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Sources of variation affecting an alternate a.m./p.m. testing plan for dairy cows Dunn, Lorne Kendall 1976

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SOURCES OF VARIATION AFFECTING AN ALTERNATE A.M./P.M. TESTING PLAN FOR DAIRY COWS BY LO-RNE KENDALL DUNN B.Sc. (Agric.) University of B r i t i s h Columbia, 1970 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of Animal Science We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA. JULY, 1976. (o) Lome Kendall Dunn, 1976 In presenting th i s thesis in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i lab le for reference and study. I further agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It i s understood that copying or pub l i ca t ion of th is thes is for f inanc ia l gain sha l l not be allowed without my written permission. Depa rtment The Univers i ty of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1 W 5 Date , I Q Q G i i ABSTRACT The f e a s i b i l i t y o f an a l t e r n a t e A.M./P.M. s a m p l i n g scheme f o r t e s t i n g t h e m i l k , f a t , p r o t e i n and l a c t o s e p r o d u c t i o n o f d a i r y cows was i n v e s t i g a t e d . I t was f o u n d ( P a r t I) t h a t t h e c o n t r i b u t i o n o f t e s t i n g , s a m p l i n g and c o m p o s i t i n g v a r i a n c e s t o t h e v a r i a n c e o f r e c o r d s b a s e d on a l t e r n a t e and 24 h o u r t e s t i n g schemes d i d n o t d i f f e r s i g n i f i c a n t l y . I n P a r t I I , i t was f o u n d t h a t a d d i t i v e c o r r e c t i o n f a c t o r s f o r e s t i m a t i n g d a i l y y i e l d s f r o m a s i n g l e A.M. o r P.M. w e i g h t were s u f f i c i e n t c o r r e c t i o n f o r a l l y i e l d v a r i a b l e s o v e r d i f f e r e n t s e a s o n s o f c a l v i n g , l a c t a t i o n numbers, s t a g e s o f l a c t a t i o n and i n d i v i d u a l s , b u t t h a t d i f f e r e n t f a c t o r s were r e q u i r e d f o r d i f f e r e n t m i l k i n g i n t e r v a l s . I n a d d i t i o n , i t was f o u n d t h a t l a c t a t i o n y i e l d e s t i m a t e s c o u l d be c a l c u l a t e d by e x t e n d i n g t h e a l t e r n a t e s i n g l e sample y i e l d s o v e r t h e r e s p e c t i v e t e s t i n t e r v a l s and summing t h e r e s u l t s , w i t h o u t any s i g n i f i c a n t b i a s , f o r d i f f e r e n t i n t e r -v a l s and f o r a l l y i e l d v a r i a b l e s . i i i TABLE OF CONTENTS PAGE INTRODUCTION 1 LITERATURE REVIEW 4 SOURCE OF DATA 10 PART I: TESTING, SAMPLING, AND COMPOSITING VARIANCES 12 MATERIALS AND METHODS 12 C o l l e c t i o n and C l a s s i f i c a t i o n of Data 12 S t a t i s t i c a l Methods 12 RESULTS AND DISCUSSION 17 PART I I : FACTORS AFFECTING MORNING AND EVENING MILK 23 AND CONSTITUENT YIELDS MATERIALS AND METHODS 23 C o l l e c t i o n and C l a s s i f i c a t i o n o f Data 23 Performance T r a i t s S t u d i e d 24 S t a t i s t i c a l Methods 24 RESULTS AND DISCUSSION 34 Fa c t o r s A f f e c t i n g an A l t e r n a t e A.M./P.M. T e s t i n g Plan - A D i s c u s s i o n 34 A n a l y s i s A 38 A n a l y s i s B 40 A n a l y s i s C 43 M i l k Y i e l d 45 Percentage M i l k F a t and Y i e l d 57 P r o t e i n Percentage and Y i e l d 6 5 Lactose Percentage and Y i e l d 74 CONCLUSIONS 83 LITERATURE CITED 86 iv LIST OF TABLES TABLE PAGE 1.1 Expected mean squares: testing and 14 sampling 1.2 Expected mean squares: compositing 15 1.3 Number of observations, means and > 17 co e f f i c i e n t s of v a r i a t i o n 1.4 Analysis of variance - Analysis A. 18 P.M.- not edited 1.5 Analysis of variance - Analysis B. 18 P.M. - not edited 1.6 Analysis of variance - Analysis C. 19 A.M. + P.M. composites - edited 1.7 Variance estimates for testing, sampling, 19 and compositing 1.8 95% confidence l i m i t s for components of 20 variance 1.9 Contribution of testing, sampling, and 22 compositing v a r i a t i o n to variance of 305 day l a c t a t i o n record 2.1 Number of observations and arithmetic 31 means of days i n milk - Analysis C 2.2 Summary of Analysis B - A l l dependent 39 variables 2.3 Summary of Analysis B - A l l dependent 41 variables 2.4 Summary of Analysis C - A l l dependent 44 variables 2.5 Mean square and variance component for 45 cows and error variance for a l l dependent variables - Analysis C 2.6 Least square constants and standard errors 47 for Season, Lactation and Period of Lactation - Analysis B V TABLE PAGE 2.7 A n a l y s i s A l e a s t square means of A.M 47 and P.M. m i l k y i e l d by l a c t a t i o n p e r i o d ( K i l o g r a m s ) 2.8 Means and l e a s t square c o n s t a n t s f o r 49 m i l k i n g , i n t e r v a l s , and the MI i n t e r a c t i o n f o r m i l k y i e l d 2.9 L e a s t square c o n s t a n t s and s t a n d a r d e r r o r s 58 f o r season, l a c t a t i o n , and p e r i o d o f l a c t a t i o n - A n a l y s i s B: F a t p e r c e n t a g e and y i e l d 2.10 A n a l y s i s A l e a s t square means o f A.M. and 58 P.M. f a t p e r c e n t a g e and y i e l d by l a c t a t i o n p e r i o d 2.11 Means and l e a s t square c o n s t a n t s f o r 60 m i l k i n g , i n t e r v a l , and the MI i n t e r a c t i o n f o r p e r c e n t a g e f a t 2.12 Means and l e a s t square c o n s t a n t s f o r 6 3 m i l k i n g , i n t e r v a l , and the MI i n t e r a c t i o n f o r b u t t e r f a t y i e l d 2.13 C o r r e l a t i o n o f m i l k y i e l d , p r o t e i n y i e l d 66 and p e r c e n t p r o t e i n 2.14 L e a s t square c o n s t a n t s and s t a n d a r d e r r o r s 6 7 f o r s e a s o n , l a c t a t i o n and p e r i o d o f l a c t a t i o n - A n a l y s i s B: Pe r c e n t a g e p r o t e i n and y i e l d 2.15 A n a l y s i s A l e a s t square means o f A.M. and 6 7 P.M. p r o t e i n y i e l d by l a c t a t i o n p e r i o d 2.16 Means and l e a s t square c o n s t a n t s f o r m i l k i n g , 6 9 i n t e r v a l , and t h e MI i n t e r a c t i o n f o r p e r -centage p r o t e i n 2.17 Means and l e a s t square c o n s t a n t s f o r m i l k i n g , 70 i n t e r v a l and t h e MI i n t e r a c t i o n f o r p r o t e i n y i e l d 2.18 C o r r e l a t i o n s o f m i l k y i e l d , l a c t o s e y i e l d , 7 5, and p e r c e n t a g e l a c t o s e 2.19 L e a s t square c o n s t a n t s and s t a n d a r d e r r o r s f o r 76 season, l a c t a t i o n and p e r i o d o f l a c t a t i o n -A n a l y s i s B: L a c t o s e p e r c e n t a g e and y i e l d TABLE PAGE 2.20 Analysis A least square means of A.M. and 7.6 P.M. lactose percentage and y i e l d by la c t a t i o n period 2.21 Means and least square constants for milking, 78 i n t e r v a l , and the MI inte r a c t i o n for lactose percentage 2.22 Means and least square constants for milking, 79 i n t e r v a l , and the MI inte r a c t i o n for lactose y i e l d i n grams 1. INTRODUCTION Col l e c t i o n of the data used i n t h i s thesis was -instigated i n 1970 i n response to two issues that had been raised i n connection with the future testing of dairy cows i n Canada. F i r s t , l i t t l e was known about the e f f i c i e n c y of estimating the l a c t a t i o n y i e l d s of protein and lactose by the t r a d i t i o n a l monthly i n t e r v a l - twenty-four hour sample testing scheme used i n Canada. Second, i n t e r e s t had been shown i n the alternate A.M./P.M. monthly i n t e r v a l testing plan as proposed by several researchers. Additional information was required as to the accuracy of the plan i n estimating yields of milk and i t s constituents. The monthly i n t e r v a l - twenty-four hour sample test-ing plan requires that milk y i e l d be measured over twenty-four hour periods (one P.M. milking and the next A.M. milking) at roughly one month i n t e r v a l s , and that a composite milk sample made of equal amounts of the P.M. and A.M. milking be analysed for milk f a t , protein, and lactose content. These results are applied to a test period that extends backward halfway to the previous test day and forward halfway to the next test day, or to the f i f t h day of freshening or dry date i f the test was the f i r s t or l a s t of a l a c t a t i o n . Test days and test periods for the alternate A.M./P.M. testing plan would be assigned i n the same manner as for the twenty-four hour sample plan. However, only one milk-ing would be measured and sampled each month instead of two, 2. and t h e s a m p l e d m i l k i n g w o u l d a l t e r n a t e betwen A.M. and P.M. f r o m month t o month. T e s t p e r i o d p r o d u c t i o n w o u l d be c a l c u -l a t e d by d o u b l i n g t h e r e s u l t o f t h e one m i l k i n g , t h e n e x t e n d -i n g t h a t e s t i m a t e o f d a i l y p r o d u c t i o n o v e r t h e t e s t p e r i o d . I t seems c e r t a i n t h a t t h e f u t u r e d a i r y cow w i l l be s e l e c t e d f o r h e r a b i l i t y t o p r o d u c e h i g h q u a l i t y p r o t e i n , r a t h e r t h a n e n e r g y i n t h e f o r m o f f a t and c a r b o h y d r a t e . Payment t o t h e d a i r y m a n f o r h i s m i l k has been d e t e r m i n e d by t h e amount o f b u t t e r f a t i n t h e m i l k , s o h i s t o r i c a l l y , s e l e c t i o n p r e s s u r e has been t o i n c r e a s e t h e b u t t e r f a t y i e l d by e i t h e r i n c r e a s i n g t h e p e r c e n t a g e f a t i n t h e m i l k a n d / o r i n c r e a s i n g t h e amount o f m i l k p r o d u c e d . R a p i d and p r a c t i c a l methods o f d e t e r -m i n i n g p r o t e i n and l a c t o s e c o n t e n t o f m i l k , i n a d d i t i o n t o f a t p e r c e n t a g e , a r e now a v a i l a b l e and i n u s e , and p r o g e n y t e s t i n g o f s i r e s and dam s e l e c t i o n f o r p r o t e i n y i e l d i s now commer-c i a l l y p o s s i b l e . However, b e c a u s e f a t c o n t e n t was e c o n o m i c a l l y more i m p o r t a n t , most r e s e a r c h e r s c o n c e r n e d w i t h t h e a c c u r a c y o f t e s t i n g p l a n s c o u l d o n l y d i r e c t t h e m s e l v e s t o t h e a c c u r a c y w i t h r e s p e c t t o m i l k and f a t y i e l d . The a n a l y s e s d e s c r i b e d i n t h i s t h e s i s w i l l document some o f t h e v a r i a b i l i t y a s s o c i a t e d w i t h p r o t e i n , as w e l l as f a t , l a c t o s e , and m i l k y i e l d s o f d a i r y cows, i n r e l a t i o n t o b o t h t e s t i n g p l a n s d e s c r i b e d above. T h e r e a r e s e v e r a l o b v i o u s a d v a n t a g e s i n r e d u c i n g t h e c o s t o f d a i r y cow t e s t i n g . I n a d d i t i o n t o s a v i n g money f o r t h e f a r m e r who t e s t s h i s h e r d , a r e d u c e d c o s t may i n d u c e more d a i r y -men t o j o i n t e s t i n g p l a n s . A d d i t i o n a l e c o n o m i e s o f s c a l e w o u l d t h e n be r e a l i z e d , and s i r e and dam s e l e c t i o n programs w o u l d 3. become more e f f i c i e n t . The alternative A.M./P.M. testing plan would be more convenient for the dairyman and would reduce herd testing costs by doubling the number of herds that could be served by each government tester. The most obvious problem with the plan i s how to correct for biases i n l a c t a t i o n y i e l d estimates as a re s u l t of d i f f e r e n t milking inte r v a l s between herds, as i d e n t i f i e d by Everett (1970a, 1970b) Two data sets were co l l e c t e d and analysed, and thi s thesis has been composed of two parts corresponding to those data sets. Part I examines the variances of f a t , protein, and lactose content due to testing, sampling, and compositing A.M. and P.M. milk samples. These variances are then discussed i n re l a t i o n to the t r a d i t i o n a l monthly i n t e r v a l - twenty-four hour sample testing plan and the proposed monthly i n t e r v a l -alternate A.M./P.M. single sample testing plan. Part II examines the possible sources of error that may a f f e c t an alternate A.M./P.M. test i n g plan, e s p e c i a l l y the eff e c t that milking i n t e r v a l would have on the accuracy of the estimate of milk, f a t , protein, and lactose y i e l d s . 4. LITERATURE REVIEW The v a r i a t i o n due to testing milk for f a t , protein, and lactose content with the Mark IV Infra-red Milk Analyzer at the Dairy Branch Laboratory i n Burnaby ( B r i t i s h Columbia Department of Agriculture) was reported by Williams and 2 Peterson (1972a). The variance components (a ) for f a t , protein, and lactose were 0.00628, 0.00167, and 0.00373 respectively. I t was suggested that the value given for protein content may have been an underestimate, and that the value reported i n t h i s thesis might be closer to the true component of variance. The formulas for combining the variance due to sampl-ing and te s t i n g single milk quantities and sampling, testing, and compositing samples for several milk quantities were given by O'Keefe (1968), Williams and Peterson (1972b), and Peterson and Williams (1971). The accuracy of the t r a d i t i o n a l 2 4-hour sample -monthly i n t e r v a l testing scheme i s well documented, and McDaniel (19 69) has reviewed and summarized several papers that compared the te s t i n g scheme results with true production based on da i l y weights and content determinations. The average standard deviations of the errors, expressed as a percentage of t o t a l y i e l d and based on four studies involving 527 l a c t a -tions were 2.71 f o r milk y i e l d , 3.54 for percentage f a t , and 4.95 f o r y i e l d of f a t . The biases i n milk y i e l d estimates were less than 1% of t o t a l y i e l d for a l l of 14 studies reviewed -5. but were higher for f a t y i e l d i n a few studies. The percentage of monthly y i e l d estimates with less than 2% error was 49%, two-thirds of the 1621 estimates were within 3% of the true y i e l d , and 1.2% of the monthly estimates were more than 10% above or below the actual monthly y i e l d . Several methods of reducing sampling frequency and costs have been investigated; i n general the 24-hour test day was retained but the test i n t e r v a l was lengthened. Houston and Hale (1932) found that f at percentages would be within 8.5 percent of the true percentage with 6 week sampling. Alexander and Yapp (1941) compared plans that had monthly samples, bimonthly samples, three samples per l a c t a t i o n and two samples per l a c t a t i o n for milk and f a t y i e l d . They concluded that bimonthly testing was s u f f i c i e n t l y accurate for p r a c t i c a l application, and that the estimates based on three samples per l a c t a t i o n were only s l i g h t l y less accurate than the bimonthly. They recommended that even two samples per l a c t a t i o n would contribute to the improvement of dairy herds. Bayley et a l . (1952) concluded that bimonthly and quarterly records of milk and f a t would be s a t i s f a c t o r y f o r proving s i r e s and for popu-l a t i o n studies, but questioned the use of the records in evaluating i n d i v i d u a l cows. They found the average percent error of 1255 Holstein records to be 3% and 5% for milk y i e l d estimates based on bimonthly and quarterly records and 4% and 6% for f a t y i e l d . More recently, Everett et a l . (1968) found that 6. a d j u s t i n g t e s t - d a y p r o d u c t i o n f o r t h e s t a g e o f l a c t a t i o n i n t h e f i r s t and l a s t t e s t p e r i o d s r e d u c e d the v a r i a n c e o f the d e v i a -t i o n o f e s t i m a t e d p r o d u c t i o n from a c t u a l p r o d u c t i o n t o 90.7, 89.0, and 75.2% o f t h e v a r i a n c e o f the d e v i a t i o n s o f t h e u n a d j u s t e d r e c o r d s f o r t h e monthly, b i m o n t h l y , and t r i m o n t h l y s a m p l i n g p l a n s . They c o n c l u d e d t h a t b i m o n t h l y and t r i m o n t h l y r e c o r d s would become more popular, because o f economic and p r a c t i c a l r e a s o n s , and t h a t c o r r e c t i n g t h e r e c o r d s f o r st a g e o f l a c t a t i o n would improve t h e a c c u r a c y o f b o t h p l a n s c o n s i d e r a b l y . M c D a n i e l (1969) i n h i s r e v i e w paper c o n c l u d e d t h a t b i m o n t h l y and t r i m o n t h l y r e c o r d s a r e s a t i s f a c t o r y f o r purposes such as h e r d a v e r a g e s , s i r e e v a l u a t i o n , group a v e r a g e s , and f o r r a n k i n g cows w i t h i n h e r d s . However, he suggested t h a t t h e i n d i v i d u a l l a c t a t i o n r e c o r d i s not a p r e c i s e e s t i m a t e o f a b s o l u t e l a c t a t i o n p r o d u c t i o n , b u t t h a t i n t h e f u t u r e , c o r r e c t i o n s f o r s t a g e o f l a c t a t i o n a t t h e f i r s t t e s t may s u b s t a n t i a l l y improve the e s t i m a t e s . P o r z i o (1953) proposed t h e a l t e r n a t e A.M.