 0.58 X21 T o t a l s t r e n g t h ( l b s ) -0.1079 1.16 X22 Strength per body weight l b s per kg 0.0215 0.46 X23 Strength per fat f r e e weight l b s per kg -O.0536 0.29 X24 Body d e n s i t y (gm per om3) 0.2373 5.63 df = 52 (N-2) * r 5L 0 .268 ; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.05 l e v e l of confidence. ** r > 0.348; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.01 l e v e l of confidence. Independent V a r i a b l e Body Weight. C o r r e l a t i o n s of body weight and other independent v a r i a b l e s . (X5 . . . . X24) and t h e i r r e s p e c t i v e percentages of variance were shown I n Table V I I . 65 TABLE VII ZERO ORDER COEFFICIENTS OF CORRELATION BETWEEN THE INDEPENDENT VARIABLE BODY WEIGHT (KG) AND OTHER INDEPENDENT "\ffiRIABLES (X5 X24) Independent Variable Correlation Variance Coefficient r2 x 100 X5 Fat free body weight (kg) 0 .9202** 84.68 X6 V i t a l capacity ( l i t e r s ) 0.4828** 23.30 X? Oxygen intake L per min 0 .5048** 25.48 X8 Oxygen intake ml per min per kg body wt. -0.5193** 26.97 X9 Oxygen intake ml per min per kg fat free wt. -O .3765** 14.18 X10 Strength (lbs) Push 0 . 6 1 8 1 * * 38.21 X l l P u l l 0 . 3477** 12.09 X12 Trunk f l e x i o n 0 .4155** 17.26 X13 Trunk extension O .6273** 39-35 X14 Knee extension right 0 .3732** 13*93 X15 Knee extension l e f t O .3893** 15.16 X l 6 Knee extension average 0.3177* 10.09 X17 Right grip 0 .2893* 8.37 X18 Left grip 0 .3146* 9.90 XI9 Back 0 .4598** 21.14 X20 Leg 0 .5283** 27.91 X21 Total strength (lbs) 0-5528** 30.56 X22 Strength per body weight lbs per kg - 0 . 4 5 1 3 * * 20.37 X23 Strength per f a t free weight lbs per kg -0.2522 6.36 X24 Body density (gm per cm3) - 0 . 5 0 4 7 * * 25.47 * r ^ 0.268; s t a t i s t i c a l l y s i g n i f i c a n t at the 0.05 l e v e l of confidence. ** r ^ 0.348; s t a t i s t i c a l l y s i g n i f i c a n t at the 0.01 l e v e l of confidence. The above data were extracted from the i n t e r c o r r e l a t i o n matrix to investigate the influence of body weight on a l l other inde-pendent v a r i a b l e s . Three independent variables - knee extension average, right grip strength, and leg grip strength - yielded s i g n i f i -cant c o r r e l a t i o n c o e f f i c i e n t s at the 0.05 l e v e l of confidence. 66 Their respective values were 0 .3177. 0 .2893, and 0 .3146 . Strength per f a t free weight lbs per kg was not correlated s i g n i f i c a n t l y with body weight. A l l other independent v a r i -ables correlated s i g n i f i c a n t l y with the independent variable body weight at the 0.01 l e v e l of confidence. Independent Variable Fat Free Weight. Coefficients of c o r r e l a t i o n between the independent variable f a t free weight and other independent variables (X6 • • • • %Zk)» together with t h e i r respective percentages of variance, were presented i n Table VIII. The data was extracted from the i n t e r c o r r e l a t l o n matrix to Investigate the influence of f a t free weight on a l l other independent varia b l e s . The s t a t i s t i c a l relationships between l e f t grip strength (r = 0 .3350 ) , strength per body weight lbs per kg (r = -O.3266) and strength per f a t free weight (r = -0.2939) with f a t free weight were s i g n i f i c a n t at the 0.05 l e v e l of confidence. A l l other independent variables were s i g n i f i c a n t at the 0.01 l e v e l of confidence except body density which yielded a non-s i g n i f i c a n t negative c o r r e l a t i o n of 0 .1621 . 67 TABLE VIII ZERO OBDEE COEFFICIENTS OF CORRELATION BETWEEN THE INDEPENDENT VARIABLE FAT FREE WEIGHT (KG) AND OTHER INDEPENDENT VARIABLES (X6 X24) Independent V a r i a b l e Correlation C o e f f i c i e n t Variance r2 x 100 X 6 V i t a l c a p a c i t y ( l i t e r s ) X 7 Oxygen intake L per min X8 Oxygen Intake ml per min per kg body wt. X 9 Oxygen intake ml per min per kg fat free wt. XIO Strength ( l b s . ) Push X l l P u l l X12 Trunk f l e x i o n XI3 Trunk extension X l 4 Knee extension r i g h t X15 Knee extension l e f t X l 6 Knee extension average X17 Right g r i p X18 L e f t g r i p X19 Back X20 Leg X21 T o t a l s t r e n g t h ( l b s ) X22 Strength per body weight l b s per kg X23 Strength per fat free weight l b s per kg X24 Body d e n s i t y (gm per cm3) 0 .5015** 0 . 5 9 7 3 * ; -0.3639 -0.3600** 0 .5898** 0.3740** 0 .4161* * 0 .6225** 0 .4223** 0 .4180** 0 .3624** O .3850** 0 .3350* 0 .4679** 0 . 5 7 0 1 * * 0 .5919* * -0.3266* -0.2939* -0.1621 25.15 35-68 13.24 12.96 34.20 13.99 17.31 38.75 17.83 17.47 13.13 14.82 11.22 21.89 32.50 35.03 10.67 8.64 2.63 df = 52 (N-2) * r £ 0.268; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.05 l e v e l of confidence. r £ 0.348; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.01 l e v e l of confidence. Normality of the D i s t r i b u t i o n of Scores Histograms of a l l the v a r i a b l e s were drawn i n order to determine the forms of the d i s t r i b u t i o n s . This was considered to be e s p e c i a l l y important i n the case of r a t i o v a r i a b l e s , i . e . , PWC170 kpm per min or str e n g t h d i v i d e d by body weight or f a t f r e e weight. The histograms were included i n Figures 1 t o 24. 68 18 16 14 OT »-o 12 ~> C D OT O or U J m 2 8 -6 -4 -2 -0 x, P W C 1 7 0 O O O O o C M C M C M C M C M » in 5 io w l l l l 0 o o C M C M C M O O C O 1 I I C M C M C M C M C M C M C M C M C M • i n * w « - O 0 ) O s 18 16 14 to &2 UJ CD ^10 OT L L s « ui m 5 6 Z x 2 P W C 1 7 0 m o m o i p o m o i n O O l C O O O ^ N C D t D i o c j S c o N ^ i n ^ r o w ^ : kpm per min Fig. I kpm permin per kg Body Weight Fig. 2 18 16 14 OT h-o UJ -3 m z> OT U. O Ct UI C D 5 Z 12 10 x 3 P W C | 7 0 o Q o o o o o o o Q Q o q o o o o o c x j ° c r i c D N ( r j i £ } 5 ; r o i_!__j_J_l±±±± P o q o o O o o q kpm per min per kg Fat Free Weight 18 16 14 ol2 ui C O r> 10 OT L L £ 8 UJ ca § 6 z BODY WEIGHT If) o 11 — o If) o 0 o 1 I — I D O cn IO O If) o If) O If) O cn cn i oo co N CD | CO 1 CD CO 1 CD CO cn CO co N CD CD If) kg Fig. 3 Fig.4 NUMBER OF SUBJECTS 5.1.1 -5.40 4.81-5.10 4.51-4.80 4.21-4.50 3.91-4.20 3.61-3.90 3.31-3.60 3.01 -3.3 0 2.71-3.00 i — i — r ~r~ 0) -T— CO - r - o " T -ro T — i — r - r - ci co i—r x o i x -< J o m 2 > m 64.01-6700 61.01-64.00 58.01-61.00 55.01-58.00 52.01-55.00 49.01-52.00 46.01-49.00 43.01-46.00 40.01-43.00 3 7.01-40.00 IN) - l — i — r NUMBER 0FJ3UBJECTS CD co O ro A 0) "T CO T—r X CO o X •< o m z > NUMBER OF SUBJECTS 2! oi 92.01-95.50 88.51-92.00 85.01-88.50 81.51-85.00 78.01-81.50 74.51-78.00 71.01-74.50 67.51-71.00 64.01-6750 60.57-64.00 57.01-60.50 53.51-57.00 50.01-53.50 6.31-6.60 6.01-6.30 5.71-6.00 5.41-5.70 31 r- 5.1 1-5.40 —* <D —* 4.81-5.10 0 4.51-4.80 4.21-4.50 3.91-4.20 3.61-3.90 3.31-3.60 ro -r~ co o 0) i—1—r co X U I •tl > n 33 m m $ m o x H ro NUMBER OF SUBJECTS * oi 00 o ro T 01 1 r 1—1—1—1—1—1—1—m—r co X 0) > r o > o ON vO 18 -16 14 -UJ -3 m => 10 CO u. o or tn m 2 8 6 -X 9 OXYGEN INTAKE n . — O O n O O O O O °°. OOOOmOQOOCQOQCPco O N * " <D in (M 01 (J [ij N CO to <r> IT) IT) \T> * j _ I I J . — — ± — — JL co oq 55 co oo <o oo °°. oq oo S —' cd iri <\j ci co ro' o co co CD io in in * * ^ * 70 co \-o UJ -3 CQ 3 CO u. o cc LU m 5 3 z 18 16 14 12 10 X | Q PUSH STRENGTH (C S (O 01 O — CM ro in in * to io OJ — o i I i -1 i i • i l B f l l O - N l O * i n i n in v- to CM - o oi oo ml per min per kg Faf Free Weight Fig. 9 lbs Fig. 10 18 16 -14 -L J 12 0Q w IO u. o 0T 8 LU CQ 5 6 3 XM PULL STRENGTH n O <t 00 ro CM — T i , m m ro CM CM CD - O O O I I ' N — in o o * 00 CM CO 0) co oo r> i i i I cn ro s ff) CD CO S 18 16 14 LU 12 -5 CD 3 to LL O cr ui CD s 3 Z 10 8 -6 -2 -X | 2 TRUNK FLEXION o i n 0 m o ino.m o m ^ CM — cn co t o w r o CM o CM CM CM I I I I I tO — CD — CD — CO — CO — CM — O) 00 CO lOrOcM O CT> CM CM co lbs lbs Fig. II Fig.12 71 X | 3TRUNK EXTENSION r CO CO <tf S in K I CM CM CM I * I N tf) tO in ro CM CM CM O co 0) <D CD <r CM — Cl I I CO r-co CM O CO 18 16 14 o w 12 CD co 10 U. o cc 8 LU m 2 6 z> z X.. RIGHT KNEE EXTENSION 14 CM in O m O Ct r> • t f 1 ro ro i ro i t CO 1 00 N CM ro to to I I CD — t N 0 in o m S * N 81 CM CM CM — 1 • I 1 CD — CO O i f W ffl N CM CM lbs Fig.13 lbs Fig. 14 X LEFT KNEE EXTENSION io n t u n . CM <J) CD to O r-CM o N in to o 00 CO | ro 1 to 1 to • to 1 to CM CM O N i CO in CM 1 0) o S in ro o CO CO IO ro ro ro ro CM CM CM co m _ r-3 N » 2 I I I I CO CM 00 — cn co * CM — — — 18 16 14 12 o LU -3 CD co 10 LL O oc 8 LU CO X . „ AVERAGE KNEE EXTENSION JJ o CO CD CM O CO 0) CD CM O 00 in ro to ro to 1 to CM CM 1 o> 1 N in ro Ct N CD CM o oo in ro ro to ro to CM CM CM m to — a lbs lbs Fig. 15 Fig. 16 CO H o LU -3 CD 3 CO u. o cc UJ CD 3 z 18 16 14 12 -I 0 -2 0 X | 7 RIGHT GRIP t L N M f CO N CD IO IO CD * ro T 1 I • i I i o * i n c D N a ) f f l o _ s c o m ^ r o N - r l o CM ® o o I 72 I8r 16 -14 CO K ° 1 9 LU 12 CD CO 10 u. o cc 8 LU CO 2 6 3 Z X | 8 LEFT GRIP m n Tt- co m O CM * co oo o W M o i n i o * M w - - o 7 7 T • ' • i i i i (o — ro i n N cn _ to i n co i n m * Ki CM - — o o lbs lbs Fig. 17 Fig. 18 18 16 14 co i-o LU 12 "3 CD 3 CO u. o cc LU CD 2 3 10 8 -2 O X | 9 BACK STRENGTH * o r> rj-<o co o co !> CO m IO i o i n m in co CM oo o CD co CD i n i n i | i n | i co CD co co CD CD CM 00 it- o CD CM CO i n i n i n lbs i n i o CM CO \t- ro i i CO CD CO fO ro ro t o 18 16 14 O LU |2 -3 CO co 10 L L O CC LU CD 5 3 Z 8 -X 2 Q LEG STRENGTH r o o o o o o o o o o r o s r t o c o N o o c n O — CM c D i n ^ r o c M — O O c n o o I I I I I 1 1 1 J . J . J l n f f l N c o o i o - CM ro i n ^ ro CM — o o cn oo N I bs F i g . 19 F ig . 2 0 CO o UJ ~3 CO r> co U. O or ui CO D z 18 16 14 12 10 X 2 | TOTAL STRENGTH O in eg cn lo t o — oo in ro cv — m m CM CM CM eg 22 2 i i i 1 > i O CM ^ CO 00 O co in CM cn m Tt-ro CM — 0) CO N CM CM CM — N «> * CO I i <fr CO co in * ro 73 18 16 14 h co k-o lu 12 --3 CO io 10 u. cc UJ m Z 8 4 -2 -X22T0TAL STRENGH PER BODY WEIGHT D O O O o O o O O O O o o O O c n ^ c n ^ c n s j - c n ^ c n f . cn * oi <j-to 2; ro ro CM CM z: ~ 2 2 cri cn oo' co' i i i i i i i i • i i • i • ^0) ,l:Cr>^J;CJ)^}-C') ,l; 0)^0)^-0) ^ ro" ro CM CM — — O d cri cri co' co' K lbs Fig. 21 lbs per kg Fig. 22 co 18 16 14 , X23T0TAL STRENGTH PER FAT FREE WEIGHT S "2 ~3 CO 3 io CO u. o cc LU CO 5 D Z * C 0 C M « j O ^ - C 0 C M < 0 in O co — r--cM r~ ro co in in * sj; !2!2 £ J CM co ro [v. — m e n « s _ m cn ro 0) 2 CM 00 o - n in ^ cn * d 2 O CO — N N S in * ' •'J1 ro ro CM ro oo TJ-CM* — — d d 18 16 14 co S l 2 - 3 CD 3'° LL ° 8 CC UI CO 2 6 Z O 2 o i cn i i in— co cn cn co X 2 4 BODY DENSITY D •L o m o u T o m o 1 0 0 "P. ° o C n c n c o c o N N C D c Q i n t n i r Q Q o O Q O Q O — Q U Q M q O O ( D i ( l ) J . ( | ) i ( l ) i ( | ) - CO c n c n o o c o r - f ^ c o c O m i n ^ o o o o o o o o o o o Q Q lbs per kg gm per cm-Fig. 23 Fig. 24 74 F i r s t Order Correlation Analysis Two f i r s t order c o r r e l a t i o n matrices of the twenty-four variables investigated i n th i s study were obtained through the University of B r i t i s h Columbia Computing Center and are presen-ted i n Appendix C. The c o e f f i c i e n t s of co r r e l a t i o n of the variables most pertinent to the analysis of the data have been extracted from the aforementioned i n t e r c o r r e l a t l o n matrices and were presented i n Tables IX and X. Variances between the variables were also included. Dependent Variable PWC170 kpm per min with the Ef f e c t of  Body Weight Held Constant. The independent variable, body weight, was s t a t i s t i c a l l y held constant i n an attempt to e l i m i -nate the influence of body size on the PWC170 k P m P e r m i n score. Correlation c o e f f i c i e n t s between the dependent variable PWG170 kpm P e r m l n a n ( 3- tbe independent variables (X5 .... X24) were included i n Table IX. Fat free weight (r = 0.4430), oxygen intake l i t e r s per min (r = 0.4872), oxygen intake ml per min per kg body weight (r = 0.5138), oxygen Intake ml per min per kg f a t free weight (r = O.3675) and body density (r = 0.4681) correlated s i g n i f i -cantly with PWC170 kpm per min at the 0.01 l e v e l of confidence. Right knee extension and knee extension average yielded corre-l a t i o n c o e f f i c i e n t s of 0.3388 and 0.2842, respectively, and were s i g n i f i c a n t at the 0 .05 l e v e l of confidence. A l l other 75 TABLE IX FIRST ORDER COEFFICIENTS OF CORRELATION BETWEEN DEPENDENT VARIABLE PWC170 KPM PER MIN AND OTHER INDEPENDENT VARIABLES WITH BODY WEIGHT HELD CONSTANT Independent V a r i a b l e 1 C o r r e l a t i o n Va r i ance C o e f f i c i e n t r 2 x 100 X5 Fa t f r e e weight (kg) 0 .4430** 19.63 X6 V i t a l c a p a c i t y ( l i t e r s ) 0.2096 4.39 X7 Oxygen i n t ake L i t e r s pe r min 0 .4872** 23.74 X8 Oxygen Intake ml per min per kg body wt . 0 .5138** 0 .3675** 26.40 X9 Oxygen intake ml per min per kg fat free wt. 13.51 XIO S t r e n g t h ( l b s ) Push -0.0176 0.06 X l l P u l l 0.0135 0.02 XI2 Trunk f l e x i o n 0.1111 1.23 X13 Trunk e x t e n s i o n 0.0170 0.03 X l 4 Knee e x t e n s i o n r i g h t 0 .3388* 11.48 X15 Knee e x t e n s i o n l e f t 0.2010 4 .04 XI6 Knee e x t e n s i o n average 0 .2842* 8.08 X17 R igh t g r i p -0.0336 0.11 X18 L e f t g r i p -0.0821 0.67 X19 Back 0.0338 0.11 X20 Leg 0.0841 0.71 X21 T o t a l s t r e n g t h ( l b s ) 0.0627 0.39 X22 S t r e n g t h per body weight l b s per kg 0.0399 0.16 X23 S t r e n g t h per fa t f r e e weight l b s pe r kg Body d e n s i t y (gm per cm5) -0.1343 1.80 X24 0 . 4 6 8 1 * * 21.91 d f = 51 (N-3) * r ^ 0 .271 ; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.05 l e v e l o f c o n f i d e n c e . r 2 0 .351; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.01 l e v e l of c o n f i d e n c e . Independent v a r i a b l e s r e v e a l e d no s i g n i f i c a n t r e l a t i o n s h i p w i th PWC170 kpm per m in . Dependent V a r i a b l e PWC170 kpm per min w i t h the E f f e c t of F a t F r e e Weight He ld Cons t an t . The independent v a r i a b l e , f a t f r e e we igh t , was s t a t i s t i c a l l y he l d cons tan t f o r the same 76 r eason as p r e v i o u s l y s t a t e d , i . e . , i n an at tempt to e l i m i n a t e the i n f l u e n c e of "body s i z e on the PWC170 s c o r e . C o r r e l a t i o n c o e f f i c i e n c y between the dependent v a r i a b l e PWC170 kpm per min and the independent v a r i a b l e s (Xg • — X24) were i n c l u d e d i n Tab le X . TABLE X FIRST ORDER COEFFICIENTS OF CORRELATION BETWEEN DEPENDENT VARIABLE PWC170 KPM PER MIN AND OTHER INDEPENDENT VARIABLES WITH FAT FREE WEIGHT HELD CONSTANT Independent V a r i a b l e C o r r e l a t i o n V a r i a n c e C o e f f i c i e n t r 2 x 100 X6 V i t a l c a p a c i t y ( l i t e r s ) 0.1391 1.93 X7 Oxygen Intake L i t e r s per min 0 .3956** 15.65 X8 Oxygen Intake ml per min per kg body wt. 0.4579 20.97 X9 Oxygen intake ml per min per kg fat free wt. 0 .4410** 19.45 X10 S t r e n g t h ( l b s ) Push -0.0949 0.90 X l l P u l l -0.0591 O.35 XI2 Trunk f l e x i o n 0.0590 0.35 X13 Trunk e x t e n s i o n -0.0857 0.73 X14 Knee e x t e n s i o n r i g h t 0 .2803* 7.86 X15 Knee e x t e n s i o n l e f t 0.1394 1 .94 X l 6 Knee e x t e n s i o n average O.2317 5*37 X17 R igh t g r i p -0.1649 2.72 X18 L e f t g r i p -0.1538 2.37 X19 Back -0.0411 0.17 X20 . Leg -O.O336 0.11 X21 T o t a l s t r e n g t h ( l b s ) -0.0618 O.38 X22 S t r e n g t h pe r body weight l b s per kg -0.0003 0.00 X23 Strength pe r f a t f r e e weight lbs pe r kg -0.0785 0.62 X24 Body d e n s i t y (gm per cm3) 0.2374 5.64 d f = 51 (N-3) * r > 0.271; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.05 l e v e l of c o n f i d e n c e . * * r 2 0.351; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.01 l e v e l of c o n f i d e n c e . 77 Once again oxygen intake l i t e r s per min ( r = 0.3956), oxygen intake ml per min per kg body weight ( r = 0.4-579) and oxygen intake ml per min per kg f a t f r e e weight ( r = 0.4410) c o r r e l a t e d s i g n i f i c a n t l y w i t h PWC170 kpm P e r m i n a t the 0-01 l e v e l of confidence. One independent v a r i a b l e , r i g h t knee extension, y i e l d e d a s t a t i s t i c a l l y s i g n i f i c a n t c o r r e l a t i o n a t the 0 .05 l e v e l of confidence of 0.2803. A l l other v a r i a b l e s revealed n o n - s l g n i f l e a n t r e l a t i o n s h i p s w i t h PWC170 kpm per min. Twenty-Second Order C o r r e l a t i o n A n a l y s i s A twenty-second order i n t e r c o r r e l a t l o n matrix was a l s o obtained to assess the i n t e r r e l a t i o n s h i p s between PWC170 kpm per min and each independent v a r i a b l e while a l l other v a r i a b l e s were h e l d constant. The r e s p e c t i v e c o r r e l a t i o n c o e f f i c i e n t s were included i n Table X I . When a l l but two v a r i a b l e s were held constant, no v a r i a b l e revealed a s t a t i s t i c a l l y s i g n i f i c a n t r e l a t i o n s h i p a t the 0.01 l e v e l of confidence w i t h PWC170 kpm per min. Four v a r i a b l e s y i e l d e d c o r r e l a t i o n c o e f f i c i e n t s which were s i g n i f i -cant a t the 0 .05 l e v e l of confidence: f a t f r e e weight ( r = 0.4414), trunk f l e x i o n ( r = 0 . 