-P.M. monthly i n t e r v a l t e s t i n g p l a n as a n o t h e r method o f r e d u c i n g h e r d t e s t i n g c o s t s . He found no b i a s i n the y i e l d e s t i m a t e s o f 150 l a c t a -t i o n s . P o l y and P o r t o u s (1966) c o n c l u d e d t h a t a r e c o r d based on s i n g l e samples was s u i t a b l e f o r r a n k i n g f e males and progency t e s t i n g o f b u l l s f o r m i l k and f a t p r o d u c t i o n . H ardouin (1967) found t h a t t h e a l t e r n a t e p l a n gave s a t i s f a c t o r y r e s u l t s under T u n i s i a n c o n d i t i o n s f o r 31 F r i e s i a n cows. The c o r r e l a t i o n between t h e s i n g l e sample and 2 4-hour sample monthly t e s t s was 7. 0.97. Nielson (1967) analysed over 6000 milk records and over 250 fat records of four breeds and compared the alternate and regular t e s t i n g plans. He found the alternate plan to be less precise but acceptable. The average absolute deviation of the alternate and regular estimates were 3.77 and 5.68% for milk and fat y i e l d respectively. Putnam and Gilmore (1968) found that 47% of 296 U.S. DHIA records were overestimated. They concluded that the alternate plan was an acceptable alternative to the t r a d i t i o n a l t e s t i n g plan. In a l a t e r paper (19 69) they stated that 800 dairymen i n Pennsylvania had switched to the A.M./P.M. testing plan after i t had been approved as an optional program, showing farmer acceptance of the plan. The fee charged by some of the counties for the alternate plan was approximately 80% of the fee for the regular test. Dickenson and McDaniel (1968) generated over 50,0 00 d i f f e r e n t estimates of l a c t a t i o n milk y i e l d from data on 450 cows. They compared 5 sampling schemes, each with test i n t e r -vals of 20, 30, and 40 days and each with 8 intervals to the f i r s t t e s t . They found that records based on A.M. and P.M. y i e l d s only were extremely biased, and the standard deviation was twice as great as the 24-hour sample plan. The alternate plan, beginning on an A.M. milking was twice as biased as the 24-hour sample plan, with standard deviation 40% greater. The alternate plan beginning on a P.M. milking was less biased than the standard plan, with standard deviation only 20% greater. The increased i n t e r v a l s did not increase the bias, but did increase the standard deviation. They concluded that accurate 8. estimates are f e a s i b l e from the alternate A.M./P.M. testing plan i f adjustments were made for a few important sources of v a r i a t i o n . Everett and Wadell (1970a) examined the sources of v a r i a t i o n a f f e c t i n g the difference between A.M. and P.M. daily-milk production on 184,521 records on 19,905 cows from give d a i l y breeds. They concluded that additive correction factors would be required to estimate d a i l y production from a single A.M. or P.M. milking, for each month of lactation/milking i n t e r v a l subclass. They point out that separate month of l a c t a t i o n correction factors might not be needed i f an estimate of l a c t a t i o n production was a l l that was required, as the biases in the test i n t e r v a l production estimates would tend to cancel themselves over the l a c t a t i o n . The same authors investigated the use of m u l t i p l i -cative rather than additive correction factors for d a i l y milk y i e l d estimates from single milking weighings (1970b). They found that the m u l t i p l i c a t i v e factors removed a larger part of the production e f f e c t and therefore reduced the e f f e c t of age and stage of l a c t a t i o n . Again, factors were required to correct for milking i n t e r v a l . Shook e t . a l . (1973) developed a quadratic equation to predict the r a t i o of P.M. to A.M. and P.M. milk y i e l d given the stage of l a c t a t i o n and the daytime milking i n t e r v a l . P.M./(A.M. + P.M.) = 0.4876 - .034351 + .002957I2 - .01957S + .000325S2 + .001326IS 9. where ' I 1 was the daytime milking i n t e r v a l i n hours.and VS' was the stage of l a c t a t i o n i n months. The r a t i o could then be applied to either an A.M. or P.M. milking to predict the d a i l y y i e l d . Another report by Shook et a l . (1975) showed the bias i n an estimate of l a c t a t i o n milk y i e l d from an alternate A.M./P.M. testing plan to be equal to that of y i e l d estimates from the standard DHIA t e s t , however, the standard deviation of the errors was 168 kg. for the alternate scheme and 118 for the 24-hour sample testing scheme. Jensen et a_l. (1974) found that milking i n t e r v a l was an important source of v a r i a t i o n for the r a t i o P.M./(A.M. + P.M.) for milk, f a t , and protein y i e l d s , and f a t %, but not for protein %. Season of calving was important for f a t y i e l d only. They tabulated adjustment factors to convert P.M. to d a i l y y i e l d s for milk, f a t , and protein, for three milking i n t e r v a l s , but not for stage of l a c t a t i o n . 10. SOURCE OF DATA A l l m i l k samples f o r t h i s s t u d y were c o l l e c t e d from the campus herd o f t h e U n i v e r s i t y o f B r i t i s h Columbia between F e b r u a r y , 1970 and September, 1971. The h e r d c o n s i s t e d o f a p p r o x i m a t e l y f i f t y m i l k i n g age a n i m a l s - 67% A y r s h i r e , 17% H o l s t e i n , and 16% J e r s e y . The m a j o r i t y o f the cows remained o u t s i d e o f the b a r n , i n an open compound or under a s h e l t e r , day and n i g h t e x c e p t f o r c o n c e n t r a t e f e e d i n g and m i l k i n g . There was no p a s t u r e d u r i n g t h e s a m p l i n g p e r i o d f o r a l l b u t a few o f the cows, wh i c h were a l l o w e d t o g r a z e a s m a l l l o t f o r o n l y a few days of t h e y e a r . A few box s t a l l s were a v a i l a b l e f o r s i c k cows, however, some e x c e p t i o n a l a n i m a l s were p r e f e r e n t i a l l y l e f t i n the b a r n when s t a l l s were a v a i l a b l A l l cows were m i l k e d t w i c e d a i l y . D u r i n g the s a m p l i n g p e r i o d i t was attempted t o a s s i g n cows randomly, as they f r e s h e n e d , t o e i t h e r a t w e l v e hour, t w e l v e hour or t e n hour (A.M. t o P.M.), f o u r t e e n hour (P.M. t o A.M.) m i l k i n g i n t e r v a l . However, t h e d e c i s i o n was not always random as the number o f m i l k i n g s t a l l s a v a i l a b l e f o r t h e e q u a l i n t e r v a l cows was f i x e d . When one was v a c a n t and more than one cow was u n a s s i g n e d , the h i g h e s t p r o d u c e r g e n e r a l l y f i l l e d i t . I n a d d i t i o n , a l l cows housed i n t h e box s t a l l s were a u t o m a t i c a l l y a s s i g n e d t o t h e t w e l v e hour i n t e r v a l s . The i m p l i c a t i o n s o f the f a i l u r e t o a s s i g n cows randomly t o t h e two m i l k i n g i n t e r v a l a r e d i s c u s s e d i n P a r t I I , S t a t i s t i c a l Methods. A l l m i l k samples were t e s t e d by a Grubb-Parsons Mark IV I n f r a - R e d M i l k A n a l y s e r (IRMA) by t h e B r i t i s h Columbia Department of A g r i c u l t u r e , D a i r y L a b o r a t o r y , 3 7 05 W e l l i n g t o n Avenue, Burnaby, B.C. 12. PART I: TESTING, SAMPLING, AND COMPOSITING VARIANCES MATERIALS AND METHODS Collec t i o n and C l a s s i f i c a t i o n of Data On December seventh and eighth 1971, milk samples were coll e c t e d from a l l cows to determine the variances i n milk constituents associated with te s t i n g , sampling, and compositing. Sampling was done according to the procedures outlined for Record of Performance Inspectors i n Canada (1969). During the afternoon milking,, four two ounce (57 grams) samples were taken from each cow, two for compositing with morning samples, and two as duplicate single samples. After completing the composite samples by adding two ounces from the morning milking, the four ounce (114 gram) composite samples were randomly assigned numbers between 1 and 312 for sequential analysis by the IRMA. The printout from the analyser, consist-ing of sampling number, percentage milk f a t , protein, and lactose was punched onto IBM data cards for analysis. S t a t i s t i c a l Methods The data was used to estimate variances associated with sampling, compositing, and testing by the infra-red milk analyser for milk f a t , protein, and lactose percentages. The variance components are: 2 a - sampling variance due to differences i n mixing the milk before sampling, and d i f f e r e n t lengths of time before samples were cooled and/or tested. 13. 2 - composite variance due to milk samples of equal sizes representing uneven quantities of milk. Equal quantities from each milking (A.M. and P.M.) were taken regardless of the amount of milk produced as recommended by the R.O.P. tester's manual (19 69) . 2 o - testing variance due to the inherent v a r i a t i o n i n milk te s t i n g equipment and techniques. I t includes the e f f e c t s of d i f f e r e n t machines, times, runs, and technicians. Two sets of samples were co l l e c t e d - the f i r s t set of duplicate single samples were used to determine the testing and sampling variances and the second set of duplicate composite samples were used to determine the variance associated with compositing. In both cases, standard analysis of variance procedures for equal subclass frequencies were used. The linear model applied to the f i r s t sample set was: Y... = a + c. +s.,.. + t, , . .> 13k 1 3(1) k ( i j ) where: ^ i j k = *"^e ° b s e r v e c ^ component percentage for the i •th , T 1 th , , cow, j sample, and k t e s t . a = the o v e r a l l mean component percentage for a l l samples c th i = the e f f e c t of the 1 cow. S j (i) = the e f f e c t of the sample from the cow. t k ( i j ) = the e f f e c t of the k t h test of the j t h sample from the i * " * 1 cow. 14. Tests, samples, and cows were considered random e f f e c t s . The expected mean squares and sample size for a l l effects are reported i n Table 1.1. The estimate of te s t i n g variances was derived from an analysis of a l l data col l e c t e d from the P.M. milking. The sampling variance estimate was computed from a si m i l a r analysis on the same data aft e r the data set was edited to remove cows that produced less than 4.77 kg. (10.5 lb.) of milk during the P.M. milking. As sampling variance i s sensitive to the amount of milk being sampled, the data set was edited so that i t would be more representative of a t y p i c a l commercial herd. Ten of the thirty-nine animals were deleted. TABLE 1.1 EXPECTED MEAN SQUARES: TESTING AND SAMPLING SOURCE SAMPLE SIZE E(MS) cows 39 samples/cows 2 2 „ 2 o~_ + 2o t s tests/samples/cows 2 t where: For the composite experiment the model assumed was: Y.., = a + c. + k . .. . + t. ,. .. 13k 1 j (1) k(13) Y^ _.^  = the observed component percentage from the i •th _ j . th , cow, 3 sample, and k t e s t . • th 15. a = the o v e r a l l mean percentage component for a l l samples th c. = the e f f e c t of the i cow. 1 k_. ^  = the e f f e c t of the composite from the i * " * 1 cow. th th t k ( i j ) = t* i e e f r e c t °f t n e k te s t of the j composite th from the i cow. The expected mean squares for t h i s model with a l l eff e c t s random are reported i n Table 1.2. TABLE 1.2 EXPECTED MEAN SQUARES: COMPOSITING SOURCE SAMPLE SIZE E (MS) cows 37 composites/cow 2 2 „ 2 °t + 2 a k tests/composite/cows 2 0-2 t Since composite milk samples are made from single 2 samples, sampling variance (a ) contributes to the t o t a l s 2 variance of compositing (a, ) . The variance of two samples i s equal to one half of 2 2 the a , or a /2. s s Therefore: 2a? = 2(a 2/2 + a 2) = a 2 + 2 a 2 . k s a s a 16. 2 The variance due to composition (°* ) m a y then be computed by: c 2 = ( 2 a 2 - a 2)/2 = ( M S ( c o m p > / c q w s ) - a 2 - c 2)/2. 2 As i s also sensitive to the amount of milk being sampled, a l l composite data was edited to eliminate cows producing less than 4.77 kg. of milk during either of the milkings - and, as with the ed i t of the afternoon milk, ten cows were deleted. In addition, two cows were deleted because of sampling errors. 2 The 95% confidence l i m i t s were calculated for a^ _, 2 2 a , and a, . As the variance component for testing was the mean square for tes t i n g i n the Analysis of Variance, the confidence l i m i t s were calculated using the quantity: P j^y2/X2 (- 025) [>&• ~ °l ~ £y 2/X 2(-0975) [J78I]J= 0.95 as given i n Sokal and Rohlf, page 153 (1969). 2 2 Approximate confidence l i m i t s for c and o were S JC calculated by Moriguti's method as described i n Snedecor (1968). 2 2 2 Because a, i s made up of the components a and a , the iC S cl 2 approximate l i m i t s f o r would be less than those calculated for a 2 k RESULTS AND!DISCUSSION In t h i s discussion, Analysis A refers to the analysis of the complete set of P.M. single samples, used to obtain the variance estimate for testing. Analysis B used the same model, but applied i t to the edited set of P.M. single samples, for the estimate of sampling variance. The composite samples were analysed i n Analysis C. Table 1.3 shows the number of observations, the grand means and the c o e f f i c i e n t s of va r i a t i o n for each of the consti-tuent percentages i n each analysis. TABLE 1.3 NUMBER :0F OBSERVATIONS, MEANS AND COEFFICIENTS OF VARIATION NUMBER OF FAT (%) PROTEIN (%) LACTOSE (%) ANALYSIS OBSERVATIONS MEAN COEFFICIENT MEAN COEFFICIENT MEAN COEFFICIENT (N) OF VARIATION . . OF VARIATION OF' VARIATION . A 156 5.69 24.96 4.28 11.92 4.72 6.99 (P.M. only) B 116 5.32 24.06 4.08 10.78 4.82 6.43 (P.M. only) C 108 5.05 21.19 4.06 10.34 4.82 6.22 (A.M. &P.M.) Tables 1.4, 1.5, and 1.6 contain the three analyses of variance tables for each dependent variable. Table 1.7 shows the best estimate of each variance component for each dependent variable, and the associated 95% confidence l i m i t s are given i n Table 1.8. 18. Examination of the c o e f f i c i e n t s of v a r i a t i o n i n Table 1.3 shows that f a t content i s much more variable than protein and lactose over a l l cows, tests, and samples. Tables 1.4, 1.5, and 1.6 would indicate that this v a r i a b i l i t y can be almost completely attributed to differences between cows. TABLE 1.4 ANALYSIS OF VARIANCE - ANALYSIS A P.M. - NOT EDITED SOURCE DEGREES OF FREEDOM MEAN SQUARES FAT (%) PROTEIN (%) LACTOSE (%) 2ows 38 8.2320 1.0446 0.4379 3amples/Cows 39 0.0054 0.0085 0.0044 Tests/Samples 78 -0.0065 0.0089 0.0050 TABLE 1.5 ANALYSIS OF VARIANCE - ANALYSIS B P.M. - EDITED SOURCE DEGREES OF FREEDOM MEAN SQUARES FAT (%) PROTEIN (%) LACTOSE (%) ^OWS 28 6.7576 0.7487 0.3873 Samples/Cows 29 0.0047 0.0107 0.0033 Tests/Samples 58 0.0057 0.0100 0.0040 19. TABLE 1.6 ANALYSIS OF VARIANCE - ANALYSIS C A.M. + P.M. COMPOSITES - EDITED SOURCE DEGREES OF FREEDOM FAT (%) PROTEIN (%) LACTOSE (%) Cows 26 4.6639 0.7232 0.3567 Composites/Cows 27 0.0065 0.0028 0.0060 Test/Composites 54 0.0043 0.0041 0.0034 TABLE 1.7 VARIANCE ESTIMATE FOR TESTING, SAMPLING, AND COMPOSITING ESTIMATE FAT (%) PROTEIN (%) LACTOSE (%) 02(D . testing 0.0065 0.0089 0.0050 0 2 ( 2 ) -s sampling 0.0 ( 4 ) 0. 0"009 o.o(4> a 2 ( 3 ) -a compositing o.o ( 4 ) 0.0 ( 4 ) 0.0005 1 - the estimate for o"t i s taken d i r e c t l y from Analysis A 2 2 - the estimate for was computed from the mean square for samples taken from Anlaysis B and a 2 from Analysis A 2 3 - the estimate for a was computed from the mean square for a 2 2 composites/cows from Analysis C, and a and a as given s t above (see notes 1 and 2) 4 - negative estimates were considered to be zero. 20. TABLE 1.8 95% CONFIDENCE LIMITS FOR COMPONENTS OF VARIANCE CONSTITUENT COMPONENT 2 a t 2 a s 2 a k Fat Protein Lactose 0.0047 to 0.0088 0.0065 to 0.0122 0.0037 to 0.0069 0.0 to 0.0009 0.0 to 0.0042 0.0 to 0.0007 0.0 to 0.0052 0.0 to 0.0002 0.0011 to 0.0059 Sampling and compositing variances are pertinent to any comparison between alternate A.M./P.M. testing and monthly two sample composite testing i n that although both schemes have the same number of tests (usually ten over the 305 day lac t a t i o n record), the number of samples and composites d i f f e r . The variance of l a c t a t i o n records contains components due to testing, sampling, and compositing, and i s therefore d i f f e r e n t f o r records calculated from alternate and composite tests. (The variance of a record i s also affected by the number of samples making up the record - thi s e f f e c t w i l l be discussed in Part I I ) . The standard record calculated from monthly tests of A.M. & P.M. composites has ten t e s t s , twenty samples, and ten composites. The variance i n a l a c t a t i o n record attributed to these affects may be calculated as: a* a 2/10 + a 2/20 + a 2/10. t. S cl The alternate A.M./P.M. test i n g scheme has ten t e s t s , ten samples and no composites. The contribution of testing and sampling v a r i a t i o n to the variance of a record may be calculated as: b * o^/lO + o-g/lO. Table 1.9 shows these variance components for each constituent and each te s t i n g scheme calculated by substituting the values i n Table 1.7 into the summations (a) and (b). Clearly the differences are very small - the alternate scheme showing less v a r i a t i o n for fat percent and lactose percent and more for protein percentage. In comparison with the between cow variance (see the r e s u l t s of Analysis C i n Part II):, the sums of te s t i n g , sampling, and compositing variance are 0.3% for percent-age f a t , 1.5% for protein, and 1.3% for lactose. These random errors are then a very small addition to the variance of a record when compared to the differences between records of d i f f e r e n t cows, and the contribution of these errors to the variance of a l a c t a t i o n record does not d i f f e r s i g n i f i c a n t l y for either the alternate or composite testing plan. TABLE 1.9 CONTRIBUTION OF TESTING, SAMPLING, AND COMPOSITING VARIATION TO VARIANCE OF 305 DAY LACTATION RECORD TESTING SCHEME COMPONENT CONTRIBUTION FAT % PROTEIN % LACTOSE % alternate A.M./P.M. al/10 + o2/10 t s 0.00065 0.00098 0.00050 A.M./P.M. composite , a?/10 + a2/20 + a 2/10 t s a 0.00065 0.00094 0.00053 PART I I : FACTORS AFFECTING MORNING AND EVENING MILK AND CONSTITUENT YIELDS MATERIALS AND METHODS C o l l e c t i o n and C l a s s i f i c a t i o n o f Data Between F e b r u a r y , 1970 and September, 1971 each cow i n t h e campus h e r d was sampled each week, once i n the a f t e r n o o n and a g a i n the n e x t morning. A f t e r t h e m i l k i n g machine was removed from each cow, the m i l k was mixed i n the b u c k e t , and f o u r ounces (114 grams) were sampled i n t o a s i x ounce p l a s t i c b o t t l e . The P.M. samples were s e a l e d and r e f r i d g e r a t e d o v e r -n i g h t and the A.M. samples were t a k e n the f o l l o w i n g morning. These samples were a n a l y s e d s e p a r a t e l y , and the f a t , p r o t e i n , and l a c t o s e percentage,-, a l o n g w i t h t h e cow number, d a t e t e s t e d and m i l k p r o d u c t i o n i n pounds were punched onto IBM c a r d s a t the B.C. Department o f A g r i c u l t u r e D a i r y L a b o r a t o r y . On r e c e i p t o f t h e s e c a r d s a t t h e U n i v e r s i t y , the i n f o r m a t i o n was t r a n s f e r r e d t o a magnetic t a p e f i l e , and c l a s s i f i e d a c c o r d i n g t o the b r e e d o f the cow, l a c t a t i o n number, day o f l a c t a t i o n , c a l v i n g d a t e , m i l k i n g i n t e r v a l , and m i l k i n g (A.M. o r P.M.). P r i o r t o a n a l y s i s , t h e d a t a s e t was e d i t e d . Any samples from a cow p r o d u c i n g l e s s than 4.54 kg. (ten pounds) of m i l k d u r i n g t h e t e s t day (P.M. p l u s A.M.), o r from any cow f r e s h l e s s t h a n f i v e o r more than 305 days was d i s c a r d e d f o r t h a t day. I t was i n i t i a l l y i n t e n d e d t o i n c l u d e b r e e d as an independent v a r i a b l e i n the a n a l y s e s , a l o n g w i t h a l l o f t h e associated interactions. However, at the end of the sampling period, data had been col l e c t e d for only thirteen Holsteins and twelve Jerseys, compared to forty-eight Aryshires, and few records spanned complete lactations. As most interactions associated with breed of cow resulted i n empty subclasses, and because many of the Jersey and Holstein cows maintained i n the herd were exceptional producers (not representative of the breed average), i t was decided to r e s t r i c t the analyses to Aryshires only. For Analyses A and B there were 3660 ind i v i d u a l records from 1830 cow/test days. Four additional records were included i n Analysis C. Performance Tr a i t s Studied Seven dependent variables were analysed i n each of Analyses A, B, and C. They were: milk (pounds), percentage f a t , protein, and lactose, and f a t , protein, and lactose production i n pounds, computed by the formula: (% constituent x pounds of milk each milking)/100. A l l values which represent weights were decoded to grams and kilograms aft e r analysis. A l l variables represented a single milking only. S t a t i s t i c a l Methods The complete data set was analysed with three models la b e l l e d A, B, and C, to determine the e f f e c t of the A.M. and P.M. milking to a l l dependent variables. A l l three analyses were done by the least squares method afte r Harvey (1960). The ef f e c t s of milking, milking i n t e r v a l , season, l a c t a t i o n , days i n milk, and a l l possible interactions were investigated with Analysis A. Milking was c l a s s i f i e d as A.M. or P.M., and i n t e r v a l as 12/12 or 10/14. The ten hour i n t e r v a l was between A.M. and P.M., and the fourteen hour i n t e r v a l between the evening and morning milking. Two seasons were defined, from October through March and A p r i l through September, aft e r Bereskin (1965). Lactation number of p a r i t y was grouped into three classes -f i r s t , second, and t h i r d or greater, and days i n milk were grouped into four "period of l a c t a t i o n " classes: p l - 4 to 61 days in milk P2 " 62 to 122 days in milk P3 " 123 to 214 days i n milk P4 " 215 to 305 days in milk The l i n e a r mathematical model assumed for Analysis A were Y i jklmn where: Y i j k l m n a + M. + I. + S k + L ] L + P m + MI.. + MS..k + MLi± + M P i m + I S j k + I L j l + I PJm + S L k l + S Pkm + L P l m + MIS. j k + M I L i j l + MIP. j m + MSL. k l + MSP. k m + ^ i l m + I S L j k l + I S P j k m + I L P j l m + S L P k l m + M I S L i j k l + M I S P i j k m + MISLP. j k l m + e . j k l m n the observed value of the dependent variable for the n^*1 observation i n the i 1 " * 1 milking, the j*"* 1 i n t e r v a l , the season, the l ^ * 1 l a c t a t i o n c l a s s , and the m*"*1 period of la c t a t i o n . a - the population mean for the dependent variable when equal subclass frequencies e x i s t s . th - the e f f e c t of the i milking. th I. - the e f f e c t of the j i n t e r v a l . 3 - the e f f e c t of the k*"*1 season. t h - the e f f e c t of the 1 l a c t a t i o n c l a s s . P - the e f f e c t of the m t h period of lactation. m th e. .. ., - the random e f f e c t associated with the n observation ljklmn of the i t n milking on the j t h i n t e r v a l i n the k t h season i n the l * " * 1 l a c t a t i o n class i n the m*"*1 l a c t a -t i o n period, which i s assumed to be independent and normally d i s t r i b u t e d with mean equal to zero and 2 variance a . The remaining terms define a l l possible interactions of each main e f f e c t with the others. These interactions may be defined as the j o i n t e f f e c t of the two, three, four, or f i v e variables included i n the i n t e r a c t i o n , a f t e r the average main eff e c t s and lower order i n t e r a c t i o n e f f e c t s have been removed. A l l independent variables i n t h i s model were assumed to be fixed e f f e c t s . There were some'subclasses i n Model A that had no observations, and they were deleted from the analysis. S p e c i f i c a l l y , no animals were sampled that were i n th e i r t h i r d or more l a c t a t i o n (lactation class three) and i n lac t a t i o n per-iod three (121 to 180 days i n milk) and milking on a 12/12 i n t e r v a l . In addition, no cows were sampled i n l a c t a t i o n period three on the 12/12 i n t e r v a l i n October through March season. Consequently, the results obtained from those i n t e r -actions of which they are a part (MISP, MILP, MSLP, and MISLP) can not be generalized to include the missing subclasses. The significance or non-significance of the interactions apply only to those subclasses that were included i n the data. The error mean square was used as the testing term for a l l effects i n this analysis. The l e v e l of significance for each F test was 0.01, and the proportion of the t o t a l sum of squares accounted for by the complete model and each e f f e c t was calculated. The li n e a r mathematical model assumed for Analysis B was: Y. ., . = a '+ M, + I . + S. + L n + P + MI. . + IS .. + IL . , + ljklmn u K j k 1 m i ] jk jl IP. + SL. , + SP. + LP, + ISL.. . + ISP.. + jm k l km lm j k l jkm ILP. n + SLP. , + ISLP., , + e. .. . jlm klm jklm ljklmn; where a l l effects are defined as i n Analysis A and were assumed to be fixed e f f e c t s . This model i s a r e s u l t of eliminating a l l effects from the model used for Analysis A that were not sign-i f i c a n t for a l l of the dependent variables i n Analysis A. The purpose of this analysis was to determine the magnitude of the effects of the A.M. and P.M. milking. Unequal subclass frequencies i n a least squares analysis w i l l cause the sums of squares and least square constants for s p e c i f i c e f f e c t s to d i f f e r between the analyses of the two models -28. when one (Analysis B) i s a subset of the other (Analysis A). By eliminating a l l non-significant interactions - i n p a r t i c u l a r those that included the variable M - the constants derived for determining A.M.-P.M. differences would more accurately r e f l e c t the magnitude of the differences that would concern a l l alternate A.M.-P.M. te s t i n g scheme. As i n Analysis A, the test i n g term for a l l effects was the error mean square. The l i n e a r mathematical model assumed for Analysis C was: Y. .. , = a + M. + I . + S, + L, + C + MI . . + MS + ML. , + ljklmn 1 j k 1 m i j lk i i 2 lm 1 ljklmn 2 ljklmn ljklmn; where the variables which are d i f f e r e n t from or were not defined for Analysis A are: Y. . = the observed value of the dependent variable for the ljklmn c n t h observation of the mt*1 cow on the i ^ milking, th th th the j milking i n t e r v a l , the k season, in the 1 la c t a t i o n c l a s s . a ='the population mean for the dependent variable when equal subclass frequencies exist and when D.., n ^ ^ ljklmn equals zero. th C = the e f f e c t of the m cow. m th th MC. = the jo i n t e f f e c t of the i milking and the m cow lm J • aft e r the average e f f e c t s of M. and C have been • l m removed. b, = the p a r t i a l regression c o e f f i c i e n t of Y. ,. . on 1 • ljklmn ^ijklmn* 29. th D. ., , = the number of days i n milk of the n observation of xjklmn the cow on the i * " * 1 milking, the i n t e r v a l , t h th the k season, and the 1 l a c t a t i o n c l a s s . = the p a r t i a l regression c o e f f i c i e n t of Y^-^imn ° n D 2 . t l . ljklmn 2 D. ., n = the square of D. ., . ljklmn ^ ljklmn t h e = the random e f f e c t associated with the n observation ' i jklmn of the m1"*1 cow, the i ^ " * 1 milking, the j*"* 1 milking t h th i n t e r v a l , the k season and the 1 l a c t a t i o n class. Individual cows were assumed as random ef f e c t s i n this study, and were included for three reasons. F i r s t , an estimate of the between cow variance component was desired for a comparison with the testing, sampling, and compositing variances given i n Part I of thi s t h e s i s . Second, by removing the e f f e c t s of individ u a l s from the error mean square, t h i s value would approximate the error expected when a single sample of milk i s used to estimate a l a c t a t i o n record. Third, i t was important to know i f cows reacted d i f f e r e n t l y to morning and evening milking. If that was the case, correction factors i n an alternate A.M./P.M. testing plan for stage of la c t a t i o n and in t e r v a l could not be applied equally to a l l cows. The MC (milking x cow) in t e r a c t i o n was then also included i n t h i s model, as a random e f f e c t . A l l other variables were assumed fixed, and the tes t i n g term for a l l variables except the main e f f e c t "milking" was the error mean square. Because of.the unequal subclass numbers, and the inclus i o n of the random e f f e c t C, no exact test of significance 30. was available for M. However, Analysis B showed "milking" to be a s i g n i f i c a n t source of v a r i a t i o n for a l l but percentage lactose, so no test for this variable was done in th i s analysis. The expected mean square for cows i s : 2 2 EMS = a + ka . c e c In order to compute the variance component due to cows i n t h i s analysis (between cow variance), k must be known. If there were equal numbers of observations for each cow, k would equal that number. The average number of observations per cow i n Analysis C was close to 76, however, because the numbers were disproportionate, the optimum value of k w i l l be less than that (Harvey, 1960). Cunningham (1969) and Searle (1971) give the formula for c a l c u l a t i n g k as: k = q-1 . /TT-1> 1 sm (W "*") t r (W ) - . ' where q i s the number of cows, (W 1) i s the inverse of the (q-1)*(q-1) symmetric submatrix of the inverse of the complete least-square c o e f f i c i e n t matrix used for Analysis C, t r i s the trace operation or sum of the diagonals and sm i s the sum of a l l elements i n the (W "S matrix. As the LSA8 computer program used for these analyses included only the inverse of the submatrix of the inverse c o r r e l a t i o n matrix (Peterson, 1965), this matrix was transformed to (W 1) by the formula: W. .