4393 ) , trunk extension ( r = -0.3544) and r i g h t knee extension ( r = 0.3571). A l l other v a r i a b l e s were not s i g n i f i c a n t l y r e l a t e d to PWC170 kpm per min. 78 TABLE XI TWENTY-SECOND ORDER COEFFICIENTS OF CORRELATION BETWEEN DEPENDENT VARIABLE PWC170 KPM PER MIN AND EACH INDEPENDENT VARIABLE WITH ALL OTHER VARIABLES HELD CONSTANT Independent V a r i a b l e s 1 C o r r e l a t i o n V a r i a n c e C o e f f i c i e n t r2 x 100 X4 Body weight (kg) 0.0827 0.68 X5 Fa t f r e e weight (kg) 0.4414* 19.48 X6 V i t a l c a p a c i t y ( l i t e r s ) -0.1341 1.79 X7 Oxygen i n t ake L i t e r s pe r min 0.0511 0.26 X8 Oxygen intake ml per min per kg body wt. -0.2038 4.15 X9 Oxygen Intake ml per min per kg fat free wt. 0.2223 4 .94 XIO S t r eng th ( l b s ) Push 0.1022 1.04 X l l P u l l 0.2409 5.80 XI2 Trunk f l e x i o n 0 .4393* 19.30 XI3 Trunk e x t e n s i o n -0 .3544* 12.56 X l 4 Knee e x t e n s i o n r i g h t 0 .3571* 12.75 X15 Knee e x t e n s i o n l e f t 0.1912 3.66 X16 Knee e x t e n s i o n average -0.3414 11.66 X17 R igh t g r i p -0.0249 0.06 X18 L e f t g r i p 0.0831 0.69 X19 Back 0.1632 2.66 X20 Leg 0.0339 0.11 X21 T o t a l s t r e n g t h ( l b s ) 0.000 0.00 X22 S t r e n g t h pe r body weight l b s pe r kg -0.0235 0.06 X23 Strength per fat f ree weight l b s pe r kg -0.0411 0.17 X24 Body d e n s i t y (gm per cm3) 0.2942 8.66 d f = 30 (N-24) * r ^ 0 .349 ; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.05 l e v e l o f c o n f i d e n c e . *« r 2 0 .449 ; s t a t i s t i c a l l y s i g n i f i c a n t a t the 0.01 l e v e l of c o n f i d e n c e . 79 Stepwise Multiple Regression Analysis The stepwise multiple regression analysis technique was employed to assess the interrelationships of two or more inde-pendent variables with each of the dependent variables: 1. PWC170 kpm per min, 2. PWC170 kpm per min per kg body weight, 3. PWC170 kpm per min per kg f a t free weight. The r e s u l t s of the stepwise multiple regression analysis were obtained through the University of B r i t i s h Columbia Computing Center - TRIP Program - and have been presented i n Tables XII, XIII, XIV, XV, XVI, and XVII. Although twenty-one Independent variables were i n t r o -duced into the multiple regression analysis, only the f i r s t three pre d i c t i o n equations developed by computer f o r each dependent variable were selected and employed i n t h i s study. The reason being that: . . . inc l u s i o n of other variables into the regression equations would r e s u l t i n a greater range of predic t i o n error caused by increasing standard error of estimate and by an Increasing error mean square i n the analysis of variance of the independent varia b l e s . (3:57-58) Dependent Variable PWC170 kpm per min. The stepwise i n c l u s i o n of the variables f a t free weight, oxygen intake ml per min per kg body weight and ri g h t knee extension were included i n Table XII. The order of sel e c t i o n was i n accor-dance with t h e i r contribution to the variance of the dependent variable PWC170 kpm per min. TABLE XII STEPWISE MULTIPLE REGRESSION ANALYSIS V/ITH PWC-,70 KPM PER MIN AS THE DEPENDENT VARIABLE ' Variable b Coefficient Standard Error PJJatLo P-Probabili1y of b R2 R Standard Error of Y P-Probability of R 2 Step I Constant 1.5295 1.7078 Pat free weight (kg) 0.1433 0.0245 34.09^0 0.0000 0.3960 0.630 1.4657 0.0000 Step II Constant -6.1652 2.2237 Pat free weight (kg) 0.1750 0.0237 54.7205 0.0000 Oxygen intake ml per min per kg body weight 0.1107 0.0301 13.5318 0 .0007 0.5227 0.733 1.3157 0.0000 StepHE Constant -6.6108 2.75^0 Pat free weight (kg) 0.1533 0.0253 36.7520 0.0000 Oxygen intake ml per min per kg body weight 0.1062 0.0293 13.1579 0.0008 Right knee extension 0.0078 0.0038 4.1687 0.0441 0.5594 0.746 1.2767 0.0000 81 The r e s u l t a n t equa t ions s e l e c t e d f o r the p r e d i c t i o n of performance on the b i c y c l e ergometer a t a h e a r t r a t e of 170 beats pe r minute were: 1 « 0.1433 X5 + 1.5295 2 = 0.1750 X5 + 0.1107 X8 - 6.1652 3 = 0.1533 X5 + 0.1062 X8 + 0.0078 X14 - 6.6108 Where: X5 = F a t f r e e we igh t . X s = Oxygen i n t ake ml pe r min pe r kg body we igh t . x l 4 = R igh t knee e x t e n s i o n . The b c o e f f i c i e n t s , s t andard e r r o r s , F - r a t i o s , F p r o b a b i l i t y of b, m u l t i p l e R 2 , m u l t i p l e R , s t andard e r r o r of Y and the F p r o b a b i l i t y o f m u l t i p l e R 2 were a l s o i n c l u d e d In Tab le XI I f o r each s u c c e s s i v e s t e p . The b c o e f f i c i e n t s , o r op t ima l we igh t s , a re the m u l t i -p l y i n g cons t an t s or we ights f o r the independent v a r i a b l e s and I n d i c a t e d the u n i t i n c r e a s e of the dependent v a r i a b l e PWC170 kpm pe r min f o r every u n i t i n c r e a s e of the independent v a r i -a b l e s i n c l u d e d i n the r e g r e s s i o n e q u a t i o n s . In s i m p l e r te rms , the b c o e f f i c i e n t s i n d i c a t e the s l o p e of the r e g r e s s i o n l i n e ( 4 : 4 2 8 ) . The s t anda rd e r r o r of es t imate i n d i c a t e s the d e v i a -t i o n between the a c t u a l and p r e d i c t e d v a l u e s and was i n c l u d e d f o r both the b c o e f f i c i e n t s and the r e g r e s s i o n e q u a t i o n s . The F- tes t was per formed to t e s t the s i g n i f i c a n c e of the r e g r e s s i o n c o e f f i c i e n t b and the p r o b a b i l i t y a s s o c i a t e d w i t h t h i s v a l ue 82 was also included. F-probability i s the p r o b a b i l i t y of obtain-ing a F value greater than or equal to the one calculated (1 :33) (see Appendix A). In the present study, the F proba-b i l i t i e s associated with the prediction of the independent variable PWC170 kpm per min were less than 0.05 and therefore a l l the b c o e f f i c i e n t s were accepted as s i g n i f i c a n t l y d i f f e r e n t from zero. The c o e f f i c i e n t of multiple determination, R2. was also calculated. R 2 i s the proportion of the t o t a l observed v a r i -ance of Y which i s accounted f o r by the regression l i n e (see Appendix A). As seen i n Table XII, the in c l u s i o n of a l l three independent variables resulted i n a variance of 0 .5594 . Variance due to error was 0 .4406 . The F p r o b a b i l i t i e s of R 2 were 0.0000 l n a l l cases, thus, s i g n i f i c a n t l y d i f f e r e n t from zero. The posi t i v e square root of R2, c a l l e d the c o e f f i c i e n t of multiple c o r r e l a t i o n , which indicates the c o r r e l a t i o n between the predicted and obtained PWC170 kpm Pe** m l n scores, were also presented i n Table XII. An analysis of variance technique was employed to assess the r e l a t i v e contribution of the independent variables included i n each of the three regression equations. The sum of squares, mean of squares and percentage of variance were presented i n Table XIII. 83 TABLE XIII VARIANCE OF THE MULTIPLE REGRESSION OF THE DEPENDENT VARIABLE PWC 1 7 0 KPM PER MIN Srim of Mean of Percentage of Squares Variance r^xlOO Step I Due to Regression 1 0.7346 Due to Fat Free Weight 1 0.7346 Due to Error 52 1.1204 Tota l Variance 1.8550 0.7346 0.7346 .0215 1.8550 39.60 39.60 60.40 100.00 Step II Due to Regression 2 O.9696 0.4848 52.27 Dae to Fat Free Weight 1 0.7965 0.7965 42.88 Due to Oxygen Intake ml per min per kg O.0698 Body Weight 1 O.O698 9.39 Due to Error 51 1.8854 0.0174 47.73 Tota l Variance 1 1.8550 1.8550 100.00 Step III Due to Regression 3 1.0377 0.3444 55.94 Dae to Fat Free Weight 1 0.7858 O.7858 42.35 Due to Oxygen Intake ml per min per kg Body Weight 1 0.0182 0.0182 3.77 Due to Right Knee Extension 1 0.0699 0.0699 9.82 Due to Error 50 0.8173 O.OI63 44.06 Total Variance 1 1.8550 1.8550 100.00 84 The p a r t i a l regression c o e f f i c i e n t , b, were converted to standard p a r t i a l regression c o e f f i c i e n t , B, through the D o l i t t l e - solut i o n Operations (4:442-444) (see Appendix A). Percentage of variance due to independent variable f a t free weight was 39«6o percent and the variance due to error was 60.40 percent. The contribution of f a t free weight increased to 42.88 percent upon the addition of the independent variable oxygen intake ml per min per kg body weight which contributed 9.39 percent variance. In the f i n a l step, with the in c l u s i o n of rig h t knee extension, the variance due to regression was 55*94 percent. Variance due to error was 44.06 percent. Dependent Variable PWC170 kpm per min per kg Body  Weight. The dependent variable PWG170 kpm per min was divided by body weight to attempt to control the influence of body size on the PWC170 kpm per min score. The independent variables contributing to the variance of dependent variable PWC170 kpm per min per kg body weight were presented i n Table XIV. The independent variables oxygen intake ml per min per kg body weight, body density and right knee extension appeared i n the stepwise multiple regression analysis. The regression equations u t i l i z e d f o r the prediction of physical working capacity expressed as PWC170 kpm per mm per kg body weight were: TABLE XIV STEPWISE MULTIPLE REGRESSION ANALYSIS WITH P W C ™ KPM PER MIN PER KG BODY WEIGHT AS THE DEPENDENT VARIABLE V a r i a b l e Coefeksient Standard E r r o r P-Ratio F-Prdbability of b R2 R Standard E r r o r ^-Probability of Y of R 2 Step I Constant 5.8236 2.3268 Oxygen i n t a k e ml per min per kg body weight 0.1873 0.0383 23.9666 0.0000 0.3155 O.565 1.7964 0.0000 Step I I Constant -63.3430 24.8222 Oxygen i n t a k e ml per min per kg body weight 0.1315 0.0406 10.4922 0.0022 Body d e n s i t y 66.7442 22.9511 8.4570 0.0054 0.4129 0.651 1.6800 0.0000 Step HI Constant -60.9332 2 9.1605 Oxygen i n t a k e ml per min per kg body weight 0.1382 0.0394 12.2921 0.0011 Right knee extension - 0.0093 0.0044 4.4240 0.0384 Body d e n s i t y 66.5909 22.2176 8.9833 0.0043 04606 0.676 1.6263 0.0000 86 1 = 0.1873 X8 + 5.8236 2 = 0.1315 Xg + 66.7442 X 2 4 - 63.3430 3 = 0.1382 X 8 + 66.5909 X2/4 - 0.0093 X l i L - 60.9332 Where: Xg = Oxygen intake ml per mm per kg "body weight. x24 = B o d y density. XiAj. = Right knee extension. The F pr o b a b i l i t y of the b c o e f f i c i e n t s were 0.0011, 0.0384, and 0.0043 f o r each of the three independent variables, respectively, and were, therefore, accepted as s i g n i f i c a n t l y d i f f e r e n t from zero. The portions of variance due to regression, R.2, were 0«3155» 0.4129, and 0.4606 f o r the regression equations i n the analy s i s . The F p r o b a b i l i t i e s of R2 were 0.0000 and conse-quently, s i g n i f i c a n t at the 0.05 l e v e l of confidence. An analysis of variance technique was u t i l i z e d to assess the contribution of the independent variables i n the regression equations to the variance of the dependent variable PWC170 kpm per min per kg body weight. The respective variance due to each independent variable, variance due to three independent variables and variance due to error were presented i n Table XV. The variance due to regression when a l l three independent variables were included was 46.06 percent. Oxygen intake ml per min per kg body weight contributed 23.25 percent to the variance of the dependent v a r i a b l e . Although f a t free weight 87 TABLE XV VARIANCE OF THE MULTIPLE REGRESSION OF THE DEPENDENT VARIABLE PWC170 KPM PER MIN PER KG BODY WEIGHT Sum of Mean of Percentage of Source of Variance df Squares Squares Varlancer* xlOO Step I Due to Regression 1 0.5853 0.5853 31.55 Due to Oxygen In-take ml per min per kg Body Weight 1 0.5853 0.5853 31.55 Due to Error 52 1.2697 0.0244 68.45 Total Variance 1 1.8550 1.8550 100.00 Step II Due to Regression 2 0.7659 O.3827 41.29 Due to Oxygen In-take ml per min per kg Body Weight 1 0.4109 0.4109 22.15 Due to Body Density 1 0.3549 0.3549 19.14 Due to Error 51 1.089 0.0214 58.71 Tota l Variance 1 1.8550 1.8550 100.00 Step III Due to Regression 3 .8544 .2826 46.06 Due to Oxygen In-take ml per min per kg Body Weight 1 0.4313 0.4313 23.25 Due to Body Density 1 0.3547 0.3547 19.12 Due to Right Knee Extension 1 0.0684 0.0684 3.69 Due to Error 50 1.001 0.020 53.94 Total Variance 1 1.8550 1.8550 100.00 88 did not appear i n the second regression analysis, body density, i . e . , r e l a t i v e leaness or fatness, contributed 19.12 percent. Variance due to ri g h t knee extension was 3*69 percent and regression due to error was 53*94 percent. Dependent Variable PWC170 kpm per min per kg Fat Free  Weight. A t h i r d stepwise multiple regression analysis was conducted to investigate the eff e c t of c o n t r o l l i n g f a t free weight by expressing the score of the Sjostrand test as PWC170 kpm per min per kg f a t free weight. Three independent variables appeared i n the following regression equations: 1 = 0.1330 X8 + 9.9671 2 = 0.1397 X8 - 0.0095 Xlk + 12.2661 3 = 0.1332 X8 - 0.0095 X14 + 7.8037 X24 + 4.1179 Where: XQ - Oxygen intake ml per min per kg body weight. X14. = Right knee extension. X24 = Body density. The c o e f f i c i e n t of multiple determination, R2, and the associated p r o b a b i l i t i e s were presented i n Table XVI. The F pr o b a b i l i t y of b c o e f f i c i e n t s were 0 .0037, 0 .0549, and 0.7470 f o r the three Independent variables, respectively. The l a t t e r two p r o b a b i l i t i e s were not s i g n i f i c a n t at the 0.05 l e v e l of confidence. The portions of variance due to regression were 0 .1829, TABLE XVI STEPWISE MULTIPLE REGRESSION ANALYSIS WITH PWC 1 7 0 KPM PER MIN PER KG PAT FREE WEIGHT AS THE DEPENDENT VARIABLE Variable b Coefficient Standard Error P-Ratio P-Probablli1y of b R 2 R Standard Error P-^obability of R2 Step I Constant 9.9671 2.3704 Oxygen intake ml per min per kg body weight 0.1330 0.0390 11.6427 0.0014 0.1829 0.428 1.8300 0.0014 Step II Constant 12.2661 3.3535 Oxygen intake ml per min per kg body weight 0.1397 0.0381 13.4474 0.0007 Right knee extension - 0.0095 0.0048 3.8437 0.0526 0.2402 0.490 1.7819 0.0010 Step HI Constant 4.1179 26.7098 Oxygen intake ml per min per kg body weight 0.1332 0.0436 9.3389 0.0037 Right knee extension - 0.095 0.0049 3.7718 0.0549 Body density 7.8037 24.5618 0.1009 0.7470 0.2417 0.492 1.7979 0.0031 90 0 .2402, and 0.241? f o r each of the r e g r e s s i o n equa t ions i n c l u d e d i n t h i s a n a l y s i s . The F p r o b a b i l i t i e s of R 2 were 0 .0014, 0 .0010, and 0 .0031. r e s p e c t i v e l y and were accep ted as be ing s i g n i f i c a n t a t the 0.05 l e v e l of c o n f i d e n c e . An a n a l y s i s o f v a r i a n c e techn ique was used to determine the c o n t r i b u t i o n of the independent v a r i a b l e s to the v a r i a n c e of the dependent v a r i a b l e PWC-J^Q kpm per min pe r kg f a t f r e e we igh t . These r e s u l t s were p resen ted i n Tab le XV I I . In the f i n a l r e g r e s s i o n e q u a t i o n , the v a r i a n c e due to r e g r e s s i o n was 24.17 p e r c e n t . Oxygen i n t a k e ml pe r min per kg body weight c o n t r i b u t e d 18.31 p e r c e n t . R igh t knee e x t e n s i o n added 4.80 pe r cen t and i n c r e a s e d the v a r i a n c e due t o r e g r e s s i o n to 23.11 p e r c e n t . Body d e n s i t y c o n t r i b u t e d a min ima l 1.06 p e r c e n t . The v a r i a n c e due t o e r r o r was 75*63 p e r c e n t . 