~ 1 = (N-l) * / V. . *V. . *C, . _ 1 ID i i 33 k3 31. where N i s the t o t a l number of observations and V\.. i s the th ( i , j ) element from the variance/covariance matrix. There were 48 indi v i d u a l Ayrshire cows included i n thi s study. Table 2.1 shows the number of observations, and the mean of the covariable 'days i n milk 1 for a l l main e f f e c t s except individuals. The number of observations per cow ranged from ten to 136 with a mean of 76. TABLE 2.1 NUMBER OF OBSERVATIONS AND ARITHMETIC MEANS OF DAYS IN MILK-ANALYSIS C VARIABLE NUMBER OF OBSERVATIONS (N) NUMBER OF COWS SAMPLED NUMBER OF LACTATIONS SAMPLED AVERAGE DAYS IN MILK a 3664 48 73 142 L l 2168 35 35 151 L2 844 24 24 122 L3 652 8 14 135 S 1(A-S) 1952 141 S 2 (0-M) 1712 143 I 1(12/12) 1856 142 I 2(10/14) 1808 142 M1(A.M.) 1832 142 M (P.M.) 1832 142 It should be noted that many cows were sampled over more than one la c t a t i o n . So, while there were only forty-eight cows, seventy-three lactations were included in the study. To some extent the e f f e c t of milking i n t e r v a l was confounded with the e f f e c t of the in d i v i d u a l animal. Of the forty-eight cows, only sixteen were sampled on both the 12/12 and the 10/14 milking inte r v a l s - thirteen animals were switched from one i n t e r v a l to the other during a la c t a t i o n , and three were switched between la c t a t i o n s . A t o t a l of eight cows had di f f e r e n t intervals over the majority of samples from two consecutive lactations, four going from 12/12 to 10/14 and four from 10/14 to 12/12. The separation of the effects of i n t e r v a l and cow, and of the interactions MI and MC i s then p a r t i a l l y defined by the sixteen animals that were sampled over both i n t e r v a l s , and p a r t i a l l y dependent on the remaining animals being assigned to int e r v a l s randomly. The e f f e c t of higher producing cows being, on occasion, p r e f e r e n t i a l l y assigned to the 12/12 i n t e r v a l would be to transfer some of the 'individual' e f f e c t (high production) to that of the 12/12 i n t e r v a l . The interactions MI and MC would likewise be affected i f l e v e l of production has an ef f e c t on A.M.-P.M. differences i n production. In order to determine the effects that in d i v i d u a l cows might have on an alternate A.M.-P.M. testing scheme, fo r t y -eight levels each of the variables C and MC were included. The addition of these ninety-six equations to the analysis required that :some of the variables f i t t e d i n Analysis A and B be deleted, i n order to not exceed the capacity of the least squares computed program used at the University. For that reason, 2 'days i n milk' was f i t t e d as two covariables, D and D , rather than as the main e f f e c t 'period of l a c t a t i o n ' as i n Analysis A and B. One of the assumptions of Covariance Analysis i s equality of slopes of the covariates on the dependent variables, within subclasses. That i s to say, for t h i s analysis, that a l l l a c t a t i o n curves may d i f f e r i n l e v e l , but not i n shape. I t i s well known that environmental factors - notably season of calving and age of cow - a f f e c t the shape of the la c t a t i o n curve of milk weights (Wood (1967), Wood (1969)), and the significance of the interactions that include P or 'period of l a c t a t i o n ' i n Analyses A and B (see Results and Discussion) would indicate the same for constituent weights and percentages. The ef f e c t s of not meeting t h i s assumption are two-fold. F i r s t , the error variance would be larger than i f the assumption had been met, thereby possibly masking some borderline e f f e c t s from being s t a t i s t i c a l l y s i g n i f -icant. Secondly, where the mean days i n milk for various subclasses d i f f e r s (notably within the 'lactation c l a s s ' variable - see Table 2.1), the least squares mean for the various levels w i l l be biased. Interpretation of the res u l t s from this analysis w i l l be limited to the e f f e c t of individuals on production and on A.M.-P.M. differences. The significance and magnitude of a l l other e f f e c t s w i l l be taken from Analysis A and B. RESULTS AND DISCUSSIONS F a c t o r s A f f e c t i n g an A l t e r n a t e A.M./P.M. T e s t i n g P l a n -A D i s c u s s i o n  The i n d e p e n d e n t v a r i a b l e s i n t h e m o d e ls u s e d f o r A n a l y s e s A, B, and C t h a t w o u l d n o t d i r e c t l y a f f e c t t h e a c c u r a c y o f an a l t e r n a t e t e s t i n g p l a n w i l l n o t be d i s c u s s e d i n t h i s s e c t i o n , o t h e r t h a n t o l i s t t h e p r o p o r t i o n o f t h e t o t a l sums o f s q u a r e s t h a t were a t t r i b u t e d t o t h o s e s o u r c e s o f v a r i a t i o n . They were i n c l u d e d i n t h e models so t h a t t h e e r r o r mean s q u a r e (us e d as t h e t e s t i n g term) w o u l d be m i n i m i z e d , and so t h a t t h e e s t i m a t e s o f c o n s t a n t e f f e c t s due t o t e r m s t h a t were i m p o r t a n t t o an a l t e r n a t e t e s t i n g p l a n w o u l d n o t be b i a s e d b e c a u s e o f d i s p r o p o r t i o n a t e numbers o f o b s e r v a t i o n s o c c u r r i n g i n t h e v a r i a b l e s t h a t were n o t . I n o r d e r t o i d e n t i f y t h o s e v a r i a b l e s t h a t c o u l d a f f e c t an a l t e r n a t e t e s t i n g p l a n , a h y p o t h e t i c a l l a c t a t i o n and a s i m p l i f i e d t e s t i n g p l a n w i l l be c o n s i d e r e d . F i r s t , i n o r d e r t o compare t h e a l t e r n a t e and t w e n t y -f o u r h o u r c o m p o s i t e t e s t i n g p l a n s , t h e a s s u m p t i o n s a r e made t h a t t h e i n t e r v a l between s a m p l e s i s e x a c t l y t h i r t y d a y s a p a r t , t h e f i r s t t e s t on t h e t w e n t i e t h day o f l a c t a t i o n a n d t h e l a s t ( t h e t e n t h ) on t h e 2 9 0 t h day, and t h a t t h e r e c o r d e x t e n d s f r o m t h e f i f t h day o f l a c t a t i o n t o t h e t h r e e h u n d r e d and f i f t h day i n c l u s i v e . Any twenthu-four h o u r sample w o u l d t h e n r e p r e s e n t t h e t h i r t y day p e r i o d e x t e n d i n g f r o m f i f t e e n days p r i o r t o t e s t day t o f o u r t e e n d a y s a f t e r . T h i s i d e a l i z e d s i t u a t i o n allows the computation of the l a c t a t i o n record by f i r s t computing the mean production of the ten samples, and then multiplying that mean by the constant 305. Second, the l a c t a t i o n i t s e l f may be s i m p l i f i e d by assuming that: 1. no diurnal v a r i a t i o n exists i n the production of milk and i t s constituents, and 2. each milking i s independent of a l l others within a l a c t a t i o n - that i s , no autocorrelation exists between successive milkings and the lac t a t i o n curve i s straight with slope zero. The variance of a mean of N samples from the popula-t i o n of 610 milkings i n the hypothetical l a c t a t i o n i s 2 2 (1 - N/610) x a e/N where a i s the within l a c t a t i o n variance and the term within the brackets i s the f i n i t e population correction. Further, the variance of the l a c t a t i o n record af t e r extending 2 2 the mean over the 610 milkings i s 610 x (1 - N/610) x a e/N. Given that the variances due to testing, sampling, and compositing are very small (Part I) they can be ignored when ca l c u l a t i n g the variance of records based on the two testing plans to be compared. The monthly i n t e r v a l - twenty-four hour composite testing plan can be considered to be based on a mean of twenty samples with variance 610 2x(l - 20/610) x a 2/20 and the alternate A.M./P.M. testing plan would be based on a 2 2 mean of ten samples with variance 610 x (1 - 10/610) x a /10. 36. 2 The important term i n these products i s oe/N; by halving the number of samples, the variance of the estimate of the lac t a t i o n 2 record has been doubled. An estimate of a i s therefore de s i r -e able i n order that the e f f e c t of halving the number of samples on the accuracy of the record i s known. The within l a c t a t i o n error variance was estimated i n Analysis C. It i s obvious that given the two assumptions l i s t e d above, any sampling plan that reduced the number of samples from twenty to ten would have the same expected error as the alternate A.M./P.M. test. This would include the bimonthly twenty-four hour test or any consecutive f i v e day test, or any other combination. In actual fact, the c u r v i l i n e a r l a c t a t i o n curve exhibited by cows for a l l milk component yiel d s does make a difference between when any given number of samples i s taken. The assumption that i n d i v i d u a l milking y i e l d s are independent from subsequent y i e l d s cannot be met. It i s well known that the majority of the error or bias i n a record estimate occurs when extending the f i r s t test back to the s t a r t of l a c t a t i o n and forward to the st a r t of the second i n t e r v a l (McDaniel, 1969). During the f i r s t two months, the cow i s r i s i n g , reaching, and f a l l i n g from her peak milk production - the curve i s not as well represented by an estimate of an average value (the single sample), as i t i s l a t e r i n the l a c t a t i o n . The greater the number of days that one sample has to be extended forward and back during t h i s period, the greater the possible error i n the cow's l a c t a t i o n record. A bimonthly plan would on average have the f i r s t test on the t h i r t y - f o u r t h day of l a c t a t i o n - but the extreme cases could be the f i f t h day or the sixty-fourth day. In t h i s respect then, a single sample testing plan at monthly in t e r v a l s would be more accurate than a bimonthly test . Autocorrelation of consecutive milk and constituent y i e l d s also adds a covariance term to the variance of the mean 2 . of N samples that was not included in the term a e/N' Because of t h i s , then consecutive milkings would be highly correlated and the variance of the mean of those ten milkings would be greater than for a mean of ten samples spaced one month apart. This e f f e c t i s further discussed i n the section describing the res u l t s of milk y i e l d below. Diurnal v a r i a t i o n i n milk and constituent could further a f f e c t the accuracy of d i f f e r e n t single sample plans. If the secretion rate of milk, f a t , protein, or lactose i s di f f e r e n t between night and day, or i f i t was the same but the i n t e r v a l between the morning and evening milking d i f f e r e d from that between evening and morning, then ten morning samples would not estimate true production as well as f i v e morning and f i v e evening; milkings. These e f f e c t s are examined i n Anlayses A, B, and C, as the variables M and the MI inte r a c t i o n . If secretion rates do d i f f e r between the evening and morning i n t e r v a l s , then i t i s important to know i f the rates d i f f e r by a constant amount. That i s , can the test day produc-tion be estimated from either the P.M. or A.M. production without bias. The text below the next three headings describes the 38. r e s u l t s of the three analyses of the data. The importance of the i n d i v i d u a l independent variables to an alternate testing plan i s discussed below the heading corresponding to the dependent variables, milk, f a t , protein, and lactose. The percentage and calculated y i e l d f o r the milk constituents have been grouped and discussed together under their respective headings. Analysis A Table 2.2 summarizes the results of Analysis A for milk, f a t , protein, and lactose y i e l d s and the three c o n s t i -tuent percentages. The f r a c t i o n of the t o t a l sums of squares accounted for by the main effects milking (M), i n t e r v a l (I), season (S), l a c t a t i o n class (L), and period of l a c t a t i o n (P) and a l l possible two-, three-, four-, and five-way interactions are given, along with the slgnficance of each category. The 2 R percentages for the complete model for milk, f a t percentage and y i e l d , protein percentage and y i e l d , and lactose percentage and y i e l d , as given beside ' t o t a l i n Table 2.2, are 64.5, 29.5, 50.0, 44.5, 56.3, 37.2, and 63.1 respectively. The t o t a l corrected sums of squares for each dependent variable i s given at the bottom of Table 2.2. The purpose of Analysis A was to determine the cate-gories that did not account for s i g n i f i c a n t amounts of va r i a t i o n i n the data, so that they could be deleted from the model for Analysis B. The discussion of t h i s analysis w i l l then be lim i t e d to pointing out those i n s i g n i f i c a n t e f f e c t s . The 39. TABLE 2.2 SUMMARY OF ANALYSIS A - ALL. DEPENDENT VARIABLES CATEGORY DEGREES OF FREEDOM R2 (1) MILK FAT PROTEIN LACTOSE [ YTFJiD % YIELD % YIELD % YIELD Total 3659 0.645 0. ,295 0.500 0.445 0. 563 0.372 0.631 M 1 0.012* 0. 012* 0.005* — 0. 015* — 0.011* I 1 0.003* 0. 015* — — 0. 003* • 0.001 0.003 S 1 0.001* 0. 008* — 0.003* 0. 001* — 0.001* L 2 0.004* 0. 007* 0.014* 0.009* 0. 002* 0.082* 0.002* P 3 0.214* 0. 021* 0.192* 0.156* 0. 146* 0.052* 0.213* MI MS 1 1 0.005* 0. 011* 0.001 0. 010* 0.002* 0.005* ML MP 2 3 0.001 0.001 —— 0.001 0.001 IS 1 0.004* 0. 001 0.004* 0.005* 0. 003* 0.002* 0.004* IL ! 2 — — 0.001 0.003* — 0.002 — IP 3 0.001* 0. 003* — 0.001 0. 002* 0.001 0.001 SL 2 0.013* 0. 004* 0.019* 0.001 0. 017* 0.012* 0.011* SP 3 0.001 0. 004* 0.001 0.007* 0. 001 0.002* 0.001 LP 6 0.027* 0. 018* 0.057* 0.005* 0. 041* 0.023* 0.022* MIS 1 v — — — — — MIL 2 — — — — — — — MH> 3 — — — — — 0.001 MSL 2 — 0. 001 0.001 MSP 3 -- — — — — — __ MLP 6? — 0. 001 0.001 ISL I 2 0.001 — — 0.001 — 0.016* 0.002* ISP 3 2 0.001 0. 001 0.002* — 0. 002* 0.021* 0.001 ILP 5 2 0.001 0. 006* —- 0.002 0. 003* 0.013* 0.001 SLP 6? 0.001 0. 007* 0.002 0.002 0. 002* 0.026* 0.002 MISL I 2 — — — — — — — MLSP 3  — — — — MSLP 6 2 — 0. 001 — — 0.001 — MTTiP 5 — 0. 001 — ISLP 3 2 0.001* 0. 002 0.002* 0.001 0. 003* 0.010* 0.001 MISLP 3 2 — — — — — — — Total CSS3 3659 36160.8 3136.74 62.16 916.78 34 .30 361.67 103.88 * Significant sources of variation. 1 Fraction of total sums of squares accounted for by fitting the effects in the completei model. 2 These categories contained empty subclasses. 3 Corrected sums of squares. CSS for yields decoded to kilograms. 40. importance of some of those effects that were deleted w i l l be discussed below, in the sections describing each dependent variable. A category was eliminated from the model only i f i t was not s i g n i f i c a n t for a l l of the dependent variables. In general, categories that remained i n the model for Analysis B, were Important sources of v a r i a t i o n over most of the dependent variables. Two int e r a c t i o n e f f e c t s , ' i n t e r v a l x l a c t a t i o n ' which was s i g n i f i c a n t for the dependent variable protein percentage only, and 'i n t e r v a l x season x l a c t a t i o n ' which was s i g n i f i c a n t for lactose percentage and y i e l d variables only were l e f t i n the model. Fourteen categories were deleted from Model A; a l l of them were interactions and a l l of them were associated with the term .'milking' or M. S p e c i f i c a l l y , the categories were MS, ML, MP, MIS, MIL,.MIP, MSL, MLP, MISL, MISP, MSLP, MILP, and MISLP. Analysis B A summary of the analysis of variance of Model B i s given i n Table 2.3. The percentages of t o t a l sums, of squares accounted for by the complete model for milk y i e l d was 64.2%, for f a t percentage and y i e l d , 29.0 and 49.7%, for protein percentage and y i e l d , 44.5 and 56.0%. and for lactose percent-2 age and y i e l d , 36.6 and 62.7%. A l l values for R for the complete Model B were, as expected, equal or lower than the values for Model A - however, the greatest difference, for lactose percentage, was only 0.6%. For a l l dependent variables 41. TABLE 2.3 SUMMARY OF ANALYSIS B - ALL DEPENDENT VARIABLES 2 (1) DEGREES R CATEGORY OF MILK FAT PROTEIN LACTOSE FREEDOM Y T E T i D % YTETiD Q, YTETiD Q. YTFJ.D Total 3659 0.642 0.290 0.497 0.445 0.560 0.366 0.627 M 1 0.052* 0.044* 0.018* 0.001* 0.070* — 0.048* I 1 0.003* 0.015* — — 0.003* 0.001 0.003* S 1 0.001* 0.008* 0.003* 0.001* — 0.001* L 2 0.004* 0.007* 0.014* 0.009* 0.002* 0.082* 0.002* P 3 0.214* 0.021* 0.19.2* 0.156* 0.146* 0.052* 0.213* MI 1 0.035* 0.051* 0.005* 0.005* 0.070* 0.009* 0.037* IS 1 0.004* 0.001 0.004* 0.005* 0.003* 0.002* 0.004* LL 2 — — 0.001 0.003* 0.001 0.002 — IP 3 0.001* 0.003* — 0.001 0.002* 0.001 0.001 SL 2 0.013* 0.004* 0.019* 0.001 0.017* 0.012* 0.011* SP 3 0.001 0.004* 0.001 0.007* 0.001 0.002* 0.001 LP 6 0.027* 0.018* 0.057* 0.005* 0.041* 0.023* 0.022* ISL l 2 0.001 — — 0.001 — 0.016* 0.002* ISP 3o 0.001 0.001 0.002* —- 0.002* 0.021* 0.001 LLP 5 2 0.001 0.006* — 0.002* 0.003* 0.013* 0.001 SLP 6 0 0.001 0.007* 0.002 0.002* 0.002* 0.026* 0.002 ISLP 3 2 0.001* 0.002 0.002* 0.001* 0.003* 0.010* 0.001 Total CSS3 3659 36160.8 3137.0 62.14 917.0 34.36 362.0 103.90 1 Fraction of total sums of squares accounted for by fitting the effects in the complete model. 