91 TABLE XVII VARIANCE OF THE MULTIPLE REGRESSION OF THE DEPENDENT VARIABLE PWC.170 KPM PER MIN PER KG FAT FREE WEIGHT Source of Variance df Sum of Squares Mean of Squares Percentage of Valance r^xlOO Step I Due to Regression 1 0.3393 0.3393 18.29 Due to Oxygen In-take ml per min per kg Body Weight 0.3393 0.3393 18.29 Due to Error 52 1.5157 0.0292 81.71 To t a l Variance 1 1.8550 1.8550 100.00 Step II Due to Regression 2 0.4456 0.2228 24.02 Due to Oxygen In-take ml per min per kg Body Weight 1 0.3364 0.3364 17.66 Due to Right Knee Extension 1 0.0798 0.0798 3.24 Due to Error 51 1.4094 0.0276 75.98 T o t a l Variance 1 1.8550 1.8550 100.00 Step III Due to Regression 3 0.4484 0.1484 24.17 Due to Oxygen In-take ml per min per kg Body Weight 1 0.3397 0.3397 18.31 Due to Right Knee Extension 1 0.0890 0.0890 4 .80 Due to Body Density 1 0.0197 0.0197 1.06 Due to Error 50 1.4066 0.0281 75.83 Tota l Variance 1 1.8550 1.8550 100.00 REFERENCES Dempster, J.H., Gagne, A.E., Hogan, R., U.B.C. TRIP (Triangular Regression Package). University of B r i t i s h Columbia Computing Center, 1968. Ferguson, G.A., S t a t i s t i c a l Analysis i n Psychology and  Education, McGraw-Hill Book Co., New York, 1959. Bakogeorge, A.P., "The Relationship of Selected Anthropo-metrical and Physiological Variables to the Balke Treadmill Test and a Terminal Step Test and Test Interrelationship," Unpublished Masters Thesis, University of Alberta, 1964. Guilford, J.P., Fundamental S t a t i s t i c s In Psychology and  Education, McGraw-Hill Book Co., Toronto, 1950. CHAPTER V DISCUSSION Observations on the Subjects The procedure of te s t i n g subjects i n two successive tests and measurement courses was followed to obtain a larger, more representative sample of physical education students. The values shown i n Table I revealed that the two groups were very s i m i l a r and that treatment of the combined groups as a single population was an acceptable procedure. The Sample Data Compared with Data from Other Studies PWCl70 k P m P e r m j- n* PWC170 k P m P e r m ^ n scores and body size measures from six studies appear i n Table XVIII. The mean PWC170 value obtained i n t h i s study was 1143 1 186.8 kpm per min. DeVries et a l . (1) also tested physical education majors with a mean age of 22.4 years and obtained a mean PWC^o score of 1266 - 276 kpm per min. Holmgren et a l . (2) obtained a higher value of 1400 ± 237-7 kpm per min but employed highly trained subjects from the Gymnastiska Centralinstituent i n Stockholm. Wendelin et a l . (3) tested medical students and reported a mean PWC170 score of 1107 - 301 kpm per min which was very s i m i l a r to the mean score obtained i n t h i s study. Tornvall (4) and Hellstrom (5) both investigated the physical working capacity of conscripts and have reported mean PWC170 values of 1064 ± 218 kpm per min and 929 kpm per min. TABLE 171II A COMPARISON OP INVESTIGATIONS DETERMINING BODY COMPOSITION AND PHYSICAL WORKING CAPACITY I I x x Pw5170 * * kpm per PWC170 P W C ^ Q PV/C170 min.per kpm per kpm per Age Weight Pat Free kpm per kg Body kg Pat min. per Type of Investigator N (Yrs) (kg) Wt.(kg) min. Weight Free Wt. M2 Subjects Miki 54 2 2 . 4 75.96 69.10 +1.35 ±10.71 ± 8 . 2 0 4 1143 ± 1 8 6 . 8 15.14 ±2.151 16.58 ±2.005 P.E. Majors DeVries et a l ( 1 ) 16 2 2 . 4 , 78.5 1266 ± 276 16.6 ± 5.2 655 ±153 P.E. Majors Holmgren et a l ( 2 ) 10 71.6 ±9.0 1400 ±237.7 P. E. Majors Wendelin et a l ( 3 ) 153 21.5 69.5 1107+ 301 Medical Students Tormvall ( 4 ) 89 19.5 68.3 ± 0 . 5 106*+ 218 Conscripts Tornvall ( 4 ) 23 2 2 . 2 + 69.3 3 . 3 1551± 151 Middle Dis-tance Runners Hellstrom (5) 47 1 8 . 0 6 6 . 3 929 1^.1 Conscripts Hellstrom ( 5 ) 4 8 74.1+ 11.2 1213+ 219 16.5+ 2.8 Wt. L i f t e r s and Wrestlers Hellstrom (5) 48 66.3+ ^.5~ 1607+ 174 24.3+ 2.5 Middle Dis-tance Runners 95 respectively. Tornvall (4) and Hellstrom (5) obtained mean values of 1551 - 151 kpm per min and 160? ± 174 kpm per min, respectively, f o r middle distance runners. Hellstrom also reported a mean PWC170 score of 1213 t 219 f o r w e i g h t l i f t e r s and wrestlers. The differences i n the scores from the afore-mentioned studies may be due to differences between samples i n respect to: 1. lean active mass, 2. superior cardiovascular respiratory e f f i c i e n c y and/or, 3. mechanical e f f i c i e n c y . The Stockholm sample of Holmgren's (2) mean PWC170 kpm per min value of 1400.00 t 237-7 and mean body weight of 71.6 ± 9.0 kg appear to confirm the description as being highly trained young men, i.e., very vigorous and slim. The scores of the middle distance runners tested by Tornvall (4) and Hellstrom (5) also exhibited s i m i l a r t r a i t s of extremely high PWC170 scores and low body weights. The differences l n test scores between these three studies and the others appear to be primarily due to differences i n cardiovascular - respiratory t r a i n i n g although European samples may also have a d e f i n i t e advantage l n the e f f i c i e n c y i n pedalling a bicycle over t h e i r non-bicycling North American counterparts. The differences i n test scores among the other groups included i n Table XVIII might, however, be due to any or a l l three factors. For 96 example, both DeVries et a l . (1) and this study tested physical education majors but DeVries et a l . (1) obtained a higher PWC170 mean score. It i s d i f f i c u l t to determine whether the higher scores are due to better t r a i n i n g or because the subjects from the study of DeVries et a l . (1) were larger. S i m i l a r l y , the conscripts tested by Tornvall (4) and Hellstrom (5) obtained the lowest scores but were also l i g h t e r i n body weight. It i s apparent, then, that i n order to u t i l i z e the Sjostrand PWC170 test as a measure of the physiological condi-t i o n of an in d i v i d u a l to perform work, a more meaningful expression of the score must be made. PWC170 kpm per min Divided by Body Size. Assuming a proportionality between body size and c i r c u l a t o r y capacity, It would appear that the larger subject would obtain a higher PWC170 score than a smaller i n d i v i d u a l , although the r e l a t i v e t r a i n i n g l e v e l s may be sim i l a r , since the task i s performed on a bicycle ergometer where the body weight i s supported. This task may be compared with the treadmill or step test methods where the work i s done i n transporting the body weight. Consequently, i n a few studies, P W C 1 7 0 has been expressed as P W C 1 7 0 kpm per min per kg body weight, i.e.., work output per unit body s i z e . These values are also presented i n Table XVIII. The conscripts which Hellstrom (5) tested obtained the lowest score of 14.1 kpm per min per kg body weight and the 97 middle distance runners, as may be expected, obtained the highest score of 24.3 - 2.5 kpm per min per kg body weight. The physical education sample employed by DeVries et a l . (1) recorded a higher work capacity score than the sample employed i n t h i s study when the influence of size was apparently removed. The sample of t h i s study seems, therefore, to be the le a s t trained of the three physical education groups and/or less s k i l l e d at r i d i n g the bicycle ergometer, but the extent of the i n f e r i o r i t y i s not great. The use of body weight has, as previously discussed i n Chapter II, several disadvantages i n making comparisons between individuals i f one wishes to relate i n d i v i d u a l differences i n working capacity to that portion of the body mass which c o n t r i -butes to the work output. Body weight includes adipose tissue which d i f f e r s considerably among individuals and does not contribute to the work output. Adipose tissue i s also l a b i l e tissue which may diminish considerably with t r a i n i n g or reduction In c a l o r i c intake or may increase with detraining or with increase i n c a l o r i c intake. Thus, ind i v i d u a l differences i n r e l a t i v e adiposity or changes i n adipose tissue proportions can create d i f f i c u l t i e s or even confusion i n the interpretation of work capacity measurements. The use of f a t free weight may be a more accurate b i o l o g i c a l reference and t h i s measure has been employed i n some recent studies investigating r e l a t i o n s h i p between maximum 98 oxygen intake and body composition. I t i s the portion of the body mass which contributes to work output and i t i s not subject to rapid changes i n r e l a t i v e proportion of body weight. Physical work capacity has also been expressed i n th i s study as PWC170 kpm per min per kg fa t free weight but no comparative data i s available i n the l i t e r a t u r e . Both PWC170 kpm per min per kg body weight and PWC170 kpm per min per kg f a t free weight appear to be a more b i o l o -g i c a l l y meaningful assessment of an individual's r e l a t i v e " f i t n e s s " to perform work on a bicycle ergometer than PWC170 kpm per min. Conversely, the expression of the Sjostrand test as PWC170 kpm per min may have l i t t l e or no meaning when comparing individual's r e l a t i v e " f i t n e s s . " Thus, the expres-sion of the PWG170 score per unit body size appears to be a good measure f o r normative tables. In an investigation of the i n t e r r e l a t i o n s h i p of variables, however, such r a t i o measures may cause c e r t a i n a n a l y t i c a l d i f f i c u l t i e s which w i l l be discussed further i n the c o r r e l a t i o n analysis. Body Density. Several methods of estimating f a t free weight are a v a i l a b l e f o r laboratory use, but the densiometric method seems to be the most common because of i t s r e l a t i v e accuracy associated with the a v a i l a b i l i t y of equipment at not too great expense. The mean value f o r body density i n t h i s study was I.078 ± 0.0041 gm per cm3 with a range from 1.047 to 99 1.095 gm Per cin3. Behnke (6:4-98) has stated that, ". . .values of density f o r healthy young men ranging i n ages between 20 and 40 f a l l between 1.021 and 1.097 gm per cm3." Keys and Brozek (7:294) described the mean density of normal young men as 1.063 gm per cm3 or 14 percent of body weight as f a t . The average value of percentage of body f a t of the subjects in- t h i s study was 9.03 percent which was lower i n comparison to the mean value given by Keys and Brozek (7). This may be expected, since the subjects i n t h i s study were physical education majors and, thus, p o t e n t i a l l y leaner than the general population of the same age range. Comparative data i s presented i n Table XIX. Generally, percentage of body fat appears to r e f l e c t physical a c t i v i t y . The sedentary sample investigated by Buskirk et a l . (9) had the highest percentage f a t (15*9 - 7.8 percent). The percentage of f a t of Von Dobeln's (10) physical education sample (10.6 percent) appears to be consistent with the value obtained f o r the sample of this study (9.03 percent). Coyne's (8) sample had the lowest percentage of f a t (3*9 - 3*2 percent) but, although the sample was described as "active students," t h i s value appears to be too low. Error may be due to the presence of gas i n the ga s t r o i n t e s t i n a l t r a c t since t h i s factor was not controlled. Coyne (8) also observed that three subjects possessed zero percent f a t which, i n r e a l i t y , i s an impo s s i b i l i t y , since a certa i n amount of l i p i d material, such TABLE XIX COMPARATIVE BODY COMPOSITION AND MAXIMUM OXYGEN INTAKE DATA OF SEVERAL INVESTIGATIONS Investigator N Body Age Wt. (Yrs) (kg) x" Pat Free Percent Wt.(kg) Fat x" x X x Max.V02 Max.V02 ml per ml per Total Max.V02 min.per min.per Pat 1 per kg Body kg Pat (kg) min. Weight Free Wt. Type of Subjects Miki * 5 4 2 2 . 4 + 7 5 . 9 6 6 9 . 1 0 1 . 3 5 " " ± 1 0 . 7 1 ± 8 . 2 0 9 . 0 3 6 . 8 6 3 . 7 7 * * ^ 9 . 7 7 ± 0 . 5 0 5 6 ± 6 . 4 5 1 5 4.41 ± 6 . 1 6 3 P.E. Majors Coyne ( 8 ) X 3 0 2 3 . 1 + 4 5 . 0 5 4 . 3 ± 7 . 2 7 2.08 ± 6 . 6 3 . 9 ± 3 . 2 2.97+ 4 . 7 5 2 . 7 ± 0 . 6 9 9 6 3 . 5 ^ ± 9 . 6 7 6 5 . 8 9 ± 1 0 . 5 9 Active Students Buskirk ( 9 ) et a l X 3 9 2 2 . 5 ± 7 8 . 6 2 . 8 ± 1 6 . 9 6 6 . 1 1 1 5 . 9 ± 7 . 8 1 2 . 5 3 . 4 ± 0.46 4 4 . 6 ± 5 . 5 5 3 . 1 ± 3 . 4 Sedentary Buskirk ( 9 ) et a l X 1 5 2 1 . 7 7 5 . 8 ± 2 . 7 ± 1 3 . 5 6 9 . 8 7 . 8 7 ± 6 . 6 5 . 9 6 3 . 9 5 ± 0 . 9 3 5 2 . 8 ± 5 . 5 5 7 . 5 ± 3 . 4 Moderately Active Buskirk ( 9 ) et a l X 5 2 0 . 2 6 5 . 8 ± 1 . 3 ± 5 . 0 6 0 . 7 5 7 . 8 7 ± 0 . 7 6 5 . 0 5 4 . 3 2 ± 0 . 3 5 6 5 . 8 ± 3 . 4 7 1 . 2 ± 3 . 4 Cross Country Runners Von Dobeln ( 1 0 ) *+ 3 5 2 6 . 1 6 9 . 3 ± 1 . 4 6 1 . 8 1 0 . 6 7 . 3 5 3 . 9 1 ± 0.09 5 6 . 4 6 3 . 2 P. E. Majors and S t a f f Welch ( 1 1 ) et a l X 28 2 3 . 7 7 5 . 3 ± 1 . 9 ± 9 . 6 64 . 0 1 5 . 1 ± 5 . 8 1 1 . 8 ± 5 . 8 3 . 7 3 ± 0 . 4 3 4 9 . 5 5 8 . 3 Not Reported M i t c h e l l et a l ( 1 2 ) X 3 6 2 0 - 2 9 7 5 . ^ 3 . 3 7 + 0 . 5 1 4 4 . 7 ± 3 . 9 Sedentary A s t r a n d ( 1 3 ) * 42 2 0 - 3 0 7 0 . 4 ± 1 . 0 4 . 1 1 ± 0 . 0 6 5 8 . 6 ± 0 . 7 Well Trained DeVries ( l ) et a l # 1 6 2 2 . 4 7 8 . 5 3 . 8 7 ± 0 . 5 3 5 0 . 5 ± 9 . 8 7 P.E. Majors Helmgren, x et a l ( 2 ) * 1 0 7 1 . 6 ± 9 . 0 3 . 9 4 ± 0 . 5 5 P.E. Majors H O O * Tests on Bicycle Ergometer x Tests on Treadmill + Estimated From Heart Rates 101 as tha t p r e sen t i n the m y e l i n sheath of nervous t i s s u e , i s e s s e n t i a l f o r normal body f u n c t i o n s . A v a l ue of 7.8? * O.76 pe rcen t f a t ob ta ined by B u s k i r k e t a l . (9) f o r c r o s s count r y runners appears t o r e f l e c t the degree of p h y s i c a l a c t i v i t y s i n c e t h i s group may be expected to be s l i m and w e l l t r a i n e d , but sample s i z e i s of r e l a t i v e importance i n making compa r i -sons , s i n c e such s m a l l samples as s i x sub j e c t s might be more u n r e p r e s e n t a t i v e of the p o p u l a t i o n f rom which they were drawn. A l l f o u r s t u d i e s c i t e d used the d e n s i o m e t r i c method f o r d e t e r -m in ing body d e n s i t y and a l s o the Keys and Brozek (7) f o rmu la f o r a s s e s s i n g percentage of body f a t . Some of the d i f f e r e n c e s i n the ob ta ined mean v a l ues f o r percentage of body f a t shown on Tab le XIX may be due to v a r i a t i o n s i n the d e n s i o m e t r i c t e c h n i q u e . Oxygen Intake L per m i n . S j o s t r a n d (14:143) has s t a t e d t h a t the amount of oxygen taken i n i s dependent on the c a r d i a c output (pu l se r a t e X s t r oke volume) and the t o t a l amount of hemog lob in . Research has r e v e a l e d t ha t s t r oke volume (15 .16 ) , hea r t volume ( 5 , 1 5 . 1 6 ) , b l ood volume (17 ,18 ,19 ,20 ) and t o t a l hemoglobin (5.18) i n c r e a s e w i t h p h y s i c a l t r a i n i n g . Thus , an i n d i v i d u a l ' s a b i l i t y to take i n oxygen (maximum oxygen in take ) has , i n r e cen t y e a r s , become a measure of c a r d i o v a s c u l a r -r e s p i r a t o r y " f i t n e s s . " Comparat ive da t a of the v a r i a b l e s oxygen i n t ake L pe r min , oxygen i n t ake ml per min per kg body weight and oxygen 102 intake ml per min per kg f a t free weight appear i n Table XIX. Differences l n oxygen intake scores from the studies included i n Table XIX may be due to differences between the samples i n respect to: 1. lean active mass, 2. superior cardiovascular - respiratory conditioning, and 3- differences i n measurement techniques. The oxygen intake L per min values appear to r e f l e c t the physiological condition of the subjects. The mean oxygen intake values obtained i n thi s study appear to be consistent with those obtained f o r physical education students by DeVries et a l . (1 ) , Holmgren et a l . (2 ) , and Von Dobeln ( 10 ) . The values i n the above studies were larger than that obtained by Buskirk et a l . (9) and Mi t c h e l l et a l . (12) f o r sedentary subjects. A high value of 4.32 ± 0.35 L per min obtained by Buskirk et a l . f o r cross country runners may be expected, i n that t h i s sample should be i n the best physiological condition. A mean oxygen intake L per min value of 4 .75 - 0.699 obtained by Coyne (8) appears to be inconsistent with the description of the sample as "active students," and i t appears to be too high. It i s , however, d i f f i c u l t to speculate on possible sources of error. Differences l n oxygen intake values may be due to differences i n measurement techniques. The mean values i n the 103 studies of Coyne (8), Buskirk e t _ a l . (9), Welch et a l . (11) and Mi t c h e l l et a l . (12) were obtained on a treadmill. Rowell (21) found that i n the non-bicycling American population, the highest maximum oxygen intake obtainable on the bicycle ergometer to be consistently below values obtained on the trea d m i l l . Von Dobeln (10) estimated maximum oxygen intake from a nomogram provided by Astrand (13). Astrand (22) has stated that the nomogram tends to underestimate oxygen intake- of untrained individuals and overestimate the capacity of the well trained. Furthermore, differences i n technique occurred i n studies employing the bi c y c l e ergometer. DeVries et a l . (1) and Holmgren et a l . (2) obtained higher oxygen intake values on the bic y c l e ergometer u t i l i z i n g the intermittent test devised by Taylor et a l . (23). The present study employed a technique o r i g i n a l l y described by D i l l (24) which was a continuous test on the bic y c l e ergometer with stepwise increases In both work load and rate of pedalling. It i s intere s t i n g to note, however, that although DeVries et a l . (1), Holmgren et a l . (2), Von Dobeln (10) and the present study tested physical education majors on the b i c y c l e ergometer, the physically smaller European samples of Holmgren et a l . (2) and Von Dobeln (10) obtained higher mean oxygen intake values. This appears to support the re s u l t s i n PWC170 scores that the European students are i n better physical condition than the North American physical education students. 