2 These categories contained empty subclasses. 3 Total corrected sums of squares. CSS for yields decoded to kilograms. * Significant sources of variation. then, reducing the complete Model A did not s i g n i f i c a n t l y increase the residual sums of squares of Model B. 2 The R values for a l l categories that do not contain the term M are i d e n t i c a l to those for the same categories i n 2 Model A. However, the R for the categories M and MI are considerably larger than those i n Model A. In general, a l l s t a t i s t i c s associated with the categories not containing the variable M are i d e n t i c a l for both models, and d i f f e r e n t for those that do contain the term. The explanation of t h i s phenomena i s related to the fa c t that equal frequencies e x i s t for the A.M. and P.M. milk-ings, and that a l l categories eliminated from Model A contained 'milking' as part of the i n t e r a c t i o n . Using the 'milking x season' interaction as an example i t can be shown that, for season one, the A.M. x subclass frequency times the subclass e f f e c t i s the negative sum of the P.M. x subclass frequency times the subclass e f f e c t , because the two effects sum to zero by d e f i n i t i o n , and the two frequencies are equal. The same facts apply to the A.M. x and P.M. x S,, subclasses. Elimin-ation of t h i s i n t e r a c t i o n from the model w i l l therefore not e f f e c t the season main e f f e c t because the A.M. and P.M. effects cancel each other. On the other hand, the frequencies for the subclasses A.M. x and A.M. x are not equal, and effects do not ar i t h m e t i c a l l y cancel themselves. The sums of squares accounted for by t h i s interaction then i s partitioned by the least squares method, into the error term and the 'M' term, but not into the categories that are s p l i t evenly between A.M. and P.M. 2 In addition to the increased R for the categories M and MI, the least square constants within the two categories for protein percentage, and the MI i n t e r a c t i o n became s i g n i f -icant for f a t y i e l d and protein percentage. Analysis C Table 2.4 contains a summary of the analysis of variance of Model C - f i t t i n g i n d i v i d u a l animals as main ef f e c t s 2 and days i n milk as two covariables. The respective R as percentage points, for the dependent variables milk, f a t percentage and y i e l d , protein percentage and y i e l d , f a t percentage and y i e l d were 78.3, 49.2, 62.5, 63.8, 73.0, 59.1, and 77.3. Model C accounted for greater than ten percentage points more of the t o t a l sums of squares than either Model A or B. This would indicate that the v a r i a b i l i t y accounted for by differences between i n d i v i d u a l cows exceeded that l o s t by not including the interactions associated with days in milk, a l l three and four-way interactions and the season x l a c t a t i o n class and i n t e r v a l x l a c t a t i o n class interactions. 2 The between cow variance component (° )• f ° r each dependent variable, was calculated by the formula: 2 2 EMS = a + ka c e c where the mean square for cows in the analysis of variance table for Analysis C was set to EMS and 'k' was calculated to be J c 68.55 by the method described i n the s t a t i s t i c a l methods section TABLE 2.4 SUMMARY OF ANALYSIS C - ALL DEPENDENT VARIABLES 2 (1) DEGREES R CATEGORY OF FAT PROTEIN LACTOSE FREEDOM YIELD % YIELD % YIELD % YIELD Total 3663 0. 783 0. 492 0. 625 0. 638 0. 730 0. 591 0. 773 M(3> 1 0. 008 0. 007 0. 003 — 0. 010 0. 007 I 1 0. 004* 0. 006* — — 0. 004* — 0. 003* S 1 0. 001* 0. 008* 0. 001* L 2 0. 022* 0. 002* 0. 015* 0. 014* 0. 034* 0. 059* 0. 018* C 47 0. 218* 0. 239* 0. 217* 0. 226* 0. 267* 0. 331* 0. 214* ME MS ML 1 0. 006* 0. 008* 0. 001* 0. 001 0. 011* 0. 001 0. 006* X 2 — — — MC 47 0. 003 0. 010 0. 007 0. 002 0. 004 0. 004 0. 004 IS 1 — 0. 002* 0. 002* — 0. 001* — Days 1 0. 011* 0. 005* 0. 022* 0. 005* 0. 004* 0. 011* Days squared 1 0. 002* 0. 016* — 0. 008* 0. 003* 0. 013* 0. 003* Total CCS^  ' 3663 36480.3 3142.0 62.75 926.0 34.57 363.0 104.73 1 Fraction of total sums of squares accounted for by fitting the effects in the complete model. 2 Total corrected sums of squares. CSS for yields decoded to kilograms. 3 No test of significance done. * Significant sources of variation. above. Table 2.5 gives the EMS values, a and a for a l l 3 c e c dependent variables. A l l y i e l d entries were computed as variances of weights i n pounds, and decoded to kilograms by div i d i n g by 2.2046 squared. TABLE 2.5 MEAN SQUARE AND VARIANCE FOR COWS AND ERROR VARIANCE FOR ALL DEPENDENT VARIABLES - ANALYSIS C MILK YIELD 1 (kg) FAT PERCENT YIELD (kg) PROTEIN PERCENT YIELD (kg) LACTOSE PERCENT YIELD (kg) MS c 164.04 16.011 0. 289 4.451 0.197 2.557 0. 477 a 2 e 2.22 0.449 0.007 0.094 0.003 0.042 0.007 a 2 2.43 0.227 0.004 0.064 0.003 0.037 0. 007 c Milk Y i e l d Table 2.2 shows that, of a l l independent variables that included the "milking" e f f e c t , only the main e f f e c t 'M' and the 'milking x i n t e r v a l ' i n t e r a c t i o n (MI) were s i g n i f i c a n t sources of v a r i a t i o n for milk y i e l d . Consequently, those i n s i g n i f i c a n t interactions were deleted from the model used for Analysis A, and the data were re-analysed i n Analysis B. The interactions that include the factor 'M' may be interpreted as the influence of the remaining factors on the difference between the A.M. and P.M. milking. I n t u i t i v e l y , given that unequal milking i n t e r v a l s e x i s t between day and night and assuming the rate of milk secretion remains r e l a t i v e l y constant throughout the twenty-four hour period, any factor that affects the y i e l d of milk should then a f f e c t the differences between the two milkings. Everett and Wadell (1970a) found that the differences between A.M. and P.M. y i e l d s changed over months of l a c t a t i o n and levels of herd production; i n both cases the differences increased as d a i l y y i e l d s increased. The l e a s t squares deviations from the mean (9.23 kg. per milking) of those main e f f e c t s i n Model B known to e f f e c t productivity are given i n Table 2.6. Period of l a c t a t i o n i s shown to have the greatest influence on productiv-i t y i n that model, with deviations ranging from +2.54 kg. to -3.27 kg. The average e f f e c t of cows on productivity, deter-mined i n Anlaysis C, was comparable to the e f f e c t of the period 2 of l a c t a t i o n . The between cow variance was 2.43 kg. (Table 2.5), which corresponds to a standard deviation of the average e f f e c t of each cow from the mean of a l l cows of 1.56 kg. The lowest and highest y i e l d i n g cows i n the herd produced an average of 6.21 kg. less than, and 4.25 kg. greater than the herd average over t h e i r respective l a c t a t i o n s . 47 . TABLE 2 . 6 LEAST SQUARES CONSTANTS AND STANDARD ERRORS FOR SEASON, LACTATION, AND PERIOD OF LACTATION - ANALYSIS B: MILK YIELD SEASON LACTATION PERIOD OF LACTATION WINTER SUMMER 1 2 3 I>1 ?2 P 3 P 4 constants -0.17 0.17 -0.37 -0.35 0.72 2.54 1.83 -1.11 -3.27 (kg.) S.E. 0.04 0.04 0.07 0.10 0.13 0.10 0.10 0.06 0.09 The e f f e c t o f l e v e l o f p r o d u c t i o n on A.M.-P.M. d i f f e r e n c e s s h o u l d then be apparent i n t h e ' m i l k i n g x p e r i o d o f l a c t a t i o n ' and ' m i l k i n g x cow' i n t e r a c t i o n s , i n A n a l y s e s B and C. L e a s t square means f o r A.M. and P.M. m i l k y i e l d s f o r each o f t h e f o u r l a c t a t i o n p e r i o d c l a s s e s , and the A.M.-P.M. d i f f e r e n c e s a re g i v e n i n Ta b l e 2 . 7 . A l l v a l u e s were t a k e n from the r e s u l t s o f A n a l y s i s A, and a r e mean r e s u l t s o v er b o t h t h e 12/12 and t h e 10/14 m i l k i n g i n t e r v a l s . The d i f f e r e n c e s were g r e a t e r w i t h i n t h e 10/14 i n t e r v a l a l o n e , and l e s s w i t h i n t h e 12/12 i n t e r v a l . TABLE 2 . 7 ANALYSIS A LEAST SQUARE MEANS OF A.M. AND P.M. MILK YIELD BY LACTATION PERIOD ( k i l o g r a m s ) P P P P 1 2 3 4 A.M. 1 2 . 5 2 1 1 . 8 8 8 . 75 6 .42 P.M. 1 1 . 0 1 1 0 . 2 4 7 . 48 5 .50 d i f f e r e n c e 1.51 1.64 1 .27 0 .92 48. Except for the small increase i n the difference between the f i r s t and second periods of l a c t a t i o n ( 4 - 6 1 days and 62 - 122 days i n milk), the differences do show a general trend to decrease as production decreases with advancing l a c t a t i o n . This i s i n agreement with Everett's work (1970a), however, his conclusion that separate correction factors are required i n estimating d a i l y production from either A.M. or P.M. y i e l d s , for each month of l a c t a t i o n i s not supported here. Differences l i k e l y do e x i s t , but the f a i l u r e to show the trend with a reasonable l e v e l of s i g n i -ficance would indicate that the differences with an i n d i v i d u a l milking. The same general trend was apparent i n Analysis C. The least squares constants f o r 'P.M. x in d i v i d u a l " ranged from -0.61 kg. to +0.7 6 kg.; i n general the constants were negative (indicating a greater A.M.-P.M. difference) for those cows that produced more than the average for the herd. However, the trend was small and s t a t i s t i c a l l y i n s i g n i f i c a n t when compared with the differences between and within i n d i v i d u a l s . Table 2.8 gives the c e l l means and least square constants for the s i g n i f i c a n t effects 'milking', ' i n t e r v a l ' , and the 'milking x i n t e r v a l ' i n t e r a c t i o n , from Analysis B. The constants for milking were calculated over both in t e r v a l s and cannot be interpreted apart from the i n t e r v a l and the int e r a c t i o n e f f e c t s . The values under the column labelled ' c e l l deviations' are the combined effects of a l l three variables, and under ' c e l l t o t a l s ' the average milk y i e l d for each combin-TABLE 2. 8 MEANS AND LEAST SQUARE CONSTANTS FOR MILKING, INTERVAL, AND THE MI INTERACTION FOR MILK YIELD LEAST SQUARE MEAN(kg.) LEAST MILKING SQUARE CONSTANTS INTERVAL (1) MI CELL DEVIATIONS CELL TOTALS A.M. X 12:12 S.E. 9.22 0. 72 0. 03 0.42 0.07 -0. 59 0.03 0. 55 9.77 P.M. x 12:12 S.E. 9.22 -0.72 0.03 0. 42 0. 07 0.59 0.03 0.29 9. 51 A.M. x 10:14 S.E. 9. 22 0. 72 0. 03 -0.42 0.07 0.59 0.03 0. 89 10.11 P.M. X 10:14 S.E. 9.22 -0.72 0.03 -0.42 0. 07 -0.59 0.03 1.73 7.49 1 - i n k i l o g r a m s ; + S.E. 5.0. ation of milking and i n t e r v a l i s given. The c e l l deviations for the 12/12 i n t e r v a l show the A.M.-P.M. difference to be small: 0.55 kg. - 0.29 kg. = 0.26 kg. in comparison with the difference i n the 10/14 i n t e r v a l : 0.89 kg. - (-1.73 kg.) = 2.62 kg. These values are s l i g h t l y higher than the average deviations of Aryshires given by Everett & Wadell (1970a) for the 720 -749 minute i n t e r v a l and the 810 - 839 minute i n t e r v a l (P.M. to A.M.). Summarizing the results discussed above, the three analyses indicate that i n estimating d a i l y production from a single milking, no corrections are required for season, p a r i t y , stage of l a c t a t i o n , or i n d i v i d u a l cows. As expected, milking i n t e r v a l would be an important source of error i f no correction was made. A d a i l y estimate of production calculated by doubling the P.M. y i e l d of a cow being milked i n a 10/14 i n t e r v a l would underestimate the true production by an average of 15% - for a cow being milked at equal twelve hour in t e r v a l s the underestimate would be only 1%. The data indicates that an additive correction would be s u f f i c i e n t f o r a l l cows, season, and periods of l a c t a t i o n . Daily production could be estimated by f i r s t subtracting a constant (the combined effects of the milking and milking x i n t e r v a l interaction) from the single sample y i e l d , and then doubling that difference. That constant for estimating d a i l y production from a P.M. milking that followed a ten hour i n t e r v a l would be: (-0.72) + (-0.59) = -1.31 kg. For the A.M. milking, the constant would be: (+0.72) + (+0.59) = 1.31 kg. Conceivably, a set of additive correction factors could be determined for a l l possible milking i n t e r v a l s ; possibly by defining the r e l a t i o n s h i p between time since l a s t milking and rate of milk secretion (see Schmidt, 1960). The estimates of d a i l y y i e l d from the weight of a single milking when the i n t e r -v a l was known would be r e l a t i v e l y simple f o r a dairyman to calculate and, should s a t i s f y herd management requirements. Everett and Waddel (1970b) and Shook et_ al_. (1973) have suggested that m u l t i p l i c a t i v e correction factors would y i e l d better estimates than the additive factors discussed above. The expectation that a cow would y i e l d a certain percentage of her d a i l y production a f t e r a certain percentage of the hours i n a day have passed would seem more r e a l i s t i c than the expectation that the A.M.-P.M. difference i s a constant for a l l cows and lev e l s of production, for a given milking i n t e r v a l . As discussed above, i t i s l i k e l y that an analysis of the r a t i o s A.M./(A.M. + P.M.) y i e l d and P.M./(A.M. + P.M.) y i e l d , i n similar models (after deleting a l l effects that include M) would show an increase i n the percentage of the t o t a l sums of squares accounted f o r by the models. However, there i s doubt that the increase would be either s t a t i s t i c a l l y or economically s i g n i f i c a n t . 52. The average P.M./(A.M. + P.M.) r a t i o for a l l cows on the 10/14 i n t e r v a l was 0.426. This r a t i o corresponds to the r a t i o calculated for summer days, on the 10/14 i n t e r v a l as published by Shook et_ a l . (1973) , and i s higher than the value 0.419 given as the average for breeds other than Holsteins. A s i m p l i f i e d r a t i o correction factor can be calculated as the r a t i o of the number of hours i n a day to the number of hours i n the i n t e r v a l since the l a s t milking. Provided that the secretion rate of milk i s r e l a t i v e l y constant over the twenty-four hour day, and that the milking i n t e r v a l i s known, the product of the single milking y i e l d and the r a t i o should approximate the dai l y y i e l d . For the 10/14 hour i n t e r v a l , the bias i n an estimate of d a i l y y i e l d from the P.M. milking would be: 17.6 kg. - 7.49 x 24/10 = -0.38 kg. for a 2.1% underestimate of true y i e l d . The bias i n an estimate from the A.M. milking would be: 17.6 kg. - 10.11 x 24/14 = 0.27 kg. for a 1.5% overestimate. Daily y i e l d estimates based on P.M. and A.M. yi e l d s of cows being milked on the 12/12 hour i n t e r v a l would under- and over-estimate the true y i e l d by 0.26 kg., or 1.3%. This method could s u f f i c e as a 'quick and d i r t y ' estimate of d a i l y or monthly y i e l d s based on the weights of single milkings, without the necessity of compiling a table of additive correction factors. Daily and/or monthly y i e l d s may be required as ess e n t i a l information i n some highly managed dairy operations for i n d i v i d u a l feed rationing and economic evaluation of indiv i d u a l cows. However, for progeny testing of b u l l s and dam selection, complete 305 day records are a l l that i s required The results of Analyses A, B, and C indicate that no s i g n i f i c a n t bias would be introduced to a complete record based on an even number of alternate P.M. and A.M. milk y i e l d s . The monthly estimates, extrapolated from a single milking would be biased upward or downward depending on the milking that was measured and the milking i n t e r v a l - however, the bias would be equal and i n the opposite d i r e c t i o n the next month provided the test milking was alternated and the i n t e r v a l had not changed Other reports (Dickenson and McDaniel (1968), Prache (1965)) have suggested that an upward bias i n a la c t a t i o n record estimate w i l l occur i f the f i r s t monthly sample was from a morning milking. The implication of these reports was that each A.M. sample bias was not completely countered by the. following P.M. sample underestimate,' throughout the declining l a c t a t i o n curve. These analyses did not support that conclusion because a relationship between production l e v e l and the A.M.