104 Oxygen Intake Divided by Body Size. Oxygen intake expressed per unit body siz e i s more prevalent i n past studies than i s the case f o r PWC170 scores. This i s , again, reason-able i n that the larger i n d i v i d u a l may inherently obtain a higher score than a smaller i n d i v i d u a l regardless of condition. These values appear i n Table XIX. The r e l a t i v e values among the studies did not a l t e r s i g n i f i c a n t l y i n r e l a t i o n to each other, which may indicate that the differences i n the scores are more dependent on the cardiovascular - respiratory e f f i -ciency of the subjects than on body s i z e . Once again, these r a t i o s appear to be very meaningful f o r normative tables but present problems i n c o r r e l a t i o n a n a l y s i s . Comparison Between the Manual and Computer Methods f o r Calculating the PWC170 Values Although the report by Howell et a l . (25) implied that both the computer c a l c u l a t i o n and the manual estimation of the best f i t t i n g straight l i n e were possible, no data was included. The present study revealed a c o r r e l a t i o n c o e f f i c i e n t of 0.9912 between the two techniques which accounted f o r 98.24 percent of the variance. Therefore, the simple and more fe a s i b l e manual technique appears to be a highly dependable method of estima-ti n g the best f i t t i n g straight l i n e i n P W C 1 7 0 c a l c u l a t i o n s . 105 Zero Order Correlation Analysis Dependent Variable PWC^Q kpm per min. Zero order c o e f f i c i e n t s of co r r e l a t i o n between the dependent variable PWC170 kpm per min and the independent variables (XZj, .... X24) appeared i n Table IV. Seven of the twenty-one independent variables correlated s i g n i f i c a n t l y at the 0.01 l e v e l of c o n f i -dence and the four variables revealing the largest variances with the dependent variable were f a t free weight (39*60 per-cent), oxygen intake L per min (38*75 percent), body weight (27.38 percent) and right knee extension (21.26 percent). Data comparing the s t a t i s t i c a l r e l a t i o n s h i p between PWC170 kpm per min and oxygen intake L per min appear i n Table XX. TABLE XX A COMPARISON OP INVESTIGATIONS DETERMINING MAXIMUM OXYGEN INTAKE AND PHYSICAL WORKING CAPACITY PWC170 kpm Oxygen Intake Corr. Investigator N Age per min L per min Coef. Type of Mean S.D. Mean S.D. Mean S.D. Subjects Mlki 54 22.4 I.35 1143 186.8 3-774 0.5056 0J6225 P.E. Majors DeVries etal.CD 16 22.4 1266 276 3.87 0.53 0.703 P.E. Majors Holmgren et a l . (2) 20 1400 237-7 3-94 0.55 0.930 P.E.Majors 106 DeVries et a l . (1) reported a co r r e l a t i o n c o e f f i c i e n t of 0.703 between the Sjostrand test and oxygen intake values. Holmgren et a l . (2) obtained a co r r e l a t i o n value of O.903 and the value obtained i n t h i s study was O.6225. Certainly, data reporting a s t a t i s t i c a l r e l a t i o n s h i p between cardiovascular parameters and PWC170 kpm per min would indicate a relat i o n s h i p between PWC170 kpm per min and oxygen intake L per min. Bevegard (26) reported a c o r r e l a t i o n c o e f f i c i e n t of 0.84 between PWC170 and stroke volume f o r 27 young male subjects. Holmgren et a l . (27) obtained a co r r e l a t i o n c o e f f i c i e n t of 0.649 f o r the same variab l e s . Kjellberg et a l . (19). Holmgren et a l . (27). Hellstrom (5) and Linroth (28) reported c o r r e l a -t i o n c o e f f i c i e n t s between PWC170 a n d - heart volume of O.96, 0.829, 0.55 and 0.49, respectively. Correlation c o e f f i c i e n t s of 0.90 and O.98 have been obtained between t o t a l hemoglobin and PWC170 by Kjellberg et a l . (20) and Linroth (28), respec-t i v e l y . Also, a co r r e l a t i o n c o e f f i c i e n t of 0.922 has been reported between d i f f u s i o n capacity of the lungs and PWC170 (27). The values reported on Table XX, however, d i f f e r greatly and the true rel a t i o n s h i p between PWC170 and oxygen intake Is d i f f i c u l t to inte r p r e t . A possible reason may be that the sample i n the present study was more homogeneous than i n the other two studies. An analysis of the standard deviations would indicate t h i s to be a f a c t . Sample homogeneity reduces 10? the i n t e r i n d i v i d u a l differences which i n turn may reduce the degree of c o r r e l a t i o n . Garrett (29:171) stated that, ". . . the size of the c o r r e l a t i o n c o e f f i c i e n t w i l l vary with heterogeneity, i . e . , the degree of scatter i n the group; and the more r e s t r i c t e d the spread of test scores, the lower the c o r r e l a t i o n . " Howell et a l . (25:38) compared c o r r e l a t i o n c o e f f i c i e n t s between body weight and PWC17Q scores f o r s p e c i f i c age groups and the highest c o e f f i c i e n t s were obtained f o r ten year olds (males, r = 0 .60 ; females, r = 0 . 5 1 ) . When the cor-r e l a t i o n c o e f f i c i e n t s were calculated over the whole age range (? to 17 years of age), the magnitude of the c o r r e l a t i o n coef-f i c i e n t s f o r males and females increased to 0.80 and 0 . 60 , respectively. Macnab (30) has also pointed out that hetero-geneity of a sample tends to increase the magnitude of the c o r r e l a t i o n c o e f f i c i e n t . On the other hand, the number of subjects i n the studies of DeVries et a l . (1) and Holmgren et a l . (2) were small and therefore, the scores may indicate a bias. Certainly, i t i s d i f f i c u l t to consider the scores a r e l i a b l e estimate of values i n a population of physical education students. The s t a t i s t i c a l r e l a t i o n s h i p between PWC170 kpm per min and body weight i n t h i s study was O .5233. Studies of children show a high r e l a t i o n s h i p between body weight and work capacity (PWC170K Gumming et a l . (31) obtained correlations of 0.897 f o r boys and O.696 f o r g i r l s . The study of Adams et a l . (32) 108 r e s u l t e d i n a c o r r e l a t i o n of 0.81 f o r boys and 0 . 7 7 f o r g i r l s when l o g a r i t h m i c weight was compared to p h y s i c a l working c a p a c i t y . Values f o r an a d u l t p o p u l a t i o n have been reported by Holmgren et a l . (2) and He l l s t r o m ( 5 ) . The former reported a c o r r e l a t i o n c o e f f i c i e n t of 0 . 7 6 2 between body weight and PWC170 kpm per min. The l a t t e r obtained a s t a t i s t i c a l r e l a -t i o n s h i p of 0.46 f o r w e i g h t l i f t e r s and O . 3 6 f o r middle distance runners. Thus, the r e l a t i o n s h i p between the two v a r i a b l e s d i f f e r s c o n s i d e r a b l y among s t u d i e s and i t appears to depend on the sample t e s t e d . G e n e r a l l y , however, performance on the b i c y c l e ergometer appears t o be enhanced by body s i z e . The c o r r e l a t i o n c o e f f i c i e n t between f a t f r e e weight and PWC170 kpm per min i n the present study was 0 . 6 2 9 7 . L o g i c a l l y , PWC170 kpm per min should be r e l a t e d to the a c t i v e muscle mass engaged i n c y c l i n g and thus, the c o r r e l a t i o n between f a t f r e e weight and PWC170 kpm per min should be higher than between body weight and PWC170 kpm per min. This r e l a t i o n s h i p i s demonstrated i n the r e s u l t s obtained i n t h i s study. The highest c o e f f i c i e n t of c o r r e l a t i o n between the dependent v a r i a b l e PWC170 kpm per min and a st r e n g t h item was O . 4 6 3 2 ( r i g h t knee e x t e n s i o n ) . H e l l s t r o m ( 5 ) I n v e s t i g a t e d the d i f f e r e n c e i n PWC170 scores and strength between 48 weight-l i f t e r s and 28 middle d i s t a n c e runners. The w e i g h t l i f t e r s scored higher than the runners i n the s t r e n g t h t e s t s but lower i n PWC170 score. This r e s u l t may be expected i n th a t Sjostrand 109 (14) implied that an Investigation of strength i s not s u f f i c i e n t to Judge an individual's physical work capacity. The study of Hellstrom (5) does not, however, contribute s i g n i -f i c a n t l y to an understanding of the true physiological r e l a t i o n s h i p between strength and PWC170. More informative data i s presented by Ahlborg (33) . who investigated the r e l a t i o n s h i p between a 6 minute maximal te s t , a 100 minute maximal te s t , strength measures and PWCj^o* The 6 minute maximal work test correlated higher with PWC^Q (0.72) than the 100 minute maximal test ( 0 . 6 1 ) . A s i m i l a r order of r e s u l t s was obtained f o r strength items where knee strength > correlated O.32 with the 6 minute test and 0.30 with the 100 minute t e s t . Total leg press correlated 0.29 and 0 . 19 . respectively. Thus, i t would appear that strength i s not highly related to work on the b i c y c l e ergometer at a heart rate of 170 beats per minute, but such re l a t i o n s h i p as does exist seems to be dependent on the type of work. The a b i l i t y to perform b r i e f heavy work appears to depend more on strength than the a b i l i t y to perform l i g h t e r work done f o r longer durations. Tornvall (4) conducted c o r r e l a t i o n analyses between strength scores and scores f o r maximal work done f o r 6 minutes, maximal work f o r 10 minutes, maximal work f o r 15 minutes and PWCi7o* The c o r r e l a t i o n c o e f f i c i e n t s were O .69. 0 . 6 8 , 0 . 6 5 . and 0.46, respectively. The c o r r e l a t i o n c o e f f i c i e n t of 0.46 110 between strength and PWC170 appears to be rather high i n view of the findings reported by Ahlborg (33)» °ut corresponds with the c o e f f i c i e n t of 0.4632 obtained i n t h i s study. There i s , however, a s i m i l a r i t y between the studies of Tornvall (4) and Ahlborg ( 3 3 ) . i n that a r e l a t i o n s h i p i s established where the contribution of strength to physical work capacity declines as the duration of the test increases. Independent Variables Body Weight and Fat Free Weight. The r e l a t i o n s h i p of body weight and f a t free weight with other independent variables (X6 . . . . X24) were reported i n Tables VII and VIII. The present study obtained a c o r r e l a t i o n c o e f f i c i e n t of 0.5048 between body weight and oxygen intake i n l i t e r s per min. Buskirk et a l . (9) and Welch et a l . (11) reported values of O.63 and 0 . 5 9 . respectively. This r e l a t i o n s h i p may be expected, i n that larger individuals would have larger oxygen forwarding capacities than smaller i n d i v i d u a l s . A value of 0.262 reported by Coyne (8) appears to be too low i n view of the other studies, but i t i s d i f f i c u l t to speculate on pos-s i b l e sources of error. The present study obtained a c o r r e l a t i o n of 0.5973 between f a t free weight and oxygen intake i n l i t e r s per min. This r e l a t i o n s h i p i s higher than that between body weight and oxygen intake, and t h i s increase was s i m i l a r l y obtained by Buskirk et a l . (9) and Welch et a l . ( 11) . The values reported I l l were 0.85 and 0 .65 , respectively. Von Dobeln (10) reported a s i m i l a r value of 0.75 f o r the above r e l a t i o n s h i p . Coyne (9 ) , Buskirk et a l . (9) and Welch et a l . (11) agreed that although oxygen intake i s not s i g n i f i c a n t l y influenced by the percentage of body weight composed of f a t , i t i s d i r e c t l y related to the size of the lean active mass. Thus, a higher relationship between oxygen intake and f a t free weight may be expected than between :oxygen intake and body weight. The findings i n t h i s study are consistent with those reported i n other studies. The strength items included i n t h i s study are consi-dered, by d e f i n i t i o n , as s t a t i c muscular strength. Fleishman (34) has stated that the r e l a t i o n s h i p between body weight and performance of s t a t i c strength tests i s high. The r e s u l t s of this study appear to indicate that although the above r e l a t i o n -ship may not be high, body weight i s s i g n i f i c a n t l y related to a l l the strength variables excepting f o r strength per f a t free weight. Generally, higher relationships between f a t free weight and strength variables were obtained. This may be expected, l n that f a t free weight i s more clos e l y associated with the size of the muscle mass than body weight. Body density correlated negatively (-0.5047) with body weight and i t was minimally related to f a t free weight ( -0 .1621) . This r e l a t i o n s h i p appears to indicate that the heavier men tended to have l i g h t e r densities and thus had higher percentages of weight accounted f o r by f a t . Whether or 112 not t h i s i s usual among physical education students i s not known; i f i t i s , i t may r e f l e c t the d i s t r i b u t i o n of body types related to success i n a va r i e t y of a t h l e t i c a c t i v i t i e s and sports. In summary, body weight, and to a greater extent, f a t free weight, appear to be related to PWC170 kpm per min, to oxygen intake i n l i t e r s per min, and to strength items included i n t h i s study. Thus, i f PWC170 kpm per min i s a measure of r e l a t i v e " f i t n e s s " of individuals, and i f oxygen intake capa-c i t y and strength are assumed to contribute to " f i t n e s s , " then, zero order correlations between PWC170 kpm per min and the l a t t e r two variables may be spurious due to the influence of body s i z e . Garrett (29:441) stated, "The c o r r e l a t i o n between two sets of test scores i s said to be spurious when i t i s due i n some part to factors other than those which determine per-formance i n the tests themselves." Consequently, i f the relationships between PWC170 and variables which contribute to "f i t n e s s , " i . e . , oxygen intake and strength, are to be investigated, i t would appear that body size would have to be controlled. This procedure i s discussed i n the succeeding sections. Dependent Variable PWC170 kpm per min Divided by Body  Size. Since PWC17Q i s related to body s i z e , i t i s l o g i c a l to divide work capacity scores by weight i n an attempt to derive 113 performance scores which r e f l e c t i n d i v i d u a l differences related to " f i t n e s s " other than body weight. In thi s study the corre-l a t i o n c o e f f i c i e n t between P W C 1 7 0 kpm per min per kg body weight and oxygen intake ml per min per kg body weight was O.5617. DeVries et a l . (1) reported a co r r e l a t i o n c o e f f i c i e n t of 0.877 f o r the same va r i a b l e s . Thus, i n t h i s study, the co r r e l a t i o n c o e f f i c i e n t between PWC170 kpm per min and oxygen intake i n l i t e r s per min was reduced when divided by body weight. A s i m i l a r decrease (from 0.6225 to 0.4117) was found when the variables were divided by f a t free weight. Con-versely, i n the study of DeVries et a l . (1), the rel a t i o n s h i p between PWC170 kpm per min and oxygen intake i n l i t e r s per min increased when both variables were divided by body weight. Although the d i v i s i o n of variables by body size would appear to have an ef f e c t s i m i l a r to p a r t i a l l i n g by c o r r e l a t i o n analysis, some d i f f i c u l t i e s l n interpretation are encountered. Howell et a l . (25:39) stated that equating subjects f o r size within a single age group by d i v i d i n g the P W C 1 7 0 scores by weight may not be e n t i r e l y s a t i s f a c t o r y , since homogeneity of the sample data may increase. In other words, the c o r r e l a t i o n c o e f f i c i e n t w i l l be reduced as occurred l n th i s study. On the other hand, Garrett (29) and McNemar (35) have implied that the co r r e l a t i o n of r a t i o variables may be spurious due to a common factor, i . e . , body weight or f a t free weight, employed as a denominator i n the r a t i o s . In t h i s case, the co r r e l a t i o n 114 c o e f f i c i e n t w i l l be i n f l a t e d . Thus, i t would appear that a more b i o l o g i c a l l y meaningful r e l a t i o n s h i p may be e s t a b l i s h e d when the i n t e r f e r i n g v a r i a b l e s are s t a t i s t i c a l l y p a r t i a l l e d i n s t e a d of expressing the performance scores as r a t i o s . When