-P.M. differences was not found, however, the non-significant trend of larger differences with increased production would have the same ef f e c t . I t i s possible that s i g n i f i c a n t monthly differences i n the A.M.-P.M. differences did e x i s t i n the data - but that they occurred within a 'period of l a c t a t i o n ' subclass that was included i n the models for Analyses A and B, and were therefore not detected. This would be a res u l t of combining ten 'month' subclasses into four 'period of l a c t a t i o n ' subclasses - a proportion of the between month va r i a t i o n would be shi f t e d to the error mean square (the testing term), at the expense of the between 'period of l a c t a t i o n 1 variance component. I t i s expected that some measure of bias w i l l occur i n a la c t a t i o n record estimate from an alternate testing plan, depending on whether the f i r s t test i s taken i n the A.M. or P.M. However, the nature of the models used i n these analyses does not allow us to prove that the bias does exi s t , or to estimate the magnitude of that bias i f i t does. A gross estimate of the accuracy of an alternate testing plan, as compared to twenty-four hour monthly testing plan may be derived from the results of Analysis C. The error mean square describes the within cow, season, i n t e r v a l , and milking v a r i a b i l i t y around the regression l i n e describing the average l a c t a t i o n , and i s an estimate of the random error associated with the measure of any one milking. It should be remembered that the error mean square would contain much of the v a r i a b i l i t y associated with the deviations of ind i v i d u a l l a c t a t i o n curves from the mean curve - as discussed i n the S t a t i s t i c a l Methods section. If the monthly samples are taken every t h i r t y days, then the la c t a t i o n record may be computed by averaging a l l y i e l d s and multiplying by 610 - the t y p i c a l number of milkings per l a c t a t i o n . The variance of the l a c t a t i o n sum i s then the 2 variance of the average sample y i e l d x 610 . The error mean square for milk i n Analysis C (Table 2 2.5) was 2.22 kg . The alternate A.M.-P.M. tes t has ten samples per l a c t a t i o n , therefore: a | = (1 - 10/610) x o^/io = 0.218 kg 2 and the variance of the l a c t a t i o n record would be: a 2(record) = 610 2 x 0.218 = 81117.8 kg 2 giving a standard error of 284.8 kg. Assuming that the monthly test day sampling scheme i s 2 based on twenty independent samples with variance 2.22 kg then: a | = (1 - 20/610) x o-2/20 = 0.107 kg 2 a 2(record) = 610 2 x 0.107 = 39814.7 kg 2 giving a standard error of 199.5 kg. The ten test days are r e l a t i v e l y independent from each other - however, the A.M. and P.M. milkings within each te s t day would be p o s i t i v e l y correlated. This would introduce a covariance term to the variance of the mean, and while the magnitude of that term was not calculated, the net result would be an increase i n the standard error of the estimated l a c t a t i o n record. 2 n _2CK { ae(A.M. + ge(P.M.) + 2cpv(A.M./P.M.) }/2 y " 6 1 o ) To > 0.107 kg 2. The standard errors for the two t e s t i n g schemes computed above represent 5.06% and 3.55% of the average t o t a l l a c t a t i o n y i e l d (5624 kg.). These values are lower than the average absolute errors of l a c t a t i o n y i e l d estimate as tabulated by McDaniel (1969). This can be partly explained by the f a c t that some of the effects i n Analysis C removed v a r i -ation from the data that would not be removed in a sampling scheme - notably the i n t e r v a l and season of calving effects and t h e i r interactions. In addition, i t i s l i k e l y that covariance would e x i s t between successive monthly samples -t h i s would tend to increase the sample mean variance i n the same manner as the covariance between A.M. and P.M. milkings would. F i n a l l y , much of the error accumulated in a l a c t a t i o n record estimate i s not random, but a r e s u l t of sampling cows at d i f f e r e n t itimes i n t h e i r lactations and by extending samples over unequal i n t e r v a l s . 57. P e r c e n t a g e M i l k F a t and Y i e l d T a b l e 2.2 shows t h a t :the independent v a r i a b l e ' m i l k i n g ' was a s i g n i f i c a n t s o u r c e o f v a r i a t i o n f o r p e r c e n t a g e f a t and y i e l d o f f a t , b u t t h e ' m i l k i n g x i n t e r v a l ' i n t e r a c t i o n was s i g n i f i c a n t o n l y f o r p e r c e n t a g e f a t . A l l o t h e r v a r i a b l e s t h a t c o n t a i n e d ' m i l k i n g ' as a term were i n s i g n i f i c a n t f o r b o t h dependent v a r i a b l e s as w e l l as m i l k y i e l d and were o m i t t e d from t h e model used f o r A n a l y s i s B. The e f f e c t t h a t p r o d u c t i v i t y might have on t h e d i f f e r -ences between A.M. and P.M. c o n t e n t and y i e l d was i n v e s t i g a t e d i n t h e same manner as f o r m i l k y i e l d . T a b l e 2.9 shows t h a t ' p e r i o d o f l a c t a t i o n ' a c c o u n t e d f o r the l a r g e s t d i f f e r e n c e s i n p r o d u c t i v i t y i n Model B f o r b o t h dependent v a r i a b l e s . : I n Model C, i n d i v i d u a l cows ac c o u n t e d f o r t h e m a j o r i t y of the sums o f squares f o r b o t h v a r i a b l e s . The between cow v a r i a n c e f o r 2 2 p e r c e n t a g e f a t and y i e l d o f f a t were 0.227% and 0.004kg. r e s p e c t i v e l y (Table 2.5). These v a r i a n c e s c o r r e s p o n d t o s t a n d a r d d e v i a t i o n s o f each i n d i v i d u a l cow's mean from the mean h e r d v a l u e o f 0.476% and 6.3 grams r e s p e c t i v e l y . The e f f e c t o f p r o d u c t i v i t y on A.M.-P.M. d i f f e r e n c e s s h o u l d then be e v i d e n t w i t h i n the ' m i l k i n g x cow' and ' m i l k i n g x p e r i o d of l a c t a t i o n ' s u b c l a s s means. 58. TABLE 2.9 LEAST SQUARES CONSTANTS AND STANDARD ERRORS FOR SEASON, LACTATION AND PERIOD OF LACTATION - ANALYSIS B: FAT PERCENT-AGE AND YIELD SEASON LACTATION PERIOD OF LACTATION WINTER SUMMER 1 2 3 P l P2 P3 P4 p e r c e n t S.E. 0. 11 0.02 -0.11 0.02 -0.16 0.03 0.04 0.04 0.12 0. 05 0.72 0.04 -0.38 0.04 0.12 0.03 0.19 0.04 y i e l d 0.1 -0.1 -3.3 -1.0 4.3 12.0 4.6 -3.6 -13.1 (grams) 0.3 0.4 S.E. 0.2 0.2 0.3 0.5 0.6 0.5 0.5 T a b l e 2.10 shows t h e d i f f e r e n c e s between morning and e v e n i n g t e s t s and y i e l d s f o r each p e r i o d o f l a c t a t i o n . There i s no c o r r e l a t i o n between the d i f f e r e n c e s and t h e c o r r e s p o n d i n g l e a s t squares c o n s t a n t s i n Ta b l e 2.9, i n d i c a t i n g t h a t no o b v i o u s r e l a t i o n s h i p between p e r i o d o f l a c t a t i o n and d i f f e r e n c e s between A.M. and P.M. y i e l d s and c o n t e n t e x i s t s . TABLE 2.10 ANALYSIS A LEAST SQUARE MEANS OF A.M. AND P.M. FAT PERCENT-AGE AND YIELD BY LACTATION PERIOD PERCENTAGE YIELD (GRAMS) P l P2 P3 P4 P l P2 P3 P4 A.M. 4. 50 4. 01 4 .53 4. 53 54.0 47.0 39.0 29.0 P.M. 4. 81 4. 40 4 . 88 5. 00 52.0 44.0 36.0 27.0 d i f f e r e n c e -0. 31 -0. 39 -0 . 35 -0. 47 2.0 3.0 3.0 2.0 5 9. The e f f e c t of a cow's productivity on the A.M.-P.M. differences was examined by comparing the sign of each individual's deviation from the o v e r a l l mean (positive i f the cow's average percentage f a t or y i e l d was greater than the mean and negative i f less) with the sign of the deviation of the 'P.M. x in d i v i d u a l ' subclass mean. If a high producing cow yielded proportionally less f a t afte r the short i n t e r v a l , then the signs of the least square means would be opposite -they would be the same i f a higher than average y i e l d i n g cow had a higher content i n the P.M. milking than the A.M. Twenty-six of forty-seven cows (55%), had the same sign for percentage f a t , and twenty-one of forty-seven (45%) had the same sign for f a t y i e l d . These re s u l t s indicate that A.M.-P.M. differences i n f a t percentage and y i e l d , unlike the differences for milk y i e l d , are not dependent on the le v e l of f a t production, or content. There i s no reason then, to expect a m u l t i p l i c a t i v e model with the r a t i o of a single milking to the d a i l y t o t a l as the dependent variable, would account for more of the va r i a t i o n than the additive model discussed here. Tables 2.11 and 2.12 give the c e l l means and least square constants for percentage f a t and y i e l d , for the s i g n i -f i c a n t e f f e cts 'milking', ' i n t e r v a l ' , and the 'milking x i n t e r v a l ' i n t e r a c t i o n , from Analysis B. TABLE 2.11 MEANS AND LEAST SQUARE CONSTANTS FOR MILKING, INTERVAL, AND THE MI INTERACTION FOR PERCENTAGE FAT ; LEAST LEAST SQUARE CONSTANTS (1) CELL CELL SQUARE MEAN (kg).'. MILKING INTERVAL MI DEVIATIONS MEANS A.M. x 12:12 4.581 -0.194 -0.267 0.209 -0.252 4. 329 S.E. 0. 013 . 0.013 0. 013 P.M. X 12:12 S.E. 4.581 0.194 0.013 -0.267 0.0 31 -0.209 0. 013 -0.282 4.299 A.M. x 10:14 S.E. 4. 581 -0.194 0.013 0.267 0.031 -0.209 0.013 -0.136 4.445 P.M. x 10:14 S.E. 4.581 0.194 0. 013 0.267 0. 031 0.209 0. 013 0. 670 5.251 1 - i n percentage; + S.E. o 61. The differences between A.M. and P.M. percentage for the 12/12 and 10/14 hour i n t e r v a l s were 0.03 and -0.81 respectively. The r e s u l t for the equal i n t e r v a l s does not agree with Erb et_ al_. (1953) who found the average cow to test higher at the P.M. milking than at the A.M. but does agree with research c i t e d by Nielson (1967). The r e s u l t for the 10/14 i n t e r v a l shows the t e s t to be higher a f t e r the shorter ten hour i n t e r v a l than the test a f t e r the fourteen hour i n t e r v a l . This agrees with Schmidt (1960) who found that the average fat secretion rate decreased a f t e r twelve hours had passed between milkings. The A.M.-P.M. y i e l d differences for the 12/12 and 10/14 intervals were 1.4 and 5.4 grams respectively. If a P.M. y i e l d was doubled i n order to estimate d a i l y y i e l d , the average r e s u l t would underestimate the true y i e l d by 2% for the 12/12 i n t e r v a l and 7% for the 10/14 hour i n t e r v a l . These correspond to the 1 and 15% biases i n estimating d a i l y milk y i e l d from the P.M. milking as discussed i n the previous section. The percentage bias was greater for f a t i n the 12/12 i n t e r v a l because the f a t content as well as the milk y i e l d was greater at the A.M. milking than the P.M. The reduction i n the percent-age f a t a f t e r the long i n t e r v a l p a r t i a l l y cancelled the increased milk production so that the percentage bias for f a t y i e l d was only one-half the bias for milk y i e l d i n the 10/14 i n t e r v a l . The r e s u l t s indicate that an additive correction factor for estimating d a i l y butterfat y i e l d from either an A.M. or P.M. measurement would be s u f f i c i e n t f or a l l cows, seasons and periods of l a c t a t i o n . Daily butterfat y i e l d could be estimated by subtracting the combined ef f e c t s of milking and the 'milking x i n t e r v a l 1 interaction from the single sample y i e l d , and then doubling the r e s u l t . The constant term to be subtracted for estimating d a i l y y i e l d from a P.M. milking,: for a cow being milked.on a 10/14 hour i n t e r v a l would be: (-1.7) + (-1.0) = -2.7 grams. The same term would be added to an A.M. y i e l d to estimate d a i l y butterfat production. A set of constants for other milking in t e r v a l s could be tabulated. The s e c r e t i o n rates of fat (grams per hour) calculated from the c e l l means of Table 2.12 were 3.46, 3.34, 3.15, and 3.87 for the A.M. and P.M. milkings af t e r the ten and fourteen hour inter v a l s respectively. The wide discrepancy between the rates during the ten hour and the fourteen hour interv a l s would introduce a large bias to an estimate of dai l y f a t y i e l d based on the r a t i o of hours i n a day to hours i n the i n t e r v a l , whereas the same technique would give small biases for milk, protein, and lactose (see discussion under the 1 sections devoted to milk, protein, and lactose). The content of f a t i n milk i s more dependent on the i n t e r v a l that the cow i s being milked on than protein or lactose (see Table 2.4) and the d a i l y y i e l d cannot be predicted by a simple r a t i o that assumes a constant secretion rate over any twenty-four hour period. A complete 305 day record from an alternate A.M./P.M. TABLE 2.12 MEANS AND LEAST SQUARE CONSTANTS FOR MILKING, INTERVAL, AND THE MI INTERACTION FOR BUTTERFAT YIELD LEAST SQUARE MEAN(gm.) LEAST SQUARE CONSTANTS (1) CELL CELL MILKING INTERVAL MI DEVIATIONS MEANS A.M. x 12:12 S.E. 41.1 1.7 0.2 -0.3 0.4 -1.0 0.2 0.4 41.5 P.M. x 12:12 S.E. 41. 