PWC170 kpm per min i s d i v i d e d by body weight, however, an i n t e r e s t i n g r e l a t i o n s h i p i s e s t a b l i s h e d w i t h body d e n s i t y , i . e . , r e l a t i v e leanness or f a t n e s s . A c o r r e l a t i o n c o e f f i c i e n t of -0.5404 was obtained f o r the above v a r i a b l e s . This may be expected, i n t h a t body d e n s i t y i s a measure of proportionate f a t and, t h e r e f o r e , the PWC170 kpm per min per kg body weight score appears to decrease as the amount of propor-t i o n a t e f a t i n c r e a s e s . An i n d i v i d u a l who i s r e l a t i v e l y heavier and f a t t e r than the m a j o r i t y of the sample w i l l have a r e l a t i v e l y lower d e n s i t y . I f h i s PWC170 kpm per min score f e l l i n the middle range of the sample scores, the e f f e c t when t h i s score i s d i v i d e d by body weight would be such that h i s new P W C 1 7 Q kpm per min per kg body weight score w i l l f a l l below the middle range f o r the sample. Incidents of t h i s k i n d i n s u f f i -c i e n t number would r e s u l t i n an increased negative c o r r e l a t i o n between body d e n s i t y and working c a p a c i t y scores (PWC170 kpm per min per kg body weight). This i s what appears to have happened i n t h i s study. Normality of the D i s t r i b u t i o n of Scores Histograms of a l l the v a r i a b l e s were drawn to determine 115 the normality of the d i s t r i b u t i o n s . Hays (36:510) has stated: Unless the d i s t r i b u t i o n s f o r X and Y are s i m i l a r i n form, i t i s not necessarily true that the obtained value of l£ y can range between -1 and +1. In fa c t , i t i s possible to produce examples where the forms of the d i s t r i b u t i o n s of X and Y are very d i f f e r e n t , and the maximum possible absolute value of r X y i s only .3 or l e s s . The variables included i n t h i s study appear to exhibit normal d i s t r i b u t i o n s ; even when the variable was expressed as a r a t i o , i . e . , PWC-L70 kpm P e r m i n P e r kg body weight. A larger sample than 5^ would have, perhaps, been more conclusive i n respect to the proper forms a f t e r d i s t r i b u t i o n of the v a r i -ables. Wendelin (3) has drawn a frequency polygon of the PWC170 scores f o r 153 male medical students and the d i s t r i b u -t i o n appears to be normal. Thus,, the d i s t r i b u t i o n s of the scores i n thi s study appear to be s i m i l a r i n form and therefore possibly did not adversely a f f e c t the c o r r e l a t i o n c o e f f i c i e n t s . Also, the apparent normality of the r a t i o variables supports the s u i t a b i l i t y of t h e i r use i n normative tables. F i r s t Order Correlation Analysis Independent Variable Body Weight Held Constant. When PWC170 kpm per min was correlated with the independent v a r i -ables (X5 .... X24) and body weight was s t a t i s t i c a l l y held constant, lower c o r r e l a t i o n c o e f f i c i e n t s were obtained than l n the zero order c o r r e l a t i o n . This may be expected, i n that the spurious e f f e c t of body weight had been controlled. There were 116 three exceptions, however, where the c o r r e l a t i o n c o e f f i c i e n t increased. In zero order c o r r e l a t i o n PWC170 kpm per min was not related to oxygen Intake ml per min per kg body weight (r = 0.1025) and to oxygen intake ml per min per kg fat free weight (r = 0.0932). In f i r s t order correlations, the corre-l a t i o n c o e f f i c i e n t s were 0.5138 and O.3675. respectively. Wilmore (37) obtained s i m i l a r results when endurance work on the b i c y c l e ergometer was compared with maximum oxygen intake. In his zero order correlations, when work output was compared with maximum oxygen intake i n l i t e r s per min, maximum oxygen Intake ml per min per kg body weight and maximum oxygen intake ml per min per kg lean body weight, the c o r r e l a t i o n c o e f f i -cients were O.836, 0.372, and O . I 8 3 , respectively. When body weight was held constant, the co r r e l a t i o n c o e f f i c i e n t s were • 0.787, 0.776, and 0.343, respectively. Wilmore (37:209) concluded that: . . . i f Max VO2 i s expressed i n terms of body weight or lean body weight f o r the purpose of gaining greater i n t e r -pretive significance, then the influence of body weight and lean body weight must be held constant when evaluating the true r e l a t i o n s h i p between Max VO2 and endurance capacity. It would seem, however, that a greater insight into the true r e l a t i o n s h i p between variables may be obtained from non-ratio variables, i . e . , PWC170 k P m P e r m i n a n d - oxygen intake i n l i t e r per min. This would appear l o g i c a l since both PWG^ -po a n d oxygen intake capacity are influenced by body s i z e . Dividing 1 1 7 only one variable by body weight and p a r t l a l l i n g body weight i n a co r r e l a t i o n analysis may increase the co r r e l a t i o n c o e f f i c i e n t , but i t may be a spurious procedure. In both Wilmore's ( 3 5 ) study and i n thi s study the zero order r e l a t i o n s h i p between body weight and oxygen intake ml per min per kg body weight were negative (r = - 0 . 4 6 3 and r = - 0 . 5 1 9 3 ) * Consequently, when work output i s correlated with oxygen intake ml per min per kg body weight with body weight held constant the negative values above are incorporated into the numerator of the p a r t i a l corre-l a t i o n formula. This negative value induces an algebraic addition instead of a substraction which would have occurred had the c o e f f i c i e n t been p o s i t i v e . The net ef f e c t i s to increase the value of the numerator which, i n turn, increases the p a r t i a l c o r r e l a t i o n c o e f f i c i e n t and i t i s , therefore, spurious and meaningless p h y s i o l o g i c a l l y . Thus, i t would appear that a more accurate and meaningful procedure may be to correlate PWC170 kpm per min and oxygen intake i n l i t e r s per min and s t a t i s t i c a l l y hold body weight constant. In zero order co r r e l a t i o n , body density did not corre-l a t e s i g n i f i c a n t l y with PWC170 k P m P e r m i n ( r = 0 . 0 7 9 8 ) . When body weight was held constant, the co r r e l a t i o n c o e f f i c i e n t between the aforementioned variables was 0 . 4 6 8 1 . In other words, subjects with greater densities obtained higher scores on the PWC170 t e s t . This i s consistent with the findings that lean active mass exhibits a positi v e influence on work done on 118 the b i c y c l e ergometer. Independent Variable Fat Free Weight Held Constant. When PWC^ -po kpm per min was correlated with the independent variables (X6 •••• X24) and f a t free weight was s t a t i s t i c a l l y held constant, lower c o r r e l a t i o n c o e f f i c i e n t s were obtained than i n zero order c o r r e l a t i o n or i n f i r s t order c o r r e l a t i o n with body weight held constant. As previously discussed, f a t free weight contributes to work output on the bicycle ergometer to a greater extent than body weight and thus, when f a t free weight i s held constant, lower c o r r e l a t i o n c o e f f i c i e n t s may be expected. There were s i m i l a r exceptions as when body weight was held constant where oxygen intake ml per min per kg body weight (r = 0.4579) and oxygen intake ml per min per kg f a t free weight (r = 0.4410) correlated higher. Wilmore (37) also reported s i m i l a r r e s u l t s , but again, these correlations do not appear to i l l u s t r a t e the true r e l a t i o n s h i p between work capacity and oxygen intake. In summary, when the e f f e c t of body size i s held constant, i . e . , body weight or f a t free weight, oxygen intake i n l i t e r s per min and r i g h t knee extension appear to be related to PWC170 k P m P e r m i n a n d thus work capacity appears to be associated to oxygen intake capacity and, to a lesser extent, strength. These relationships are, however, r e l a t i v e l y low and PWC170 kpm per min appears to be influenced more by f a t free 119 weight than any other single v a r i a b l e . It would appear that had other studies which investigated the relat i o n s h i p between PWC170 kpm and physiological parameters such as heart volume, stroke volume, and t o t a l hemoglobin p a r t i a l l e d out the effect of f a t free weight, the co r r e l a t i o n c o e f f i c i e n t s may not have been as high as reported. Twenty-Second Order Correlation Analysis A twenty-second order c o r r e l a t i o n analysis was conducted between PWC170 a n d - each independent variable with a l l other variables held constant. Fat free weight (r = 0.4414), trunk f l e x i o n (r = 0.4393), trunk extension (r = 0.3544), and ri g h t knee extension (r = 0.3571) were s i g n i f i c a n t l y correlated at the 0.05 l e v e l of confidence. No variable was correlated at the 0.01 l e v e l of confidence. Interpretation of t h i s procedure i s e s p e c i a l l y d i f f i c u l t , i n that the physiological parameters are not Isolated parameters, but are intimately r e l a t e d . For example, the c o r r e l a t i o n c o e f f i c i e n t between PWC170 kpm per min and oxygen Intake i n l i t e r s per min through t h i s procedure was 0.0511, while i n f i r s t order c o r r e l a t i o n with f a t free weight held constant, the value was 0.3956. Thus, i t i s d i f f i c u l t to determine whether b i o l o g i c a l meaningful relationships may be obtained through t h i s procedure. Stepwise Multiple Regression Analysis The stepwise multiple regression technique has been 120 extensively employed i n psychology and other sciences and has been found to be a useful research t o o l . In the present study, this technique was employed f o r the following reasons: 1. to control possible spurious effects i n l i n e a r c o r r e l a t i o n due to a common dependence upon a t h i r d variable, and 2. to assess the contribution of more than one variable to the variance of physical work capacity. A stepwise multiple regression analysis was conducted on the following dependent variables: 1. PWC170 kpm per min X i , 2. PWC170 kpm per min per kg body weight X2. and 3. PWC170 kpm per min per kg f a t free weight X3. Dependent Variable PWC170 kpm per min. In the f i r s t regression analysis, where the effect of body size was not con-t r o l l e d , three independent variables were included i n the regression equations. Pat free weight, oxygen intake ml per min per kg body weight and r i g h t knee extension contributed 42.35 percent, 3*77 percent, and 9*82 percent, respectively, to the variance of PWC170 kpm per min. Total variance due to regression was 55'94 percent. The e f f e c t of f a t free weight on PWC170 kpm per min has been diseussed previously. The weight of the subject was 121 supported on the b i c y c l e ergometer and therefore, larger subjects with corresponding larger lean active mass and c i r -culatory capacity might be expected to accomplish more work. The predictive capacity of oxygen intake l n l i t e r s per min i n r e l a t i o n to PWC170 kpm per min appears to be n e g l i g i b l e , although f i r s t order c o r r e l a t i o n analysis with f a t free weight held constant had indicated that the two variables were s i g n i -f i c a n t l y related (r = 0.3956). The question which a r i s e s , therefore, i s why oxygen intake i n l i t e r s per min was not selected as a predictor variable i n the multiple regression analysis? F i r s t l y , f a t free weight and oxygen intake i n l i t e r s per min were very s i m i l a r i n t h e i r a b i l i t y to predict PWC170 kpm per min (PWC170 k P m P e r m l n versus oxygen intake l i t e r s per min = 0.6225; PWC170 kpm per min versus f a t free weight = 0.6293; oxygen intake l i t e r s per min versus f a t free weight = 0.5973). Thus, the correlations were very much of the same order i n size and selecting one to predict PWC170 kpm per min automati-c a l l y excluded the other as a useful predictor v a r i a b l e . In t h i s study, the computer co r r e c t l y selected f a t free weight as the variable with s l i g h t l y more predictive value. Secondly, PWC170 kpm per min was seen to correlate more highly (r = 0.4579) with oxygen intake ml per min per kg body weight than with oxygen intake i n l i t e r s per min (r = 0.3956) when f a t free weight was held constant (Table IX). The effect of the multiple regression analysis was to repeat t h i s process 122 exactly. Thirdly, i t seems necessary to explain why oxygen intake ml per min per kg body weight should have a higher p a r t i a l cor-r e l a t i o n than oxygen intake l i t e r s per min with PWC170 kpm per min when the zero order c o r r e l a t i o n between oxygen intake ml per min per kg body weight and PWC170 kpm per min was 0.1025 and the zero order c o r r e l a t i o n between oxygen intake l i t e r s per min and PWC170 kpm per min was 0.6225. This was due to the . cor r e l a t i o n of -0.3639 between f a t free weight and oxygen intake ml per min per kg body weight i n contrast with the cor-r e l a t i o n of 0.5973 between f a t free weight and oxygen intake i n l i t e r s per min. The ef f e c t of including the negative c o r r e l a -t i o n i n the f i r s t order p a r t i a l c o r r e l a t i o n was as previously described, and t h i s i s also applied to the multiple regression analysis. The c o r r e l a t i o n between body weight and oxygen intake ml per min per kg body weight was -0.5193 and between, body weight and PWC17Q kpm per min was 0.5233» and had body ; weight been selected as the f i r s t predictor variable i n the , multiple regression analysis, the r e l a t i v e contribution of oxygen intake ml per min per kg body weight to the prediction of PWC170 kpm per min might well have been greater than i t was i n the analysis as developed i n th i s study. As seen from the above and from Tables VII and VIII, a measure of body size (body weight or f a t free weight) corre-lates negatively with a r a t i o measure i n which either body 123 weight or f a t free weight appears i n the denominator. This appears to be the r e s u l t of weight co r r e l a t i n g with i t s re c i p r o c a l value, somewhat modified by the value of the numera-tor i n the r a t i o measures. Since the influence of body size on PWC170 appears to have been dealt with adequately i n the multiple regression analysis, the further i n c l u s i o n of t h i s dimension i n the independent variable oxygen intake ml per min per kg body weight would appear to be redundant. The i n c l u s i o n of oxygen intake l i t e r s per min would seem to be a more s a t i s f a c t o r y substitute and would have greater meaning from a physiological viewpoint. But the net predictive contribution of oxygen intake i n l i t e r s per min would be very low, since the regres-sion analysis showed that the choice of f a t free weight as the i n i t i a l predictor variable v i r t u a l l y denies to oxygen intake any role as a predictor v a r i a b l e . The greater predictive value of oxygen intake ml per min per kg body weight i s apparently.a s t a t i s t i c a l a r t i f a c t created by the fa c t that body weight was less highly correlated with oxygen intake i n l i t e r s per min (r = 0 . 5 0 4 8 ) than f a t free weight with oxygen intake i n l i t e r s per min (r = 0 . 5 9 7 3 ) . Right knee extension contributed 9 . 8 2 percent to the variance of PWC170 kpm per min. This does imply that strength contributes to physical work capacity as measured by the Sjostrand test, but i t s significance as a predictor variable i s 124 n e g l i g i b l e . This r e s u l t i s consistent with the findings of Ahlborg (33) and Tornvall (4), who reported that the contribu-t i o n of strength to work output, although important f o r short heavy work, i s i n s i g n i f i c a n t i n the PWC170 t e s t . It would appear, then, that when the Sjostrand test i s expressed as PWC170 kpm per min i t i s related s l i g h t l y more to the f a t free body weight than to cardiovascular measures and very l i t t l e to strength factors, and appears to have l i t t l e or no b i o l o g i c a l significance i n distinguishing, other than body size, the physiological capacities measured i n t h i s study. Dependent Variable PWC170 kpm per min per kg Body  Weight. When the dependent variable was divided by body weight, the t o t a l variance due to regression decreased to 46.06 percent. The d i f f i c u l t i e s involved with r a t i o variables are that the c o e f f i c i e n t of multiple determination may be decreased due to greater homogeneity of the sample, or i t may be a spurious one because of the employment of a common denominator i n the r a t i o s . Nevertheless, some interesting relationships may be explored. The contribution of oxygen intake ml per min per kg body weight (23.25 percent) to the variance of PWC170 kpm per min per kg body weight may be interpreted as a quantitative assess-ment of the r e l a t i o n s h i p between the a b i l i t y to take i n oxygen and the a b i l i t y to perform work on the bicycle ergometer at a 125 heart r a t e of 170 beats per min. T h i s i s c o n s i s t e n t w i t h the zero order and f i r s t order c o r r e l a t i o n s obtained i n t h i s study and the zero order c o r r e l a t i o n s r e p o r t e d i n other s t u d i e s ( 1 , 2 , 3 7 ) . Consequently, i t does appear t h a t oxygen i n t a k e c a p a c i t y i s a s s o c i a t e d to PWC170 although the r e l a t i o n s h i p i s not l a r g e . The c o n t r i b u t i o n of body d e n s i t y t o the v a r i a n c e of PWC170 kpm per min per kg body weight was 19.12 p e r c e n t . Although the e f f e c t of body weight was c o n t r o l l e d , body d e n s i t y i n d i c a t e s p r o p o r t i o n a t e f a t , i . e . , i n d i v i d u a l s w i t h the same body weight may have d i f f e r e n t percentages of body f a t and f a t f r e e weight. Thus, i t appears that as body d e n s i t y i n c r e a s e s , the PWC170 kpm per min per kg body weight scores i n c r e a s e . A s i m i l a r r e l a t i o n s h i p was found when PWC170 kpm was compared t o body d e n s i t y when body weight was s t a t i s t i c a l l y h e l d c o n s t a n t . I f body composition may be conceived as r e f l e c t i n g p h y s i o l o g i -c a l c o n d i t i o n , i . e . , " f i t t e r " i n d i v i d u a l s have l e s s f a t , then t h i s measure appears to be b i o l o g i c a l l y meaningful and may be a r e l a t i v e l y important c r i t e r i a i n p r e d i c t i n g work c a p a c i t y as; measured on the b i c y c l e ergometer. The s t r e n g t h item, r i g h t knee extension, was a g a i n i n c l u d e d i n the r e g r e s s i o n a n a l y s i s , but c o n t r i b u t e d a minimal 3.69 p e r c e n t . 126 Dependent Variable PWCiyp kpm per min per kg Fat Free  Weight. The d i v i s i o n of P W C 1 7 0 kpm per min by f a t free weight did not r e s u l t i n a greater insight into the relationships between va r i a b l e s . Oxygen intake ml per min per kg body weight contributed 18.31 percent to the variance of the dependent var i a b l e . Oxygen intake ml per min per kg f a t free weight was not included into the regression analysis as might have been expected, but t h i s appears to be due to a s l i g h t l y higher r e l a t i o n s h i p between oxygen intake ml per min per kg body weight and the dependent variable than when oxygen intake was divided by f a t free weight (r = 0.4277 to r = 0 .4117 ) . Body density contributed 1.06 percent, which appears to be l o g i c a l i n that f a t free weight i s not related to body density. Eight knee extension, again, contributed a minimal 4.80 percent. Although the t o t a l variance due to regression i s only 24 .17, and these variables may not be applicable f o r predictive purposes, the values do reveal relationships between physical work capacity and oxygen intake capacity and strength. Oxygen intake capacity i s associated with PWCi70» although not exactly to the same degree as f a t free weight. Physical work capacity i s also associated with strength, but the r e l a t i o n s h i p i s mini-mal. Furthermore, physical work capacity appears to be associa-ted with some physiological parameters not included i n this study. REFERENCES DeVries, H.A., Klafs, C.E., "Prediction of Maximal Oxygen Intake from Submaximal Tests," Journal of Sports  Medicine and Physical Fitness, Volume 5, 1965, pp. 207-214. 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Kjellberg, S.R., Rudhe, U., Sjostrand, T., "Increase of the Amount of Hemoglobin and Blood Volume l n Connec-t i o n with Physical Training," Acta Physiologlca  Scandinavica, Volume 19, 1950, pp. 146-151. 19- Kjellberg, S.R., Rudhe, U., Sjostrand, T., "The Amount of Hemoglobin i n Relation to the Pulse Rate and Heart Volume During Work," Acta Physiologlca Scandinavica, Volume 19. 1950, pp. 152-169. 20 . Kjellberg, S.R., Rudhe, U., Sjostrand, T., "The Relation of the Cardiac Volume to the Weight and Surface Area of the Body, the Blood Volume and the Physical Capacity f o r Work," Acta Radlologioa, Volume 31 , 1949, pp. 113-122. 2 1 . Rowell, L.B., "Commentary," Canadian Medical Association  Journal, Volume 96, 1967, p. 735. 129 22 . Astrand, P.O., Work Tests on the Bicycle Ergometer. Dept. of Physiology, Gymnastika Centralinstituent, Stockholm, Sweden. 23 . Taylor, H.L., Buskirk, E., Henschel, A., "Maximum Oxygen Intake as an Objective Measure of Cardlo-Respiratory Performance," Journal of Applied Physiology, Volume 8, 1955. PP. 73-80. 24. D i l l , D.B., "Assessment of Work Performance," Journal of Sports Medicine and Physical Fitness, Volume 6, 1966, pp. 3-8. 25 . Howell, M.L., Macnab, R.B., The Physical Work Capacity of Canadian Children, Canadian Association of Health Physical Education and Recreation, 1968. 26 . Bevegard, S., "Studies on the Regulation of the C i r c u l a -t i o n of Man," Acta Physiologica Scandinavica, Volume 57, (Suppl. 200) , 1962-63. 27 . Holmgren, A., Astrand, P.O., "DL and the Dimensions and Functional Capacities of the Oxygen Transport Systems i n Humans," Journal of Applied Physiology, Volume 21 , 1966, pp. 1463-1470. 28. Linroth, K., "Physical Work Capacity i n Conscripts During M i l i t a r y Service," Acta Medica Scandinavica, Volume 157. (Suppl. 324, 1957. 29 . Garrett, H.E., S t a t i s t i c s i n Psychology and Education, David McKay Co., Inc., New York, I966. 30 . Macnab, R.B., "Commentary," The Canadian Medical Associa-t i o n Journal, Volume 96, 1967, p. 750. 3 1 . Cumming, G.R., Cumming, P.M., "Working Capacity of Normal Children Tested on the Bicycle Ergometer," The  Canadian Medical Association Journal, Volume 21 , 1966, pp. 1807-1814. 32 . Adams, H.A., Bengtsson, E.B., Birwan, H., Wegelius, C , "The Physical Working Capacity of Normal School Children (Sweden)," Pedia t r i c s, Volume 28, 1961, pp. 243-257. 130 33* Ahlborg, B... "Capacity, f o r Prolonged Physical Exercise i n Relation to Some Anthropometric and Other Data," Forvarsmedicin, Volume 3, (Suppl. 1 ) , pp. 194—202. 3 4 . Fleishman, E.A., The Structure and .Measurement of Physical Fitness, Prentice H a l l Inc., New Jersey, 1964. 3 5 . McNemar, Q., Psychological S t a t i s t i c s , John Wilson and Sons, New York, 1962. 36. Hays, W.L., S t a t i s t i c s , Holt Rinehart and Winston, New York, 1933". 37 . Wllmore, J.H., "Maximal Oxygen Intake and Its Relationship to Endurance Capacity on a Bicycle Ergometer," Research Quarterly, Volume 40, 1969, pp. 203-210. CHAPTER VI SUMMARY AND CONCLUSIONS The purpose of t h i s study was to determine the i n t e r r e -lationships between oxygen intake capacity, strength, body composition and physical working capacity. The subsidiary problems were: 1. to determine which s t a t i s t i c a l procedure, i . e . , zero order correlations, f i r s t order p a r t i a l c o r r e l a -tions, twenty-second order p a r t i a l correlations or stepwise multiple regression analysis, gave the greatest insight into the physiological r e l a t i o n -ships between the variables selected f o r th i s study, 2. to determine the form i n which the variables inves-tigated have most meaning b i o l o g i c a l l y , i . e . , as raw scores, as scores divided by body weight, or as scores divided by fa t free weight, 3. to determine the accuracy of cal c u l a t i n g PWC^yo by graphical estimation of the best f i t t i n g straight l i n e as compared with computer calculated values obtained by the least squares regression method. F i f t y - f o u r subjects from the School of Physical Educa-t i o n and Recreation at the University of B r i t i s h Columbia participated i n t h i s study. The Sjostrand PWC170 test was 132 conducted to estimate physical working capacity and an " a l l out" ride on the bic y c l e ergometer was administered to deter-mine maximum oxygen intake values. Body density was determined by the hydrostatic weighing technique and body f a t was calculated by the formula derived by Keys and Brozek (1). A comprehensive strength test was also conducted on a l l the subjects. The s t a t i s t i c a l analysis of the data were obtained through the Computing Center at the University of B r i t i s h Columbia (Program - Triangular Regression Package) (2). A zero order c o r r e l a t i o n analysis was conducted to assess the accuracy of the graphic method i n the c a l c u l a t i o n of PWC170 scores. A zero order c o r r e l a t i o n analysis was also conducted to i n v e s t i -gate the int e r r e l a t i o n s h i p s between a l l the variables when no variables were held constant. Two f i r s t order c o r r e l a t i o n analyses were conducted to Investigate the interrelationships between a l l the variables when a measurement of body size was held constant. The two measures of body size were body weight and f a t free weight. A twenty-second order c o r r e l a t i o n matrix was evolved i n order to investigate the relationships between two variables when a l l other variables were held constant. Histograms of a l l the variables were drawn to determine the forms of the d i s t r i b u t i o n s of the scores. Three stepwise multiple regression analyses were constructed to determine the interrelationships between each of 133 the dependent variables (PWC17Q kpm per min; PWC170 kpm per min per kg body weight; PWC170 kpm per min per kg f a t free weight) with two or more of the independent va r i a b l e s . On the basis of the s t a t i s t i c a l analysis and within the l i m i t a t i o n s of t h i s study, the following conclusions appear to be warranted: 1. The conventional graphic technique appeared to estimate the PWC170 scores accurately. 2. The r e s u l t s obtained i n t h i s study appeared to sup-port the use of performance scores divided by f a t free weight as the most b i o l o g i c a l l y meaningful way i n which to express performance capacity data. Fat free weight had s i g n i f i c a n t relationships with PWC170 kpm per min, oxygen intake i n l i t e r s per min and with most of the strength vari a b l e s . This showed that investigations of i n d i v i d u a l d i f f e r e n -ces i n various performance measures included i n thi s study would have to take into account the r e l a t i v e muscle mass. The d i v i s i o n of performance scores by fat free weight appeared to be the preferred method f o r comparisons of Individuals' "true" a b i l i t i e s or capacities without regard to differences i n body size or body f a t . Conse-quently, t h i s procedure appeared to be very appropriate f o r use i n normative tables. The 134 apparent normality of the d i s t r i b u t i o n of v a r i -ables divided by f a t free weight supported the s u i t a b i l i t y of t h e i r use i n normative tables. 3« In zero order correlations, the c o r r e l a t i o n c o e f f i -cients between PWC170 k P m P e r m i n a n ( i oxygen intake i n l i t e r s per min or strength (lbs) appeared to be spurious since the relationships -between these variables appeared to be par t l y due to i n d i v i d u a l differences i n body s i z e . 4. Although variables divided by f a t free weight appeared to be the most b i o l o g i c a l l y meaningful way to express performance capacity data, t h e i r employment i n co r r e l a t i o n analyses presented ce r t a i n d i f f i c u l t i e s , /when o r i g i n a l variables were transformed into r a t i o variables by means of div i d i n g by body weight or f a t free weight, the cor r e l a t i o n c o e f f i c i e n t s were d i f f e r e n t (smaller) from the c o e f f i c i e n t s of c o r r e l a t i o n between variables i n the o r i g i n a l form. They were also d i f f e r e n t (larger) from the values of the f i r s t order p a r t i a l c o e f f i c i e n t s when body size was held constant. Thus, d i v i d i n g o r i g i n a l variables by body weight or f a t free weight had a d i f f e r e n t effect from p a r t i a l l i n g out body weight or fat free weight. This could be attributed to 135 s t a t i s t i c a l a r t i f a c t . Dividing by body size appeared to influence spread or dispersion of scores with a corresponding effect on the size of the c o r r e l a t i o n c o e f f i c i e n t s . F i r s t order p a r t i a l correlations of non-ratio variables, with f a t free weight held constant, appeared to be the best s t a t i s t i c a l procedure i n providing insight into the physiological r e l a t i o n -ships between oxygen intake capacity, strength and physical working capacity (PWCi7o). The complex twenty-second order c o r r e l a t i o n analysis did not appear to provide any more insight into the interpretation of the r e l a t i o n s h i p between variables than was provided by the more simple f i r s t order c o r r e l a t i o n a n a l y s i s . The zero order c o r r e l a t i o n analysis, f i r s t order p a r t i a l c o r r e l a t i o n analysis and stepwise multiple regression analysis showed the following apparent relationships to exist between the variables explored i n t h i s study: i ) Fat free weight had the highest zero order cor-r e l a t i o n with PWC170 kpm per min and c o r r e l a -ted almost as highly with oxygen intake i n l i t e r s per min. It was also s i g n i f i c a n t l y related to most of the strength v a r i a b l e s . In 1 3 6 stepwise multiple regression analysis, f a t free weight appeared to be the best single predictor of PWC170 kpm per min. In f i r s t order p a r t i a l regression analysis, when fat free weight was held constant, the c o e f f i -cients of c o r r e l a t i o n between other variables were lower i n most instances than those obtained i n zero order c o r r e l a t i o n a n a l y s i s . It was evident that f a t free weight was the common factor In the relationships between many of the variables included i n t h i s study. Oxygen intake i n l i t e r s per min was s i g n i f i -cantly related to physical working capacity (PWC170 kpm per min) i n zero order and f i r s t order c o r r e l a t i o n analysis, ( s i g n i f i c a n t at the 0.01 l e v e l of confidence). In the step-wise multiple regression analysis, oxygen intake i n l i t e r s per min did not contribute to the prediction of PWC170 kpm per min. This would, however, have been the best single predictor i n the absence of f a t free weight. The apparent contribution of oxygen intake i n ml per min per kg body weight to the predic-t i o n of PWC170 kpm per min was considered to be a s t a t i s t i c a l a r t i f a c t and also devoid of 13? any physiological meaning. When PWC170 kpm per min was divided by body weight, the best single predictor was oxygen intake ml per min per kg body weight. When PWC170 kpm per min was divided by f a t free weight, oxygen intake ml per min per kg body weight remained the best single predictor variable: t h i s e f f e c t appeared to be due to the effect on the corre-l a t i o n size of the smaller dispersion of oxygen Intake ml per min per kg f a t free > weight scores. H i ) Strength of the ri g h t leg extensor muscles (lbs) correlated s i g n i f i c a n t l y with PWC170 kpm per min i n zero order and f i r s t order c o r r e l a t i o n analysis ( s i g n i f i c a n t at the 0.05 l e v e l of confidence). This variable made a small con-t r i b u t i o n to the prediction of physical working capacity i n a l l three stepwise multiple regression a n a l y s i s . Thus, i n th i s study, absolute strength correlated more highly than r e l a t i v e strength (lbs per kg body weight or fat free weight), not only with PWC170 kpm per min but also with PWC170 kpm per min divided by body weight or f a t free weight, iv) Body density correlated s i g n i f i c a n t l y with 138 PWC]_70 kpm per min per kg body weight i n zero order c o r r e l a t i o n analysis and with PWC270 kpm per min when body weight was s t a t i s t i c a l l y held constant ( s i g n i f i c a n t at the 0.01 l e v e l of confidence). In stepwise multiple regres-sion analysis, the contribution of body density to the prediction of PWC170 kpm per min per kg body weight was only s l i g h t l y less than oxygen intake ml per min per kg body weight, / i n t h i s study, i t appeared that when the PWC170 kpm per min was divided by body weight or when body weight was s t a t i s t i c a l l y held constant, the physical working capacity score increased with greater density. Thus, leaner subjects appeared to a t t a i n higher PWC170 kpm per min per kg body weight scores. On the basis of the findings i n th i s study, the follow-ing recommendations appear to be warranted: 1. The extent of the int e r r e l a t i o n s h i p s of the v a r i -ables investigated i n th i s study should be established f o r the treadmill and bench stepping t e s t s , so that the r e l a t i v e physiological s i g n i -ficance of these tasks can be more e f f e c t i v e l y compared and evaluated. 