1 -1.7 0.2 -0.3 0.4 1.0 0.2 -1.0 40.1 A.M. x 10:14 S.E. 41.1 1.7 0.2 0.3 0.4 1.0 0.2 3.0 44.1 P.M. x 10:14 S.E. 41.1 -1.7 0.2 0.3 0.4 -1.0 0.2 -2.4 38.7 1 - i n grams; + S.E. t e s t i n g scheme f o r b u t t e r f a t y i e l d would be c a l c u l a t e d by t h e method d e s c r i b e d f o r m i l k y i e l d i n t h e p r e v i o u s s e c t i o n . There i s no e v i d e n c e t h a t any b i a s would e x i s t i n the complete r e c o r d p r o v i d e d t h a t an e q u a l number of A.M. and P.M. t e s t s had been made and t h a t t h e m i l k i n g i n t e r v a l had n o t changed over the l a c t a t i o n . U s i n g t h e e r r o r mean square f o r f a t y i e l d from A n a l y s i s C (Table 2.5) i t i s p o s s i b l e t o d e t e r m i n e t h e e f f e c t o f h a l v i n g t h e number o f samples from twenty (the monthly t e s t day s a m p l i n g scheme) t o t e n (the a l t e r n a t e A.M./P.M. t e s t i n g 2 2 2 p l a n ) . a e f o r f a t y i e l d was 0.007 kg. or 70 gramsf The a l t e r n a t e t e s t i n g p l a n has t e n samples p e r l a c t a t i o n , t h e r e -f o r e : a - = (1 - 10/610) x a 2/10 =6.9 grams 2 where y i s the average y i e l d p e r sample, and t h e v a r i a n c e o f t h e l a c t a t i o n r e c o r d would be: a r e c o r d = 6 1 ° 2 x 6 ' 9 ^ 2 = 2 5 6 - 7 ^ • L i k e w i s e t h e v a r i a n c e o f a b u t t e r f a t r e c o r d based on a monthly t e s t day p l a n ( i g n o r i n g the c o m p o s i t i n g and t e s t i n g v a r i a n c e s -see d i s c u s s i o n i n P a r t I) would be: a - = (1 - 20/610) x a 2/20 = 3.4 grams 2 y 6 Record = 6 1 0 x 3 ' 4 9 2 = 126.51 k g 2 . The s t a n d a r d e r r o r s f o r r e c o r d s based on the two p l a n s a r e 16.02 kg. and 11.25 kg. r e s p e c t i v e l y , w h i c h a r e o n l y 6.38 and 4.48% of t h e average t o t a l l a c t a t i o n y i e l d (251 k g ) . I t i s l i k e l y t h a t t h e s t a n d a r d e r r o r f o r r e c o r d s samples by the monthly test day plan i s an underestimate, due to the auto-co r r e l a t i o n of the A.M. and P.M. y i e l d s within each t e s t day (see discussion for milk y i e l d above) - however, the difference between the two standard errors i s small - i n d i c a t i n g that the random error associated with each independent test does not contribute much to the error of a l a c t a t i o n record. The standard errors as a percentage of t o t a l y i e l d are greater for butterfat than for milk y i e l d , which corresponds to the compar-isons of milk and f a t record errors as compiled by McDaniel (1969), however, the values are considerably smaller than other studies have indicated (McDaniel, 1969). The discussion on the standard errors for milk y i e l d records given i n the previous section i s also applicable to the values for f a t . Protein Percentage and Y i e l d Table 2.2 shows that the two-way interactions that included the term 'milking' with 'season', 'lactation', and 'period of l a c t a t i o n ' were i n s i g n i f i c a n t sources of v a r i a t i o n for the dependent variables protein percentage and y i e l d . A l l three-, four-, and five-way interactions i n Analysis A, and the 'milking x cow' interaction in Analysis C (Table 2.4) were also i n s i g n i f i c a n t . Table 2.3 shows that the independent variable 'milking' and the 'milking x i n t e r v a l 1 i n t e r a c t i o n were s i g n i -f i c a n t sources of v a r i a t i o n for both dependent variables i n Analysis B. The e f f e c t that these two variables would have on a single milking sampling plan i s discussed below. The correlations of milk y i e l d , protein y i e l d , and protein percentage, calculated for a l l milkings sampled, are given i n Table 2.13, and indicate that protein y i e l d increased as milk y i e l d increased - however, because the r e l a t i v e rate of increase was not so great with protein as with milk, the protein percentage decreased. Percentage protein was, there-fore, negatively correlated with both milk and protein y i e l d s . TABLE 2.13 CORRELATIONS OF MILK YIELD, PROTEIN YIELD, AND PERCENTAGE PROTEIN MILK . PROTEIN  YIELD PERCENTAGE YIELD 1 -0.64 0.93 1 -0.35 1 Tables 2.14 and 2.15 show that the y i e l d of protein per milking and the A.M.-P.M. differences in y i e l d were affected by 'period of l a c t a t i o n ' in same way as milk y i e l d was (Tables 2.6 and 2.7). The A.M.-P.M. differences for protein y i e l d were not tabulated because the four values for P-^  to P^ di f f e r e d by less than 0.00%. However, the modifying e f f e c t of the negative c o r r e l a t i o n between protein percentage and y i e l d i s apparent when the P^ and P^ A.M.-P.M. differences are compared. These differences were the largest and smallest of the four values for both milk and protein y i e l d ; the A.M.-P.M. y i e l d differences creased 44% for milk but only 35% for protein. The MP milk y i e l d protein percent protein y i e l d 67. TABLE 2.14 LEAST SQUARE CONSTANTS AND STANDARD ERRORS FOR SEASON, LACTATION AND PERIOD OF LACTATION - ANALYSIS B: PROTEIN PERCENTAGE AND YIELD SEASON LACTATION PERIOD OF LACTATION WINTER SUMMER 1 2 3 P l P2 P3 P4 percent 0.04 -0.04 0.04 0.15 -0.19 -0.33-0.26 0.15 0.44 S.E. 0.01 0.01 0.01 0.02 0.03 0.02 0.02 0.01 0.02 y i e l d -0.5 0.05 -0.8 0.0 0.8 6.4 4.7 -2.2 -8.8 S.E. 0.2 0.2 0.2 014 0.04 0.3 0.3 0.2 0.3 TABLE 2.15 ANALYSIS A LEAST SQUARE MEANS OF A.M. AND P.M. PROTEIN YIELD BY LACTATION PERIOD P l P2 P3 P4 A.M. _ 42.0 40.9 33.7 26.5 P.M. 37.5 36.4 29.0 22.9 difference 4.7 5.5 4.7 3.6 68. i n t e r a c t i o n for protein y i e l d did show the same general trend as i t did for milk y i e l d - the A.M.-P.M. differences were influenced by the stage of l a c t a t i o n ; most l i k e l y by the change in d a i l y productivity associated with stage of l a c t a t i o n . However, the inter a c t i o n was i n s i g n i f i c a n t s t a t i s t i c a l l y (implying that the differences were small and variable compared with the unexplained v a r i a b i l i t y ) , and had less influence r e l a t i v e to the changes i n productivity than milk y i e l d did. The same trend was evident within the effects of cows and the 'milking x cow' in t e r a c t i o n , i n Analysis C. The standard deviation of the mean protein y i e l d s of a l l cows was 5.48 grams (calculated from the between cow variance - Table 2. and the greatest deviation of a cow's average production from the mean of a l l cows was twenty-four grams. 66% of a l l cows had greater than average A.M.-P.M. differences i n protein y i e l d i f t h e i r y i e l d was above the herd mean, or less than average i f t h e i r d a i l y y i e l d was below. Again, while an individual's productivity did seem to influence the A.M.-P.M. differences i n protein y i e l d , the trend was s t a t i s t i c a l l y i n s i g n i f i c a n t and was exhibited by only 66% of a l l cows sampled. Table 2.16 gives the percentage protein c e l l means and l e a s t square constants f o r the effects 'milking', 'interval and the 'milking x i n t e r v a l ' i n t e r a c t i o n , from Analysis B. 'Interval' was not a s i g n i f i c a n t e f f e c t for percentage protein, but was included because of the significance of the MI in t e r -action. The c e l l means and least square contants for protein y i e l d are given i n Table 2.17. TABLE 2.16 MEAN AND LEAST SQUARE CONSTANTS FOR MILKING, INTERVAL, AND THE MI INTERACTION FOR PERCENTAGE PROTEIN LEAST SQUARE LEAST SQUARE CONSTANTS 1 CELL CELL MEAN MILKING INTERVAL MI DEVIATIONS MEANS A.M. X 12:12 3.74 -0.02 -0.03 -0. 03 -0.08 3.67 S.E. 0.01 0.02 0. 01 P.M. x 12:12 3. 74 0.02 -0. 03 0.03 0.02 3.77 S.E. 0.01 0.02 0.01 A.M. x 10:14 3. 74 -0. 02 -0. 03 0.03 0.04 3.79 S.E. 0.01 0.02 . . 0.01 P.M. X 10:14 3. 74 0. 02 -0.03 -0. 03 0.02 3. 75 S.E. 0.01 0. 02 0.01 TABLE 2.17 MEAN AND LEAST SQUARE CONSTANTS FOR MILKING, INTERVAL, AND THE MI INTERACTION FOR PROTEIN YIELD (GRAMS) LEAST SQUARE LEAST SQUARE CONSTANTS 1 CELL CELL MEAN (GM.) MILKING INTERVAL MI DEVIATIONS MEANS A.M. X 12:12 S.E. 33.5 2.6 0.1 1.3 0.3 -2.6 0.0 1.3 34. 8 P.M. X 12:12 S.E. 33.5 -2.6 0.1 1.3 0.3 2.6 0. 0 1.3 34.8 A.M. X 10: 14 S.E. 33.5 2.6 0.1 -1.3 0.3 2.6 0.0 3. 9 37.4 P.M. X 10:14 S.E. 33.5 -2.6 0.1 -1.3 0.3 -2.6 0.0 -6.5 27..0 1 - i n grams + S.E. The A.M.-P.M. differences for percentage protein and y i e l d of protein for the 12/12 i n t e r v a l were 0.10% and 0.0 grams respectively, i n d i c a t i n g that the secretion rate of protein (grams/hour) i s constant over a twenty-four hour period. The difference i n the A.M. and P.M. percentage was due to the differences i n milk y i e l d over the two twelve hour periods. Cows tested 0.04% lower and produced 10.4 grams less protein at the P.M. milking after the ten hour i n t e r v a l than the A.M. milking after the longer fourteen hour i n t e r v a l . Again the secretion rate remained constant over both i n t e r v a l s , at 2.7 grams/hour - however, the rate was lower than the rate for the cows milked at equal inter v a l s (2.9 grams/hour). An estimate of dai l y protein y i e l d based on the y i e l d and test of one P.M. milking would underestimate true production by 0% for the 12/12 in t e r v a l and by 16% for the 10/14 i n t e r v a l ; these biases are comparable with the respective 1% and 15% underestimate of twenty-four hour milk y i e l d based on one P.M. y i e l d . These re s u l t s f o r protein y i e l d indicate that an additive correction factor, to be subtracted from a P.M. y i e l d or added to the A.M. y i e l d before multiplying by two for an estimate of d a i l y y i e l d , would be s u f f i c i e n t for a l l cows, lac t a t i o n s , seasons, and periods of la c t a t i o n . The constant term to be subtracted for estimating daily y i e l d from a P.M. milking, for a cow being milked on 10/14 hour i n t e r v a l would be: (-2.6) + (-2.6) = -5.2 grams. The constant would be 0.0 grams for estimating d a i l y protein y i e l d from either milking of a cow being milked i n the 12/12 hour i n t e r v a l . Other correction factors for other intervals could be determined and tabulated. Daily protein y i e l d may be more accurately estimated from a single sample by cal c u l a t i n g the secretion rate (grams/ hour) over the i n t e r v a l that was sampled and extending that rate over twenty-four hours. This technique would be equivalent to using a m u l t i p l i c a t i v e or r a t i o correction factor as discussed i n the milk y i e l d section, except that the factors would be based e n t i r e l y on the r a t i o of twenty-four hours to the hours i n the i n t e r v a l that was sampled. The fact that the average rate of protein secretion i n th i s study was constant between the A.M.-P.M. and P.M.-A.M. in t e r v a l s , for both the 12/12 and 10/14 hour i n t e r v a l s , indicates that a r a t i o technique would estimate d a i l y y i e l d with very l i t t l e bias, provided that the milking i n t e r v a l was known. Using the data i n Table 2.17, dai l y y i e l d estimated from a P.M. milking(after a ten hour interval) would be: (24/10) x 27.0 = 64.8 grams. The actual production was: (37.4 + 27.0) = 64.4 grams. The 0.4 gram difference i s due to rounding the rates of milk secretion to one decimal place. If the d a i l y milk y i e l d was known then the single test could be extended over the twenty-four hour milk y i e l d , rather than f i r s t computing the single milking y i e l d of protein and extending that value to twenty-four hours as discussed above. 73. Percentage protein for the single A.M. and P.M. milkings on the 12/12 i n t e r v a l (Table 2.16), d i f f e r e d from the average (or the value that i s estimated by the t r a d i t i o n a l composite test) by only 1.3%; the difference for the two 10/14 i n t e r v a l milkings was only 0.5%. These biases would be negative or positive depending on whether the percentage was derived from an A.M. or P.M. sample however, they are small enough to allow a very simple estimate of da i l y protein y i e l d from a single sample without the requirement for correction factors. An estimate of the 305 day protein y i e l d from an alternative A.M./P.M. testing plan would be calculated by the method described for milk y i e l d . Provided that the milking i n t e r v a l does not change over the l a c t a t i o n , and that an equal number of A.M. and P.M. samples are tested, the estimate should not contain any s i g n i f i c a n t bias. The standard error for a l a c t a t i o n record for protein y i e l d based on the alte r n a t i v e A.M./P.M. testing plan was calculated from the error mean square from Analysis C. a 2 = 0.003 kg 2 = 30 grams 2 a | = (1 - 10/610) x a^/lO = 2.95 grams 2 2 where a — i s the variance of the mean of ten samples, and the y * variance of the record i s : 2 = 610 2 x 2.95 g 2 = 109.8 kg 2 a record and the standard error i s : a . = /109..8 kg 2 = 10.48 kg. record . This standard error i s only 5.14% of the average l a c t a t i o n y i e l d of 204 kilograms. The standard error for a record based on the t r a d i -t i o n a l twenty-four hour sampling plan would be: a | = (1 - 20/610) x a 2/20 = 1.45 gram 2 a2 , = 610 2 x 1.45 g 2 = 53.99 kg 2 record 3 3 2 a , = /53.99 grams =7.3.5 kg. record 3 3 This value represents only 3.60% of the average l a c t a t i o n y i e l d . These values include that l i t t l e accuracy i s lo s t (that i s due to random v a r i a t i o n i n protein y i e l d of a single milking) by halving the number of samples from twenty per l a c t a t i o n to ten, and that the random error for protein y i e l d i s less than that for y i e l d when viewed as a proportion of the t o t a l l a c t a t i o n production (standard errors for f a t represented 6.38% and 4.48% of the t o t a l f a t y i e l d ) . The reader i s directed to the section for Milk Y i e l d above for a discussion on the estimates of the standard error of records. Lactose Percentage and Y i e l d A l l interactions that contained the term 'milking' i n Analysis A were i n s i g n i f i c a n t sources of v a r i a t i o n for lactose y i e l d and percentage, except the 'milking x i n t e r v a l ' i n t e r -action (Table 2.2). These results were sim i l a r to those for milk, f a t , and protein y i e l d and f a t and protein percentages. In Analysis B (the reduced model) the MI interaction was s i g n i f i c a n t , but 'milking' and ' i n t e r v a l ' were not, for percentage lactose. A l l three e f f e c t s were s i g n i f i c a n t for y i e l d of lactose. The correlations of milk, lactose y i e l d and percent-age lactose are given i n Table 2.18. TABLE 2.18 CORRELATIONS OF MILK YIELD, LACTOSE YIELD, AND PERCENTAGE LACTOSE MILK LACTOSE YIELD PERCENTAGE YIELD milk y i e l d 1 0.39 0.99 lactose % 1 0.51 lactose y i e l d 1 Yi e l d of milk and lactose were very highly correlated and the pos i t i v e c o r r e l a t i o n of percentage lactose with both milk and lactose y i e l d indicates that a proportional change i n milk y i e l d would be accompanied by a s l i g h t l y larger proportional change i n lactose y i e l d . Table 2.19 shows that 'period of l a c t a t i o n ' affected lactose productivity more than 'season' and 'lactation', and the differences between the least square means for A.M. and P.M. over the four 'periods of l a c t a t i o n ' (Table 2.20) shows the differences to be p o s i t i v e l y correlated with the least square constants for P^ to P^. This c o r r e l a t i o n i s sim i l a r to that discussed for milk y i e l d and protein y i e l d - however, where the e f f e c t was moderated by the negative c o r r e l a t i o n of percentage protein and y i e l d for protein, i t was magnified by 76. TABLE 2.19 LEAST SQUARES CONSTANTS AND STANDARD ERRORS FOR SEASON, LACTATION AND PERIOD OF LACTATION - ANALYSIS B: LACTOSE PERCENTAGE AND YIELD SEASON LACTATION PERIOD OF LACTATION WINTER SUMMER 1 P P P P *1. 2 3 4 p e r c e n t 0.00 -0.00 0.17 -0.10 -0.07 0.09 0.12 -0.05 -0.17 S.E. 0.01 0.01 0.01 0.01 0.02 0.01 0.01 0.01 0.01 y i e l d -0.8 0.8 (grams) S.E. 0.2 0.2 -0.5 -2.3 2.8 13.4 10.0 -6.2 -17.2 0.4 0.6 0.7 0.5 0.5 0.4 0.5 TABLE 2.20 ANALYSIS A LEAST SQUARE MEANS OF A.M. AND P.M. LACTOSE PER-CENTAGE AND YIELD BY LACTATION PERIOD PERCENTAGE YIELD (GRAMS) A.M. 5.10 5.08 4.93 4.81 64.0 60.8 43.4 31.4 P.M. 5.05 5.06 4.83 4.83 55.8 52.2 37.3 27.1 d i f f e r e n c e s 0.05 0.02 -0.2 -0.02 8.2 8.6 6.1 4.3 t h e p o s i t i v e c o r r e l a t i o n o f l a c t o s e p e r c e n t a g e and y i e l d . The change i n t h e A.M.-P.M. y i e l d d i f f e r e n c e s f r o m P^ t o P^ r e p r e s e n t e d a 50% d r o p ( f r o m 8.6 grams t o 4.3 grams) - wh e r e a s t h e d i f f e r e n c e f o r m i l k y i e l d o v e r t h e same p e r i o d was 44% and 35% r e s p e c t i v e l y . The e f f e c t t h a t t h e p r o d u c t i v i t y o f cows m i g h t have on A.M.-P.M. d i f f e r e n c e s i n l a c t o s e y i e l d s was examined by c o m p a r i n g t h e s i g n s o f t h e l e a s t s q u a r e c o n s t a n t s f o r cows and t h e P.M. x cow 1 i n t e r a c t i o n e f f e c t , as d i s c u s s e d f o r f a t y i e l d . T h i r t y - f i v e o f f o r t y - s e v e n cows (74%) had d i f f e r e n c e s i g n s f o r t h e two e f f e c t s - i n d i c a t i n g t h a t cows t h a t p r o d u c e d more t h a n t h e h e r d a v e r a g e f o r l a c t o s e h ad l a r g e r t h a n a v e r a g e A.M.-P.M. d i f f e r e n c e s and v i c e v e r s a . T h i s c o r r e s p o n d s t o t h e 74% o f cows w i t h t h e same s i g n f o r m i l k y i e l d , 55% f o r f a t y i e l d and 66% f o r y i e l d o f p r o t e i n . T h e s e r e s u l t s i n d i c a t e t h a t a r e l a t i o n s h i p between l e v e l o f l a c t o s e p r o d u c t i o n and t h e A.M.