2. F i r s t order p a r t i a l correlations with f a t free 139 weight held constant should be used to esta b l i s h a more meaningful relationship between the Sjostrand PWC170 test and such physiological para-meters as stroke volume, heart volume, blood volume and t o t a l hemoglobin. A biochemical analysis of the acid buffering, f a t t y a c i d and carbohydrate u t i l i z a t i o n capacities of subjects at a heart rate of 170 beats per minute may enhance the understanding of the physiological manifestations of such work tasks as the Sjostrand PWC170 t e s t . REFERENCES Keys, A., Brozek, J., "Body Fat i n Adult Man," Physiologi- c a l Reviews, Volume 33, 1953. pp. 245-325. Dempster, J.H., Gagne, A.E., Hogan, R., U.B.C. TRIP (Triangular Regression Package), University of B r i t i s h Columbia Computing Center, 1968. BIBLIOGRAPHY A. BOOKS Astrand, P.O. Experimental Studies of Physical Working Capacity i n Relation to Sex and Age. Copenhagen, Ejnar Munksgaard, 1952. . Work Tests on the Bicycle Ergometer. Dept. of Physiology, Gymnastika Centralinstituent, Stockholm, Sweden. Clarke, H., Clarke, D. Developmental and Adapted Physical  Education. Prentice H a l l Inc., New Jersey, 1963. Consolazio, F.C., Johnson, R.E., Pecora, L.J. 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"Determination of Physical Working Capacity," Acta  Medioa Scandinavica. Volume 132, (Suppl. 215 ) , 1948. Welch, B.E., Riendeau, R.P., Crisp, C.E., Isenstein, R.S. "Relation of Maximum Oxygen Consumption to Various Compon-ents of Body Composition," Journal of Applied Physiology, Volume 12 , 1958, pp. 395-398. Wendelin, H., Heikklnen, P., Hirvonin, L. "The Physical Fitness of University Students," Journal of Sports Medicine  and Physical Fitness. Volume 5-6, 1965-1966, pp. 2 2 4 - 2 3 2 . Wilmer, J.H. "Maximal Oxygen Intake and Its Relationship to Endurance Capacity on a Bicycle Ergometer," Research  Quarterly, Volume 4 0 , 1969, PP- 203-210. Wyndham, CH. "Submaximal Tests f o r Estimating Maximum Oxygen Intake," Canadian Medical Association Journal, Volume 96, 1967, PP. 7 3 6 - 7 4 1 . Wyndham, C.H., Strydom, N.B., Maritz, J.S., Morrison, J.F., Peter, J., Potzieter, Z. "Maximum Oxygen Intake and Maximum Heart Rate During Strenuous Work," Journal of  Applied Physiology, Volume 1 4 , 1959, PP- 927-936. C. UNPUBLISHED REFERENCES Bakogeorge, A.P. "The Relationship of Selected Anthropometri-c a l and Physiological Variables to the Balke Treadmill Test and a Terminal Step Test and Test Interrelationship." Unpublished Master's Thesis, University of Alberta, Edmonton, 1964. 147 Boyd, W.R. "A Phase Plane Analysis of Physical Working Capacity." Unpublished Master's Thesis, University of B r i t i s h Columbia, 1967. C a r r a l l , P.J. "Heart Hate Responses to Bicycle Ergometer Exercise as a Function of Physical Fitness." Research Unit Report 6-M 1967. University of Alberta, 1967. Coyne, L.L. "The Relationship of Maximal Oxygen Intake to Body Composition and Total Body Weight i n Active Males." Unpublished Master's Thesis, University of Alberta, 1963 • Yuhasz, M. "The Effects of Sports Training on Body Fat i n Man with Prediction of Optimal Body Weight." Unpublished Doctoral Dissertation, University of I l l i n o i s , 1962. Zahar, W.E.R. " R e l i a b i l i t y and Improvement with Repeated Performance of the Sjostrand Work Capacity Test." Unpub-li s h e d Master's Thesis, University of Alberta, 1965« APPENDIX A STATISTICAL TREATMENT 149 STATISTICAL TREATMENT Calculation of PWCipc The value of PWC170 was deter-mined "by a manual method and by computer. In the manual procedure, f o r each test a graph was prepared with the steady state heart rate plotted against work load at each of the three l e v e l s of work. The best f i t t i n g straight l i n e through the. three points determined the PWC170 value corresponding to a heart rate of 170 beats per min. The computer procedure was very similar, i n that a regression relationship was developed between the two variables and the PWC^^Q value was extrapolated from the regression l i n e . The computer program was developed s p e c i f i c a l l y f o r t h i s study at the University of B r i t i s h Columbia Computing Center. The means, standard deviations and c o r r e l a t i o n c o e f f i -cient of the two techniques were obtained through the U.B.C. Computing Center - Triangular Regression Package Program (1). The means were calculated using the following formula: where k = variable n = number of observations The standard deviations were determined employing the following formula: 150 where k = variable n = number of observations In determining the c o r r e l a t i o n c o e f f i c i e n t between variables X m and X c the following formula was used: rme = jg?=i X m l X c l - nX mX c (n-l) S m S c where X m = manual estimations of PWC170 Xc = computer estimations of PWC170 Correlation Analysis. The U.B.C. Computing Center program TRIP (1) was also u t i l i z e d to determine means, standard deviations and c o r r e l a t i o n c o e f f i c i e n t s of a l l the variables included i n t h i s study and the s t a t i s t i c a l treatment have pre-viously been discussed. The i n t e r c o r r e l a t l o n matrices of the twenty-four variables involved are presented i n Appendix C. Multiple Regression Analysis - Stepwise Procedure. The TRIP (1) program was employed to obtain the "best f i t " of a set of observations of independent and dependent variables by an equation form (1:4?): Y = b Q + b]Xi + b 2X 2 + ... + bmXm where Y = dependent variable XjX 2 = independent variables bobi = c o e f f i c i e n t s to be determined In the stepwise procedure, the regression equations are 151 obtained by adding one variable at a time. The variable added i s that one which makes the greatest improvement i n "goodness of f i t " or, i n other words, the greatest contribution to the variance of the dependent va r i a b l e . a) b C o e f f i c i e n t s . The following formula was employed: b i = SytiY f o r 1>1 Si where b i = b c o e f f i c i e n t of the i t h variable S y = standard deviation of the dependent variable S i = standard deviation of the i t h independent variable t^Y = p a r t i a l l y inverted matrix *>o = X y - £ m = 1 b X where X y = mean of the independent variable m = number of independent variables b) F-ratios and associated p r o b a b i l i t y for each b i . An F-test was performed to test the significance of each regression c o e f f i c i e n t b i . The F-value was calculated by the formula: 1 f — — r 2 F i (l.n-m-l) = b l s.e.(bi) where n = number of observations m = number of independent variables 152 If the P p r o b a b i l i t y i s less than 0 .05 , i t i s usually concluded that bj[ i s s i g n i f i c a n t l y d i f f e r e n t from zero (1 :49 )• The standard error of Y. The standard error of Y, sometimes called the standard error of estimate, i s the number where n = number of observations m = number of independent variables Y i = the i t h observed value of Y Yi = the i t h predicted value of Y B.2, the c o e f f i c i e n t of multiple determination. R 2 i s the proportion of the t o t a l observed variance of Y which i s accounted f o r by the regression l i n e . Thus, .n _ 2 is i-i <*i - Y ) where Yi = the i t h predicted value of Y Yj^ = the i t h observed value of Y Y = the mean of the observed value of Y R, c o e f f i c i e n t of multiple c o r r e l a t i o n . The posi-t i v e square root of R 2 i s called the c o e f f i c i e n t of multiple c o r r e l a t i o n . It i s the same co r r e l a t i o n of Y and Y. 153 f) F-value f o r the entire equation. This p r o b a b i l i t y i s the p r o b a b i l i t y of obtaining a value of R 2 greater than or equal to the one calculated. If th i s p r o b a b i l i t y i s less than 0 . 05 , i t i s usually concluded that R 2 i s s i g n i f i c a n t l y d i f f e r e n t from zero. The F-value i s calculated by: 0 / ™ v, m 11 _ R 2 n-m-1 F (m,n-m-1) = *• 1-R2 m where n = number of observations m = number of independent variables g) B C o e f f i c i e n t s . The B c o e f f i c i e n t s were determined through the D o l l t t l e - s o l u t i o n Operations (2:442). Example of the operation i s presented f o r the dependent variable PWC170 kpm per min X^. Dependent Variable X i Column Number 2 3 4 1 Check Row Variable *5 * 8 * l 4 X l Sum Instructions A r 5 k 1.0000 -0.3639 0.4223 0.6293 1.6877 B A* (-A2) -1.0000 +0.3639 -0.4223 -0.6293 -1.6877 C 1.0000 -0.0904 0.1025 1.0121 D A x B3 -0.1324 0.1537 0.2290 0.2503 E C +D 0.8676 0.0633 0.3315 1.2624 F E * (-E3) -1.0000 -0.0730 -0.3821 -1.4551 G r i 4 k 1.0000 0.4632 1.7951 H A x B4 -0.1783 -0.2658 -0.7127 I E X F4 -0.0046 -0.0242 -0.0916 J G + H + I 0.8171 0.1732 0.9903 K J * (-J4) -1.0000 -0.2120 -1.2120 154 B 1 1 M 5 8 ) = " K 1 Bl8(5l4) = -P1+ (-K1)(F4) Bl5(8l4) = -B + (-K1)(B4) + (B (514))(B3) Coe f f i c i e n t of multiple determination R 2 was then expressed as: H1(5814) = B15.814 r 1 5 + B18.514 r l 8 + B 1 1 4 . 5 8 r l l 4 Analysis of variance. Analysis of variance tech-nique was employed to assess the contribution of independent variables to the variance of dependent variabl e s . An example of the c a l c u l a t i o n Is i l l u s t r a t e d i n the following Table ( 3 ) . 155 ANALYSIS OF VARIANCE FOR DEPENDENT VARIABLE X Source of Variance df Sum of Squares Mean of Percent Squares of Variance Step I Due to Re-gression 1 . due to Xj 1 Error N-2 To t a l V a r i - N-l ance Step II Due to Re-gression 2 due toXj 1 due to 2§ 1 Error N-3 Tota l V a r i -ance N-l Step III Due to Re-gression 3 due to X5 1 due t o X s l due toXl4- 1 Error N--4 Tota l V a r i -ance ( N - I ) S | R | . X 5  ( N - 1 ) s f r y x 5 V 5 (N-1)S|(1-E 2.X 5) (N-l)Sy ( N - D s V ^ . B ^ . x S (N-l)sV yx5.B y x 8 < x 5 ( N - I ) S | ( I - H | . X 5 X ( f c l ) S y (N-l)S^yR|.x5x8xl4 (N-l)Syryx 5 .Byx5.x 8 x l2 1 / ( N - l ) S y r y x 8 . B y 8 > X 5 X l i + (N-l)sVyxl4. Byxl4.X 5X 8 (N-l) (1-R|.x5x8xl4) Sum-of Sum of Squares Squares df Total Variance (4-l)S 2y N-l (N^l)S y WhereJ y = dependent variable X N = number of observations df = degrees of freedom X^XQX^ = independent variables APPENDIX B SAMPLE DATA SHEETS 157 THE SJOSTRAND TEST OF PHYSICAL WORK CAPACITY NAME AGE WEIGHT DATE SCHOOL •" Test 1 Test 2 Test 3 Min. KP = Min. KP. = Min time 1 r n t p 1 time ra+.f* 1 time time 2 rate 2 time rate 2 time rate time 3 rate 3 time rate 3 time rate time 4 rate 4 time rate 4 time rate time 5 rate 5 time rate 5 time rate time 6 rate 6 time rate 6 time rate 180 170 160 150 140 130 120 110 100 TSTT "36TT 540 720" 1260 TWO W0RK LOAD (KPM) 158 BODY DENSITY TEST NAME TIME ROOM TEMP. WEIGHT DRY, IN SWIM SUIT VITAL CAPACITY IN WATER WEIGHT IN WATER SPIROMETER READING WHEN WEIGHED DATE PLACE WATER TEMP. TRIAL lb s . 1 2 3 4 TRIAL TRIAL 1 2 3 4 1 2 3 4 kgs. LITRES kgs. LITRES WEIGHT OP EQUIPMENT IN WATER kgs, BODY DENSITY DETERMINATIONS BY UNDERWATER WEIGHING CALCULATIONS  NAME DATE Conversions (1) Weight of Body i n A i r lbs.*2.2046 = Kgs. (2) Temp. - of Water °P - 32 = x 5= °C (3) Temp, of A i r °p - 32 = x £=' ° c 9 (4) Barometer Pressure M i l l i b a r s = mmHg. (5) Density of Water at °c Water Temp. Scale Weight at (A) F u l l I n s p i r a t i o n (6) Lowest Weight = Kgs. (7) Weight of Sinkers = Kgs. (8) Weight without Sinkers = Kgs. C o r r e c t i o n f o r A i r l n Lungs (9) Best V.C. submerged at Room T.emp.( °C)= L i t r e s A.T.P.S. (10) V.C. Corrected f o r 37°C (Sat.) V.C. Y 310 x 310= L i t es Corrected B.T.P.S. 1 273"+Room T.emp.^ c I (11) 30$ of Corrected V.C. .30 x (10) = L i t r e s Res. Lung V o l . (12) A i r Inhaled at Weigh. Corrected f o r 37°C. (Sat) hi** 3102 ^ = _ x _ J 1 0 ° = L i t . Corrected B.T.P.S. 273° + Room Temp.°C 1 (13) Add (11) and (12) = L i t r e s T o t a l Lung V o l . at 37°C (14) M u l t i p l y (13) by Density of Water at Water Temp, x Density = Lung V o l . (15) i n Kgs. Weight without Sinkers Kgs. (8) Pl u s Lung Volume i n Kgs. Kgs. (15) (16) Weight of Body i n Water (Corrected f o r A i r i n Lungs) = Kgs.(8*15) Body = Weight of Body l n A i r xDensity of Density Weight of Body l n A i r - C o r . Wt. of Water at Body i n Water Water Temp. = , (1) x (5) = x = (1) - (16) 1 _ _ _ _ #Body Fat (4.201 - 3.813 x 100 = % 5 1 Body Wt. = Kgs. l b s . Fat Wt. = Kgs. l b s . Fat Free Wt.= Kgs. l b s . 160 VITAL CAPACITY NAME . ROOM TEMPi TRIAL 1 . TRIAL 2 , TRIAL 3 DATE TIME BAROMETRIC PRESSURE L i t r e s L i t r e s L i t r e s OXYGEN CONSUMPTION DATA SHEET DATE BAR PRESS SUBJECT AGE ROOM TEMP. TYPE OP EXERCISE REL. HUMIDITY Min.of Exercise H. R. 45-60 sec. Temp. Vent. Corr.Fact. x Volume Corr.Vol. L/M St a r t j Sample 1 ! » 2 tt 3 It 4 • • • ' It 5 tt 6 - -Sample Determined % RQ True 0 2xCorr. Vdl.=0 2 Intake L/M co 2 o 2 N 2 1 2 3 4 5 6 TIME OF EXERCISE AND WORK LOAD: MIN Kp RPM Kpm/M 162 STRENGTH VARIABLES NAMEs D A T E . TESTER Hand Grip 1. Right Grip T r i a l 1. 2. 3. 2. Left Grip T r i a l 1. 2. 3. 3. Pushing Strength T r i a l 1. 2. 3. 4 . P u l l i n g Strength T r i a l 1. 2. 3. 5. Back L i f t T r i a l 1. 2. 3. 6. Leg L i f t T r i a l 1. 2. 3. 7. Trunk Flex T r i a l 1. 2. 3. 8. Trunk Extension T r i a l 1. 2. 3. 9. Knee Ext. Right T r i a l 1. 2. 3. 10. Knee Ext. Left T r i a l 1. 2. 3. 163 COMPOSITE DATA SHEET NAME V i t a l Capacity l i t r e s = PWC 1 7 0 Kgm/min/Kg body weight = Kgm/min/Kg fat free weight= 0 2 INTAKE Litres/min mls/kg/min Actual body wt.= mls/kg/min fat free weight= STRENGTH Push P u l l Trunk Flezion Trunk Extension Knee Ext. Right Knee Ext. Left Knee Ext. Average TOTAL DYNAMOMETER  Combined Strength Right Grip = Left Grip = Back = Leg " "" = Tota l T o t a l Strength Actual Body Weight Tot a l Strength Fat Free Weight APPENDIX C RAW SCORES AND CORRELATION MATRICES RAW SCORES (1966-1967) PWC170kpm Subiect 1 Min IO68.O 2 1175.6 3 1125.9 4 824.4 5 1179.0 6 1147.5 7 1024.3 8 1564.0 9 1406.9 10 1106.8 11 977.1 12 979.3 13 977.7 14 766.8 15 1014.5 16 925.2 17 1083.0 18 712.8 19 1481.4 20 1190.0 21 1181.0 22 1243.5 23 1274.0 24 1224.7 25 1299.4 26 940.0 27 1336.2 PWC17okpni/ Min/Bodv Wt. PWCi7okpm/Min/ Body Wt. Pat Free Fat Free Wt. kgs. Wt. kas. V i t a l Capacity L i t r e s 13.45 16.27 15.^7 11.22 14.98 16.24 14.25 19.00 19.76 14.06 14.56 10.52 11.42 12.90 14.00 16.45 15.73 11.77 17.46 15.78 16.17 13.34 16.95 13.64 13.62 10.57 15.65 14.53 17.92 16.26 13.24 16.80 17.15 16.28 20.61 20.56 15.68 15.54 12.29 12.84 13.89 14.89 17.98 16.54 12.67 19.56 17.06 17.97 15.30 17.19 16.51 17.88 12.14 17.17 79.37 72.24 72.80 73.48 78.69 70.65 71.90 82.32 71.21 78.70 67.10 93.10 85.62 59.42 72.46 56.24 68.83 60.56 84.82 75-41 73.02 93.21 75.18 89.81 95.37 88.91 85.40 73.50 65.59 69.23 68.26 70.19 66.91 62.91 75.90 68.43 70.59 62.87 79.69 76.12 55.20 68.11 51.46 65.46 56.26 75.7^ 69.83 65.72 81.28 74.13 74.18 72.69 77.44 77.80 4.98 4.98 5.41 5.83 5.19 5.04 5.35 5.9^ 6.41 6.15 5.09 5.96 6.52 3.92 4.56 4.08 4.77 4.93 6.55 6.57 6.60 5.22 5.19 4.53 6.25 5.88 5.71 H ON vn RAW SCORES (1966-1967 Con't.) Oxygen Intake Oxygen Intake Oxygen Intake Subject I/Min ml/Min/Body ml/Kin/Fat Weight Free Weight Trunk Pull Push Strength Strength Strength lbs. lbs. lbs. 160.0 106.0 160.0 108.0 96.0 189.5 132.0 94.0 160.0 106.0 98.0 115.0 124.0 78.0 183.0 124.0 93.0 130.0 132.0 100.0 145.0 132.0 119.0 189.5 122.0 92.0 140.0 138.0 98.0 170.0 94.0 141.0 88.0 110.0 123.0 150.0 148.0 111.0 160.0 99.0 85.0 189.5 122.0 103.0 130.0 93.0 75.0 120.0 97.0 72.0 153.0 108.0 109.0 105.0 140.0 103.0 196.0 131.0 111.0 130.0 122.0 102.0 155.0 112.0 80.0 170.0 128.0 99.0 130.0 150.0 113.0 176.5 130.0 99.0 135.0 144.0 98.0 235.0 125.0 108.0 176.5 1 4.03 50.77 2 3.86 53.43 3 3.40 46.70 4 2.79 37.97 5 3.56 45.24 6 3.40 48.12 7 3.20 44.51 8 4.35 52.84 9 3.85 54.07 10 3.90 49.56 11 2.92 43.52 12 4.09 43.93 13 4.53 40.12 14 3.20 53.85 15 3.80 52.44 16 2.99 53.17 17 3.44 49.98 18 3.57 58.95 19 5.13 60.48 20 4.60 61.00 21 3.65 49.99 22 3.74 40.12 23 4.03 53.60 24 3.72 41.42 25 3.62 37.96 26 3.50 39.37 27 4.64 54.33 54.83 58.85 49.11 40.87 50.72 50.81 50.87 57.31 56.26 52.25 46.45 51.32 46.01 57.97 55.79 58.10 52.55 63.46 67.73 65.88 55.54 46.01 54.36 50.15 49.80 45.20 59.64 RAW SCORES (1966-1967 C o n ' t . ) Trunk Right Knee Lef t Knee Knee Extension Right Grip Lef t Grip Subject Extension Extension Extension Average Strength Strength l b s . l b s . l b s . l b s .  1 170.0 361.5 411.5 386.0 2 160.0 310.0 302.5 306.0 3 150.0 310.0 295.0 302.0 4 183.0 228.5 250.0 239.2 5 222.0 373.0 373.0 373.0 6 125.0 302.5 310.0 306.2 7 183.0 257.5 272.5 265.0 8 242.5 373.0 319.5 346.0 9 165.0 361.5 339.5 350.5 10 165.0 265.0 295.0 280.0 - . -11 85.0 295.5 295.0 295.0 152 122 -0 12 215.5 329.0 350.0 339.0 13 250.0 242.5 250.0 246.2 14 110.0 228.5 215.5 222.0 15 189.5 280.0 265.0 272.0 16 135.0 189.5 250.0 219.7 17 130.0 280.0 257.5 268.7 18 125.0 170.0 215.5 192.7 19 212.0 306.0 339.5 322.7 20 167.5 242.5 228.5 235.5 21 189.5 339.5 319.5 329.5 22 272.5 250.0 269.0 159.0 23 120.0 287.0 272.5 280.0 24 202.5 356.0 298.5 327.0 25 170.0 287.5 339.5 313.5 26 222.0 302.5 302.5 302.5 27 222.0 302.5 257.5 280.0 l b s . l b s . 163 139 142 121 131 123 129 130 138 126 127 108 137 121 153 142 122 110 155 141 1  122 136 120 143 121 127 108 121 122 102 96 153 103 111 94 126 117 137 132 147 125 133 112 153 129 152 135 121 118 179 158 143 132 RAW SCORES (1966-1967 don't.) Back Leg Total Total Total Body Subject Strength Strength Strength Strength Strength Density l b s . l b s . l b s . /Body Wt. Aat Free Wt. 1 737 1470 2 480 978 3 612 1400 4 528 1084 5 559 1370 6 465 1100 7 594 1092 8 635 1235 9 500 1186 10 696 1168 11 500 970 12 535 1350 13 542 1332 14 512 734 15 520 1040 16 390 770 17 386 1265 18 464 775 19 650 1300 20 439 1147 21 510 1095 22 511 1290 23 452 1320 24 540 1268 25 632 1359 26 642 1500 27 608 1411 2509 14.34 15.48 1.081 1721 10.81 11.90 I.076 2266 14.12 14.85 1.088 1871 11.55 12.43 1.082 2193 12.64 14.17 1.074 1800 11.56 12.20 1.084 1944 12.26 13.92 1.067 2155 H . 8 7 12.88 1.080 1918 12.22 12.71 1.091 2160 12.45 13.88 1.073 1744 11.79 12.58 1.084 2141 10.43 12.19 1.062 2138 11.33 12.74 1.071 1481 11.30 12.17 1.082 1803 11.29 12.01 1.085 1358 10.95 11.97 1.078 1889 12.45 13.09 1.088 1444 10.82 11.64 1.082 2193 H . 7 3 13.13 1.072 1855 11.16 12.05 1.081 1877 11.66 12.95 1.074 2046 9.96 11.42 1.066 2054 12.39 12.57 1.091 2095 10.58 12.81 1.054 2230 10.61 13.91 1.065 2479 12.65 14.52 1.066 2294 12.18 13.37 1.077 RAW SCORES (1967-1968) P w C 1 7 G k p m Subject Min PWCnookprn/ Min/Body Wt. P W G170kpm/Min/ Body Wt. Fat Free Pat Free Wt. kgs. Wt. kgs. V i t a l Capacity L i t r e s 1 956.8 2 1280.8 3 1069.5 4 1398.4 5 1311.3 6 1006.2 7 1055.3 8 795.7 9 1379.4 10 1147.5 11 1155.7 12 1296.0 13 970.7 14 1059.0 15 1178.9 16 1273.1 17 1336.6 18 1011.0 19 1565.9 20 1314.7 21 1025.3 22 1243.2 23 1105.4 24 1100.4 25 1040.7 26 1244.2 27 1181.2 15.31 18.64 16.40 19.70 13.95 15.25 15.03 13.22 16.11 17.66 12.90 16.59 13.31 15.94 14.77 16.18 12.01 15.18 18.46 15.84 13.53 16.97 15.77 16.97 15.14 16.28 15.39 15.92 19.88 17.71 20.30 16.48 17.56 15.61 15.23 17.25 18.70 16.11 18.21 16.34 17.49 15.86 18.47 14.00 16.12 19.67 16.92 14.76 17.34 16.81 17.95 15.54 16.91 15.96 62.48 68.72 65.21 70.99 94.01 6^.99 70.19 60.21 85.62 64.98 89.59 78.13 72.91 66.45 79.83 78.70 111.24 66.91 84.82 83.01 75.75 73.25 70.08 64.86 68.72 76.43 76.77 60.11 64.41 60.38 68.90 79.55 57.29 67.61 52.25 79.94 61.36 71.72 71.18 59.42 60.54 74.32 68.94 95.44 62.70 79.62 77.70 69.46 71.71 65.74 61.29 66.96 73.59 74.01 3.32 5.83 4.85 5.13 5.75 4.20 5.11 5.05 5.65 3.60 5.73 5.81 4.38 5.46 4.68 5.50 4.80 5.63 5.65 4.82 6.53 4.42 4.85 5.75 4.50 5.05 H o\ RAW SCORES (1967-1968 Con't.) O x y g e n O x y g e n Subject, Intake Intake O x y g e n " Intake ml/ Min/Fat Free Wt. Trunk P u l l Push Strength Strength Strength l b s . l b s . l b s . 150.0 102.0 137.0 100.0 79.0 132.0 123.0 83.0 86.0 110.0 81.0 179.0 156.0 122.0 219.0 119.0 91.0 122.0 130.0 88.0 179.0 100.0 88.0 142.0 125.0 91.0 190.0 95.0 145.0 102.0 82.0 100.0 162.0 130.0 90.0 157.0 101.0 88.0 152.0 110.0 111.0 122.0 96.0 93.0 137.0 150.0 79.0 132.0 150.0 85.0 117.0 125.0 75.0 157.0 140.0 .120.0 168.0 127.0 119.0 152.0 135.0 109.0 157.0 118.0 100.0 179.0 114.0 89.0 132.0 106.0 85.0 101.0 101.0 82.0 127.0 121.0 109.0 168.0 150.0 130.0 137.0 1 3.12 49.94 2 4.42 64.32 3 3.96 60.73 4 3.46 48.74 5 3.57 37.97 6 3.09 46.82 7 3.55 50.58 8 3.29 54.64 9 4.88 57.00 10 3.68 56.63 11 3.63 40.52 12 4.29 54.98 13 3.62 49.65 14 3.72 48.58 15 3.63 45.47 16 3.69 46.89 17 4.48 40.27 18 3.73 55.75 19 4.43 52.25 20 4.65 56.02 21 3.49 46.07 22 3.42 46.69 23 3.79 54.08 24 3.45 53.19 25 3.52 51.22 26 3.63 47.49 27 4.10 53.41 51.90 68.62 65.58 50.22 44.88 53.94 52.51 62.96 61.05 59.97 50.61 60.27 60.92 3.39 8.84 53.52 46.94 .49 55.64 59 59.84 50.24 47.69 57.65 56.29 52.57 49.33 55.40 RAW SCORES (1967-1968 Con't.) Trunk Right Knee Left Knee Knee Extei Subject Extension Extension Extension Average l b s . l b s . l b s . l b s . Strength Strength l b s . l b s . 123 140 114 106 144 129 134 111 147 130 140 115 130 110 117 119 128 111 117 97 133 130 130 120 120 115 112 98 147 122 120 130 128 110 130 127 121 111 179 168 150 138 172 135 127 108 137 111 150 133 133 105 137 128 1 127.0 226.0 262.0 244.0 2 136.0 236.0 251.0 243.5 3 108.0 219.0 202.0 210.5 4 213.0 301.0 277.0 289.0 5 157.0 255.0 277.0 266.0 6 97.0 241.0 255.0 248.0 7 196.0 329.0 291.0 310.0 8 152.0 269.0 277.0 273.0 9 241.0 367.0 301.0 334.0 10 157.0 213.0 219.0 216.0 11 173.O 284.0 291.0 287.5 12 168.0 255.0 277.0 266.0 13 196.O 277.0 226.0 251.5 14 173.O 226.0 162.0 194.0 15 168.0 219.0 226.0 222.5 16 173.0 262.0 277.0 269.5 17 241.0 269.0 262.0 265.5 18 233.0 241.0 241.0 241.0 19 162.0 301.0 310.0 305.5 20 226.0 348.0 357.0 352.5 21 202.0 255.0 319.0 287.0 22 157.0 348.0 310.0 329.0 23 152.0 226.0 277.0 251.5 24 142.0 262.0 269.0 265.5 25 127.0 269.0 301.0 285.0 26 142.0 173.0 269.0 221.0 27 219.0 291.0 291.0 291.0 SAW SCORES (1967-1968 Con't.) ! Blck Lei Total Total Total Body Subject Strength Strength Strength Strength/ Strength/ Density I D S , lbs. lbs. Body Wt. Fat Free Wt. kgs/cnH 1 5 3 8 1178 1979 14.37 14.93 1 . 0 9 0 2 5 1 5 1102 1837 12.12 12.94 1.084 3 416 1 0 3 0 1719 11 . 9 6 - 12 . 9 1 1.081 4 540 1035 1820 11.63 11.98 1.094 5 460 1100 1837 8.86 10.47 1.059 6 5 0 5 1080 1840 12 . 6 5 14.57 1 . 0 6 5 7 5 1 0 1280 2 0 3 0 13.12 12.82 1.087 8 445 943 1 6 2 4 12 . 2 3 14.10 1.065 9 5 7 5 9 6 8 1782 9.44 10.11 1.083 10 535 1 0 9 2 1841 12.85 13 - 6 1 1.086 11 5 4 0 1110 1913 9-69 12.08 1.047 12 5 3 0 1 0 9 0 1870 10.86 11 . 9 2 1.077 13 4 5 8 1 0 9 0 1783 11 . 0 9 13.61 1 . 0 5 1 llj 428 780 1418 9.68 10 . 6 2 1.077 15 498 1 0 3 5 1802 10.24 10.99 1.082 IS 470 1040 1760 10.14 11.58 1.067 17 580 1138 1 9 5 6 7.98 9 - 3 0 1 . 0 6 2 18 5 0 0 1040 1797 12.83 13-00 1.084 1 9 5 8 5 1770 2087 H.16 H.89 1 . 0 8 5 20 602 1390 2 3 3 9 17.78 13.65 1.084 21 615 1 0 5 2 1 9 5 5 11.71 12.77 1.078 22 515 1115 1937 11.99 12 . 2 5 1.096 2 3 4 9 0 1080 1805 11.68 12.45 1.084 24 460 993 1701 11.89 12.59 1.086 2 5 4 9 2 1142 1917 12.65 12.99 1 . 0 9 5 26 380 810 1428 8.47 8.80 1 . 0 9 1 2 7 6 5 8 1 5 7 5 2498 14.76 15.31 1.092 1 1.0000 0.6412 0.7128 0.5233 0.6293 0.4091 0.6225 0.1025 0.0932 0.3116 0.1927 0.3035 0.3395 0.4632 0.3614 0.3959 0.1240 0.0982 0.2662 0.3373 0.3338 - 0 . 2 0 5 8 -0 .2427 0.0798 10 1.0000 0.5166 0.3728 0 . 3 9 H 0.3373 ZERO ORDER CORRELATION COEFFICIENTS 3 4 5 6 8 1.0000 0.9323 •0.3091 •0.1216 0.0117 0.2239 0.5617 0.4199 •0.2144 •0.1360 0.0717 •0.1867 0.1678 0.0398 0.1422 •0.1295 •0.1975 •0.1425 •0.0965 0.1325 O.I696 •0.0528 0.5409 1.0000 -0.1481 -0.0872 0.0775 0.2398 0.4277 0.4117 •0.1439 -0.1225 -0.0276 -0.1156 0.1997 0.0736 0.1672 -0.1977 -0.1851 -0.0975 -0.0762 -0.1079 0.0215 -0.0537 0.2374 1.0000 0.9202 0.4828 0.5048 -0.5193 -0.3765 0.6181 0.3477 0.4155 0.6273 0.3732 0.3893 0.3177 0.2893 0.3146 0.4598 0.5283 0.5528 -0.4513 -0.2522 -0.5054 1.0000 0.5015 0.5973 •0.3639 -0.3600 O.5898 0.3740 0.4161 0.6225 0.4223 0.4180 0.3624 0.3850 0.3350 0.4679 0.5701 0.5919 -0.3266 -0.2931 -0.1625 1.0000 0.4759 -0.1060 -0.0682 0.2681 0.2722 0.3072 0.3596 0.4158 O.3525 0.3904 0.2994 0.2782 0.3101 0.3570 0.3834 -0.1419 -0.0812 -0.0928 1.0000 0.4147 0.4734 0.3774 0.3429 0.2194 0.4961 0.2976 0.1895 0.2504 0.0830 0.1392 0.3426 0.3661 0.3781 -0.1471 -0.1630 -0.0275 1.0000 0.9250 -0.2967 -0.0972 -0.2323 -0.2266 -0.0904 •0.1740 -0.0702 -0.2411 •0.1882 -0.1440 •0.2049 -0.2162 0.3042 0.0939 0.4729 1.0000 -0.2306 -0.0764 -0.1931 -0.1405 -0.0804 -0.1686 -0.0677 -0.3259 -O.I896 -0.1190 -0.1949 -0.2065 0.1608 0.1085 0.1294 11 12 13 14 15 16 17 18 1.0000 0.1859 1.0000 0.2279 0.4551 1.0000 0.1712 0.4775 0.4011 1.0000 ZERO ORDER CORRELATION COEFFICIENTS (Con't.) NAME 10 15 0.4353 16 0.4100 17 0.2697 18 0.5006 19 0.5420 20 0.5603 21 0.6105 22 0.0229 23 0.1427 24 -0.3144 19 19 1.0000 20 0.6298 21 0.8002 22 0.3652 23 0.4779 Zk -0.0997 11 12 0.2052 0.4071 0.2364 0.4208 0.2382 0.3921 0.3359 0.3520 0.3691 0.3652 0.3157 0.3084 0.3716 0.3735 -0.0182 -O.0767 0.0291 0.0033 -0.0889 -0.2137 20 21 1.0000 0.9642 1.0000 0.4722 0.4810 0.5714 0.5893 -0.0691 -0.0836 13 14 0.2637 0.7602 0.2462 0.9H3 0.1430 0.4483 0.2703 0.4119 0.4674 0.4823 0.4449 0.5677 0.4831 0.6014 -0*1450 0.2287 -0.0534 0.2839 -0.2856 -0.0399 22 23 1.0000 0.8972 1.0000 0.4411 0.0372 15 16 1.0000 0.8852 1.0000 0.4182 0.4432 0.4353 0.4498 0.5746 0.5350 0.5719 0.5396 O.6326 0.5991 0.2444 0.2831 0.3223 0.3391 -0.0245 0.0089 24 1.0000 17 18 1.0000 0.7539 1.0000 0.3406 0.4967 0.4699 0.5245 0.5419 0.6285 0.2463 0.3265 0.2349 0.3949 0.0500 -0.1101 H -O FIRST ORDER PARTIAL CORRELATIONS (BODY WEIGHT PARTIALLED) NAME 1 1 1.0000 2 0.9908 3 0.9377 4 0.0000 5 0.4430 6 0.2096 7 0.4872 8 0.5138 9 0.3675 10 -0.0176 11 0.0135 12 0.1111 13 0.0170 14 0.3388 15 0.2010 16 0.2842 17 -0.0336 18 -0.0821 19 0.0338 20 0.0841 21 0.0627 22 0.0399 23 -0.1343 24 0.4681 10 10 1.0000 11 0.4094 12 0.1622 13 0.0055 14 0.1462 15 0.2689 16 0.2866 17 0.1207 18 0.4103 19 0.3693 2 3 1.0000 0.9426 1.0000 0.0000 0.0000 0.4375 0.1268 0.1933 0.1720 0.4627 0.3685 0.4936 0.4151 0.3445 0.3885 -0.0313 -0.0674 -0.0320 -0.0765 0.0655 0.0377 0.0097 -0.0294 0.3209 0.2778 0.1827 0.1441 0.2665 00.2285 -0.0440 - 0 : i 6 3 5 -0.1111 -0.1476 -0.0004 -0.0335 0.0828 0.0024 0.0485 -0.0316 0.0354 -0.0514 -0.1421 -0.0951 0.4688 0.1905 11 12 1.0000 0.0486 1.0000 0.0134 0.2745 0.0477 0.3821 0.0809 0.2928 0.1416 0.3349 0.1533 0.3123 0.2545 0.2563 0.2513 0.2156 4 5 0.0000 0.0000 1.0000 0.0000 0.1668 0.0000 0.3932 0.0000 0.3405 0.0000 -0.0375 0.0000 0.0686 0.0000 0.1472 0.0000 0.0949 0.0000 0.1482 0.0000 0.2172 0.0000 0.1659 0.0000 0.1888 0.0000 0.3169 0.0000 0.1224 0.0000 0.1288 0.0000 0.2525 0.0000 0.2552 0.0000 0.2538 0.0000 -0.1610 0.0000 0.8958 13 14 1.0000 0,2311 1.0000 0.0272 0.7195 0.0636 0.9011 -0.0517 0.3833 0.0987 0.3344 0.2588 0.3772 6 7 1.0000 0.3072 1.0000 0.1934 0.9174 0.1400 0.8296 -0.0441 0.0964 0.1271 0.2068 0.1338 0.0123 0.0831 0.2669 0.2899 0.1364 0.2040 -0.0088 0.2854 0.1101 0.1905 -0.0763 0.1519 -0.0239 0.1132 0.1441 0.1370 0.1356 0.1597 0.1377 0.0972 0.1048 0.0478 -0.0427 0.2001 0.3055 15 16 1.0000 0.8719 1.0000 0 .3466 0.3870 0.3578 0.3887 0.4837 0.4619 8 9 1.0000 0.9214 1.0000 0.0361 0.0029 0.1041 0.0628 -0.0212 -0.0435 0.1489 0.1326 0.1304 0.0699 0.0358 -0.0258 0 . U 7 0 0.0591 H -0.1110 -0.2446 -0.0306 -0.0809 0.1248 O.O658 0.0957 0.0051 0.0995 0.0020 0.0916 -0.0110 -0.0449 0.0151 0.2855 -0.0761 17 18 1.0000 0.7295 1.0000 0.2442 0.4176 FIRST ORDER PARTIAL CORRELATIONS (BODY WEIGHT PARTIALLED) (Con't.) NAME 10 11 12 13 20 0.3502 0.1659 0.1151 0.1717 21 0.4104 0.2296 0.1897 0.2101 22 0.4302 0.1658 0.1365 0.1987 23 0.3924 0.1287 0.1228 0.1390 24 -0.0029 0.1073 -0.0048 0.0468 19 20 21 22 19 1.0000 20 0.5132 1.0000 21 0.7378 0.9501 1.0000 22 0.7228 0.9379 0.9823 1.0000 23 0.6911 0.8576 0.9037 0.9072 24 0.1731 0.2702 0.2723 0.2766 14 15 16 17 18 0.4704 0.5110 0.4797 0.4211 0.1858 0.4683 0.5438 0.5110 0.4717 0.2166 0.4617 0.5359 0.5041 0.4569 0.2071 0.3900 0.4788 0.4412 0.3324 0.2376 0.4446 0.5748 0.5531 0.5162 0.0597 23 24 1.0000 -0.1081 1.0000 FIRST ORDER PARTIAL CORRELATIONS (FAT FREE WEIGHT PARTIALLED) NAME 8 1 2 3 4 I 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 2k 1.0000 0.9304 0.9915 -0.1835 0.0000 0.1391 0.3956 0.4579 0.4410 -0.0949 -0.0591 0.0590 -0.0857 0.2803 0.1394 0.2317 -0.1649 -0.1538 -0.0411 -0.0336 -0.0618 -0.0003 -0.0785 O.2374 10 1.0000 0.9321 -0.5076 0.0000 0.0847 0.3724 0.5597 0.4062 -0.1781 -0.0984 -0.0234 -0,1429 0.2436 0.1005 0.2013 -0.0902 -O .I676 -0.0976 -0.0333 -0.0756 0.1384 -0.0932 0.5321 11 1.0000 -0.1740 0.0000 0.1406 0.3654 0.4268 0.4092 -0.1149 -0.0972 0.0095 -0.0786 0.2619 0.1216 0.2141 -0.1785 -0.1661 -0.0644 -0.0324 -0.0701 -0.0074 -0.0832 0.2271 12 1.0000 0.0000 0.0631 -0.1431 -0.5057 -0.1237 0.2382 0.0098 0.0915 0.1780 -0.0434 0.0129 -0.0434 -0.1797 0.0172 0.0846 0.0116 0.0257 -0.4074 0.0467 -0.9214 13 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 14 1.0000 0.2542 0.0949 0.1392 -0.0397 0.1057 0.1252 0.0700 0.2601 0.1818 0.2587 0.1331 0.1352 0.0986 0.1000 0.1242 0.0268 0.0795 -0.0133 15 1.0000 0.8462 0.9202 0.0387 0.1606 -0.0401 0.1979 0.0624 -0.0827 0.0454 -0.1986 -0.0805 0.0890 0.0387 0.0379 0.0634 0.0158 0.0879 16 1.0000 0.9137 -0.1091 0.0451 -0.0954 -0.0001 0.0750 -0.0258 0.0711 -0.1174 -0.0755 0.0319 0.0034 -0.0010 0.2105 -0.0144 0.4503 17 1.0000 -0.0242 0.0673 -0.0510 0.1145 0.0847 -0.0213 0.0722 -0.2175 -0.0785 0.0600 0.0135 0.0087 0.0490 0.0033 0.0770 18 H 10 11 12 13 14 15 16 1.0000 0.3953 0.1734 0.0379 0.1205 0.2573 0.2607 1.0000 0.0359 -0.0068 0.0158 0.0580 0.1167 1.0000 0.2755 0.3661 0.2822 0.3186 1.0000 0.1948 0.0049 0.0283 1.0000 0.7087 0.8975 1.0000 0.8666 1.0000 FIRST ORDER PARTIAL CORRELATIONS (FAT FREE WEIGHT PARTIALLED) (Cont'd.) NAME 10 11 12 13 14 15 16 17 18 17 18 19 20 21 22 23 24 0.0571 0.3982 0.3727 0.3377 0.4015 0.2824 0.4087 -0.2742 0.1101 0.2410 0.2368 0.1346 0.2010 0.1186 0.1564 -0.0308 0.2763 0.2482 0.2121 0.0953 0.1735 0.0689 0.1441 -0.1629 -0.1338 0.0838 0.2547 0.1401 0.1818 0.0788 0.1724 -0.2389 0.3416 0.3167 0.3555 0.4390 0.4810 0.4279 0.4704 0.0321 0.3069 0.3450 0.4721 0.4470 0.5260 0.4436 0.5121 0.0484 0.3530 0.3740 0.4436 0.4348 0.5H9 0.4558 0.4997 0.0737 1.0000 0.7186 0.1968 0.3302 0.4221 0.4265 0.3941 0.1236 1.0000 0.4082 0.4309 O.5666 0.4895 0.5473 -0.0599 19 20 21 22 23 24 19 20 21 22 23 24 1.0000 0.5001 0.7345 0.6202 0.7279 -0.0272 1.0000 0.9466 0.8479 0.9400 0.0291 1.0000 0.8851 0.9898 0.0158 1.0000 0.8869 0.4160 1.0000 -0.0111 1.0000 TWENTY-SECOND ORDER PARTIAL CORRELATIONS NAME 1 2 3 1 1.0000 2 0.1993 -1.0000 3 0.5308 0.9951 -1.0000 4 0.0827 -0.2355 0.2336 5 0*4414 0.2561 -0.2580 6 -0.1341 -0.2189 0.2180 7 0.0511 0.1384 -0.1361 8 -0.2038 0.2667 -0,2657 9 0.2223 -0.2557 0.2575 10 0.1022 0.1488 -0.1415 11 0.2409 0.0415 -0.0535 12 0.4393 0.1494 -0.1450 13 -0.3544 0.0159 -0.0314 14 0.3571 0.1006 -0.0759 15 0.1912 0.0806 -0.0807 16 -0.3414 -0.0522 0.0443 17 -0.0249 0.2842 -0.2958 18 0.0831 -0.3983 0.4022 19 0.1632 -0.2257 0.2286 20 0.0339 -0.1364 0.1428 21 0.0 0.0 0.0 22 -0.0235 0.2646 -0.2733 23 -0.0411 -0.1264 0.1283 24 0.2942 0.1409 -0.1186 10 11 12 10 -1.0000 .11 0.3563 -1.0000 12 0.2342 -0.1548 -1.0000 13 -0.1983 -O.0367 0.2402 14 -O.2062 -0.0765 0.0710 15 0.0615 -0.1939 -0.0229 16 0.1863 0.1172 0.0015 8 -1.0000 0.8432 O.0769 -0.2558 -0.4160 0.4459 0.3520 -0.2857 -0.1624 -0.0352 -0.0048 -0.0835 -0.0268 0.1178 -0.0897 0.1735 0.1115 0.0 -0.3979 0.2470 0.0552 13 -1.0000 0.3768 0.1368 .0.3249 -1.0000 -0.1545 0.2600 0.3214 -0.3613 -0.2477 0.0706 0.0254 -0.0137 0.0223 0.0432 0.0393 -0.0082 0.2265 0.2887 0.3895 0.0 0.3514 -O.5232 -O.1369 14 -1.0000 0.3785 -1.0000 0.1407 -0.1453 -1.0000 -0.1981 0.3426 0.9753 -1.0000 -0.1434 0.3269 0.1161 -0.1912 0.0239 -0.0400 -0.1487 0.1539 0.0774 -0.1897 -0.0653 0.0931 -0.0596 0.2909 -0.2962 0.2264 0.0729 -0.1343 0.0632 -0.0452 0.0450 -0.3178 0.0033 0.0507 _ 0.0292 0.1499 -0.1363 0.1119 ^ 0.0497 0.2017 0.0615 -0.1234 ^ 0.0754 -0.1203 0.0738 -0.0278 0.0176 0.2802 0.2868 -0.3214 0.0843 0.2674 0.1057 -0.1502 0.0 0.0 0.0 0.0 0.0312 -0.2204 0.2389 -0.1876 -0.0796 0.0170 -0.2845 0.2693 0.0921 0.0303 0.2627 -0.2779 15 16 17 18 -1.0000 -0.3515 0.8309 -1.0000 0.6949 -1.0000 TWENTY-SECOND ORDER PARTIAL CORRELATIONS (Cont'd) NAME 10 11 12 13 17 -0.4327 0.1106 0.2389 -0.3025 18 0.3480 0.1249 0.0150 0.2563 19 -0.1005 0.3597 0.2728 0.1845 20 -0.0856 0.3293 0.2172 0.0671 21 0.0 0.0 0.0 0.0 22 0.2857 -0.2190 -0.1944 0.2763 23 -0.1455 -0.0370 -0.0023 -0.2703 24 -0.3751 0.0788 -0.0892 -0.0695 19 20 21 22 19 -1.0000 20 -0.8622 -1.0000 21 0.0 0.0 0.0 22 -0.0042 0.0358 0.0 -1.0000 23 0.5590 0.5706 0.0 0.7903 24 0.1736 0.1949 0.0 0.2014 14 15 16 17 18 0.0722 -0.0590 -0.0196 0.0816 0.0 -0.0338 0.0179 -0.2408 0.0444 0.0097 0.2083 0.2191 0.0 -0.1788 0.0327 0.0224 -0.0139 0.0257 -0.0396 -0.1510 0.0 0.0615 0.0107 0.2040 -1.0000 0.6655 -0.1740 -0.1519 0.0 -0.0695 0.1694 -0.1565 -1.0000 -0.2364 -0.2712 0.0 0.1187 0.0801 0.0992 23 24 -1.0000 -0.2558 -1.0000 

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