-P.M. d i f f e r e n c e s p r o b a b l y does e x i s t , and t h a t t h e r e l a t i o n s h i p i s v e r y s i m i l a r t o t h a t d i s c u s s e d f o r m i l k y i e l d . T a b l e 2.21 g i v e s t h e c e l l means and l e a s t s q u a r e c o n s t a n t s f o r t h e e f f e c t s o f ' m i l k i n g ' , ' i n t e r v a l ' , and t h e 'M x I ' i n t e r a c t i o n f r o m A n a l y s i s B, f o r p e r c e n t a g e l a c t o s e . The d i f f e r e n c e s between A.M. and P.M. f o r t h e 12/12 and 10/14 i n t e r v a l s was 0.0 6 and -0.07 r e s p e c t i v e l y - t h e f a c t t h a t a l l f o u r p e r c e n t a g e s a r e v e r y c l o s e t o t h e o v e r a l l mean o f 4.98% r e f l e c t s on t h e 0.99 c o r r e l a t i o n o f m i l k and l a c t o s e y i e l d s . The c e l l means f o r y i e l d o f l a c t o s e a r e g i v e n i n T a b l e 2.22. The A.M.-P.M. d i f f e r e n c e s f o r t h e 12/12 and 10/14 TABLE 2.21 MEANS AND LEAST SQUARE CONSTANTS FOR MILKING, INTERVALS, AND THE MI INTERACTION FOR LACTOSE PERCENTAGE LEAST SQUARE MEAN (gm. ) LEAST SQUARE CONSTANTS ^ CELL DEVIATIONS CELL MEANS MILKING INTERVAL MI A.M. X 12:12 S.E. 4. 98 0. 00 0. 01 0.02 0.01 -0. 03 .0.01 -0.01 4.97 P.M. X 12:12 S.E. 4.98 -0. 00 0.0.1. 0.02 0.01 0.03 0.01 0.05 5.03 A.M. X 10:14 S.E. 4.98 0. 00 0.01 -0.02 0.01 0. 03 0.01 0.02 5. 00 P.M. X 10:14 S.E. 4.98 -0.00 0. 01 -0. 02 0. 01 -0.03 0.01 -0.05 4.93 1 - + S.E. ex? TABLE 2.22 MEANS AND LEAST SQUARE CONSTANTS FOR MILKING, INTERVAL, AND THE MI INTERACTION FOR LACTOSE YIELD IN GRAMS LEAST SQUARE MEAN(gm.) LEAST SQUARE CONSTANTS (1) CELL DEVIATIONS CELL MEANS MILKING INTERVAL MI A.M. X 12:12 S.E. 46.5 3.7 0.2 2.3 0.4 -3.3 0,2 2.7 49.2 P.M. X 12:12 S.E. 46. 5 -3.7 0.2 2.3 0.4 3.3 0.2. 1.8 48.3 A.M. X 10:14 S.E. 46. 5 3.7 0.2 -2.3 0.4 3.3 0.2 4.7 51.1 P.M. X 10:14 S.E. 46. 5 -3.7 0.2 -2.3 0.4 -3.3 0.2 -9.2 37.3 1 - 1 grams; + S.E. 8.0. int e r v a l s were 0.9 grams and 13.8 grams respectively. The bias i n an estimate of daily lactose y i e l d based on the lactose y i e l d of one P.M. milking with no correction would be a 1% underestimate (12/12 interval) or a 16% underestimate (10/14 i n t e r v a l ) , which i s very close to the results obtained for the y i e l d s of milk and protein. These values, and the fact that a l l interactions that included 'milking' as a term were i n s i g n i f -icant (except the MI interaction) indicate that - as for milk, f a t , and protein, an additive correction factor to be added to an A.M. milking or subtracted from a P.M. milking would be s u f f i c i e n t correction for a l l season, lactations, cows, and periods of lactations to estimate one half of a d a i l y y i e l d . The correction factor for the 10/14 hour i n t e r v a l would be: (-3.7) + (-3.3) = -7.0 grams and for the 12/12 i n t e r v a l ; the correction would be: (-3.7) + (3.3) = -.0.4 grams. Factors could be determined and tabulated for a l l milking i n t e r v a l s . Estimates of d a i l y y i e l d s calculated by extending the lactose secretion rate would be biased i n the same order as estimates of d a i l y milk y i e l d , and could be used as a simple technique for quick estimates for management purposes. A d a i l y y i e l d estimate based on a P.M. milking a f t e r a 10 hour i n t e r v a l would be: (24/10) x 37.3 = 89.5 grams 81. using the average 10/14 y i e l d figures from Table 2.22. The actual production should be: 37.3 + 51.1 =88.4 grams which indicates a bias i n the estimate of +1.2%. As with milk, f a t , and protein, a 305 day estimate of lactose y i e l d , calculated from alternate A.M. and P.M. milk samples at monthly i n t e r v a l s by the same method as described for f a t should not be biased - provided that the milking i n t e r -v a l does not change and that an even number of samples are taken over the l a c t a t i o n . The standard error for a l a c t a t i o n record based on 10 samples (the alternate A.M./P.M. testing plans) would be: a 2 = 0.007 kg 2 = 70 grams 2 a|- = (1-10/610) x a 2/10 = 619 grams 2 a 2 r e c o r d = 6 1° 2 x 6 - 9 V = 2 5 6 ' 7 5 k^ a , = /256. 7=5 = 16.02. kg. record ^ The standard error for a record based on 20 samples (the t r a d i t i o n a l 24 hour testing plan) would be: o-l = (1 - 20/610) x a 2/20 =3.4 grams 2 2 = 610 2 x 3.4 g 2 = 126.51 kg 2 a record • • a , = 11.25 kg. record ^ These two values represent 5.65% and 3.97% of the average l a c t a t i o n y i e l d of lactose for this data (283.5 kg.). As for a l l other dependent variables, the e f f e c t of halving the number 82. of samples on the v a r i a b i l i t y of a 305 day record i s very small, and the random error that contributes to the v a r i a t i o n i n the lactose record i s s l i g h t l y smaller (proportional to t o t a l yield) for lactose than i t i s for f a t . Additional sources of error i n that may a f f e c t a 305 day y i e l d estimate are discussed i n the section for milk y i e l d . 83 . CONCLUSIONS P a r t I : The v a r i a n c e s a t t r i b u t e d t o t e s t i n g , s a m p l i n g , and c o m p o s i t i n g m i l k samples were d e t e r m i n e d , and t h e i r combined c o n t r i b u t i o n t o t h e v a r i a n c e o f a l a c t a t i o n r e c o r d b a s e d on t h e 2 4-hour-monthly sample t e s t i n g p l a n and on t h e a l t e r n a t e A.M./P.M.-monthly sample p l a n was computed. The c o n t r i b u t i o n o f t h e t h r e e s o u r c e s o f v a r i a t i o n t o t h e l a c t a t i o n r e c o r d s d i d n o t d i f f e r s i g n i f i c a n t l y between t h e two t e s t i n g p l a n s , and were o n l y 0 .3%, 1.5%, and 1.3% o f t h e between cow v a r i a t i o n f o r p e r c e n t a g e f a t , p r o t e i n , and l a c t o s e r e s p e c t i v e l y . P a r t I I : The a n a l y s i s o f 3660 s i n g l e m i l k i n g w e i g h t s o f m i l k , f a t , p r o t e i n , and l a c t o s e and p e r c e n t a g e f a t , p r o t e i n , and l a c t o s e showed t h a t t h e A.M.-P.M. d i f f e r e n c e s f o r a l l d e p e n d e n t v a r i a b l e s were n o t a f f e c t e d by s e a s o n o f c a l v i n g , p a r i t y , s t a g e o f l a c t a t i o n , o r i n d i v i d u a l cow, o r by any combin-a t i o n o f t h o s e i n d e p e n d e n t v a r i a b l e s . However, m i l k i n g i n t e r v a l d i d a f f e c t t h e d i f f e r e n c e between A.M. and P.M. y i e l d s and c o m p o s i t i o n f o r a l l v a r i a b l e s . A d d i t i v e c o r r e c t i o n f a c t o r s f o r e s t i m a t i n g d a i l y y i e l d s f r o m a s i n g l e A.M. o r P.M. w e i g h t were f o u n d t o be s u f f i c i e n t c o r r e c t i o n f o r a l l y i e l d v a r i a b l e s -however, s e p a r a t e f a c t o r s f o r t h e two m i l k i n g i n t e r v a l s were r e q u i r e d . The f a c t o r s f o r m i l k , f a t , p r o t e i n , and l a c t o s e were - 1 . 3 1 k g . , - 2 . 7 g., - 5 . 2 g., and - 7 . 0 g. r e s p e c t i v e l y f o r c o r r e c t i n g y i e l d s f o r cows b e i n g m i l k e d on t h e 10/14 h o u r i n t e r v a l , and - 0 . 1 3 k g . , - 0 . 7 g., 0 .0 g., and - 0 . 4 g. r e s p e c -t i v e l y f o r y i e l d s o f cows b e i n g m i l k e d on t h e 12/12 i n t e r v a l . 84. Daily y i e l d would be calculated from single milkings with the appropriate correction factor (CF) by the equation: A.M. + P.M. = (A.M. + CF) x 2 or : A.M. + P.M. = (P.M. - CF) x 2. There was an ind i c a t i o n that the A.M.-P.M. differences of milk, protein, and lactose y i e l d s were affected by product-i v i t y - that i s the differences were p o s i t i v e l y correlated with l e v e l of production. However, the relationship was not so large or stable to warrant separate factors for stage of la c t a t i o n or l e v e l of an individual's production. I t was found that the secretion rate of protein remained constant between morning and evening for both milking i n t e r v a l s , leading to the p o s s i b i l i t y of extending the secretion rate of one i n t e r v a l over the next i n order to estimate daily production. The same technique would lead to biases for milk, f a t , and lactose as the secretion rate did not remain constant for those variables, however, for milk and lactose the bias would be small. I t was concluded that l a c t a t i o n y i e l d estimates for a l l y i e l d variables, calculated by extending the alternate A.M./P.M. single sample yie l d s over the respective test i n t e r -vals and then summing the res u l t s , would not be s i g n i f i c a n t l y biased, as the ind i v i d u a l test i n t e r v a l biases would tend to cancel themselves over the l a c t a t i o n . This would only hold provided that an even number of samples were taken, and that the 85. milking i n t e r v a l did not change over the l a c t a t i o n . The e f f e c t of reducing the number of samples from 20 per l a c t a t i o n to 10 on the standard error of the l a c t a t i o n record was examined. This comparison considered only the day to day v a r i a t i o n and not the error that could be introduced by sampling stages of l a c t a t i o n that are unrepresentative of a test i n t e r v a l . For a l l y i e l d variables, the contribution of the random day to day v a r i a t i o n to the standard error of a l a c t a t i o n record estimate was less than 6.5% of the t o t a l l a c t a t i o n y i e l d . The l a c t a t i o n record standard errors were larger for the alternate A.M./P.M. estimates than the standard 24-hour sample estimates for a l l y i e l d variables - however, autocorrelation between successive A.M. and P.M. milkings would increase the variance of a record calculated by the i n hour testing scheme, and the increase in the S.E. from the i n hour test to the single sample test would be <42%. 86. LITERATURE CITED Alexander, M.H. and W.W. Yapp, 1949. Comparison of estimating milk and fat production i n dairy cows. J. Dairy S c i . 32: 621. Bayley, N.D., R.M. L i s s , J.E. S t a l l a r d , 1952. A comparison of bimonthly and quarterly testing with monthly testing for estimating dairy c a t t l e production. J. Dairy S c i . 35: 350. Bereskin, B. and A.E. Freeman, 1965. Genetic and Environmental Factors i n Dairy Sire Evaluation I. Effects of herds, months, and year seasons on o2 and l a c t a t i o n records; r e p e a t a b i l i t y and h e r i t -a b i l i t y . J. Dairy S c i . 48: 347. Canadian Dept. of Agriculture, R.O.P. Inspector's Manual, Production and Marketing Branch, Livestock Di v i s i o n , Canadian Dept. of Agriculture, Jan. 29, 1969. Cunningham, E.P., 1969. A note on the estimation of variance components by the method of f i t t i n g constants. Biometrika, Vol. 56: 683-684. Dickenson, F.N. and B.T. McDaniel, 1968. Single-milking y i e l d vs. 24-hour y i e l d at three inte r v a l s for estimating l a c t a t i o n milk production by the Test Interval Method. J. Dairy S c i . 51: 985. Erb, R.E., M.M. Goodin, R.A. Morrison, and A.O. Shaw, 1953. Lactation Studies V. Cause of Variation i n the Fat Percentage of Milk. Wash. Agr. Exp. Stat. C i r c . 229. Everett, R.W. e t . a l . , 1968. Accuracy of monthly, bimonthly, and trimonthly dairy herd improvement association records. J. Dairy S c i . 51: 1051-1058. Everett, R.W. and L.H. Waddell, 1970a. Sources of va r i a t i o n a f f e c t i n g the difference between morning and evening d a i l y milk production. J. Dairy S c i . 53: 1424. Everett, R.W. and L.H. Wadell, 1970b. Sources of var i a t i o n a f f e c t i n g r a t i o factors for estimating t o t a l d a i l y milk y i e l d from in d i v i d u a l milkings. J. Dairy S c i . 53: 1430. 87. 11. H a r d o u i n , J . , 1967. R e s u l t s o b t a i n e d by a s i m p l i f i e d method o f a l t e r n a t e m i l k r e c o r d i n g . Anim. B r e e d i n g A b s t r . 35: 1147. 12. Harvey, W.R., 1960. L e a s t squares a n a l y s i s o f d a t a w i t h unequal s u b c l a s s numbers. ARS-20-8 U.S.D.A. B e l t s v i l l e , M a r y l a n d . 13. Houston, J . and R.W. H a l e , 19 32. The E r r o r s I n v o l v e d i n C e r t a i n Methods o f E s t i m a t i n g the L a c t a t i o n Y i e l d o f M i l k and B u t t e r f a t . J . D a i r y Res. 4, 1: 37-47. 14. Jens e n , E.L., G.E. Shook, L.P. Johnson, and F.N. D i c k e n s o n , 19 74. E s t i m a t i o n o f d a i l y y i e l d s o f m i l k f a t and p r o t e i n from one m i l k i n g . J . D a i r y S c i . 57: 648. 15. Mahadevan, P., 1951. The E f f e c t o f Environment and H e r e d i t y on L a c t a t i o n . I . M i l k Y i e l d . J . Agr. S c i . 41: 80. 16. M c D a n i e l , B.T., 1969. A c c u r a c y o f Sampling P r o c e d u r e s f o r E s t i m a t i n g L a c t a t i o n Y i e l d s . J . D a i r y S c i . 52: 1742-1761. 17. N i e l s o n , E., 1967. The use o f A l t e r n a t e A.M. and P.M. monthly t e s t i n g t o e s t i m a t e 305 day p r o d u c t i o n f o r d a i r y cows. M.S. T h e s i s , U n i v e r s i t y o f New Hampshire, Durham. 18. O'Keefe, M.G., 1968. Use o f s i n g l e o r composite m i l k samples f o r t h e d e t e r m i n a t i o n o f f a t . J . D a i r y Res. 35: 291-294. 19. P e t e r s o n , R.G., 1965. W r i t e - U p f o r S u b r o u t i n e LSA8 Dept. o f Anim. S c i . , F a c u l t y o f A g f i . , U n i v e r s i t y o f B r i t i s h Columbia. 20. P e t e r s o n , R.G. and C.J. W i l l i a m s , 1971. V a r i a b i l i t y i n M i l k F a t , P r o t e i n and L a c t o s e Content o f Herd B u l k M i l k s i n B r i t i s h Columbia. Mimeographed Nov. 1971. U n i v e r s i t y o f B r i t i s h Columbia. 21. P o l y , J . and M. P o r t o u s , 1966. The a c c u r a c y o f a l t e r -n a t i n g m i l k r e c o r d i n g , Anim. B r e e d i n g A b s t r . 34: 2872. 22. P o r z i o , G., 1953. A new method o f m i l k r e c o r d i n g . Anim. B r e e d i n g A b s t r . 21: 1659. 23. P r a c h e , M., 1965. Study o f m i l k r e c o r d i n g on a l t e r n a t e m i l k i n g s . D a i r y S c i . A b s t r . 30: 779. 88. 24. Putnam, D.N. and H.C. Gilmore, 1968. Evaluation of an alternate A.M. and P.M. monthly testing plan and i t s application for use i n the Dairy Herd Improve-ment Association Program. (Abstr.). J. Dairy S c i . 51: 985. 25. Putnam, D.N. and H.C. Gilmore, 1969. Alternate A.M.-P.M. testing for Dairy Herd Improvement Association Program- operational procedures. J. Dairy S c i . 52: 945. 26. Schmidt, G.H., 1960. Ef f e c t of Milking Intervals on the Rate of Milk and Fat Secretion. J. Dairy S c i . 43: 213-219. 27. Searle, S.R., 1971. Topics i n Variance Component Estimation. Biometrics Vol. 27: 1-6. 28. Shook, G.E., E.L. Jensen, W.J. Tyler, and F.N. Dickenson, 1973. Factors Affecting Estimates of Daily Milk Y i e l d from a Single Milking. 68th Annual Meeting of the American Dairy Science Association, Wash. State University, Pullman, June 25. 29. Shook, G.E., L.P. Johnson, and F.N. Dickenson, 1975. Bias and precision of several sampling schemes for estimating l a c t a t i o n milk y i e l d . J. Dairy S c i . 58: 772. 30. Snedecor, G.W. and W.G. Cochran, 1968. S t a t i s t i c a l Methods. 6th ed., Iowa State College Press, Ames. 31. Sokal, R.R. and F.J. Rohlf, 1969. Biometry. W.J. Freeman and Company, San Francisco. 32. van Vleck, L.D. and CR. Henderson, 1961. Variance and Covariance Components i n Part Lactation Milk and Fat Records. J. Dairy S c i . 44: 1870. 33. Williams, C.J. and R.G. Peterson, 1972a. Report on Bulk Milk Sampling Study. Dept. of Anim. S c i . , University of B r i t i s h Columbia. 34. Williams, C.J. and R.G. Peterson, 1972b. Within Herd Variation of Bulk Milk Composition. Proc. Western Section, American Society of Anim. S c i . , Vol. 23. 35. Wood, P.D.P., 1967. Algebraic Model of the Lactation Curve i n Cattle. Nature 216: 164-165. 36. Wood, P.D.P., 1969. Factors Af f e c t i n g the shape of the Lactation Curve i n Cattle. Anim. Prod. 11:307-316. 

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