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The prediction of university freshman performance on the basis of high school achievement in British.. Crompton, Onesia 1958

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THE PREDICTION OF UNIVERSITY FRESHMAN PERFORMANCE ON THE BASIS OF HIGH SCHOOL ACHIEVEMENT IN BRITISH COLUMBIA by ONESIA CROMPTON B.A., University of B r i t i s h Columbia, 19^7  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF ARTS i n the College and Faculty of EDUCATION  We accept t h i s thesis as conforming to the required  standard  THE UNIVERSITY OF BRITISH COLUMBIA October, 1958  The Prediction of University Freshman Performance on the Basis of High School Achievement i n B r i t i s h Columbia Abstract  This study was an attempt to determine the r e l a t i o n s h i p at the University of B r i t i s h Columbia between high school achievement, as represented by grade twelve r e s u l t s , and university performance, as represented by f i r s t year standing. The aim of the work was to provide counsellors, both at the University of B r i t i s h Columbia and i n the secondary schools of t h i s province with pred i c t i v e information f o r use i n counselling. The high school variables used were l e t t e r grade average, percentage average, standing at f i r s t attempt, recommendation, number of Departmental examinations written, and major subjects taken. The c r i t e r i o n of university performance used was f i r s t \ year standing i n A p r i l . A sample of 737 students was chosen from the Faculty of Arts and Science during the academic year of 1957-58. The students chosen had completed their f i n a l year i n a public high school i n B r i t i s h Columbia, were not repeating any f i r s t year u n i v e r s i t y courses, and had had an uninterrupted secondary education. They had registered f o r at least f i f t e e n units of course work, which included English 100-101, Mathematics 100 or 101, a foreign language, a science, and an e l e c t i v e . Results of t h i s study can therefore be used adequately only with students of comparable high school background and with similar freshman programmes. Literature relevant to the areas investigated i n t h i s study was reviewed. By use of the Chi-Square technique and of a method of p a r t i t i o n i n g Chi-Square, i t was determined whether the difference i n freshman performance was s i g n i f i c a n t among the students grouped according to the various high school variables, and where the d i f ference l a y . Contingency c o e f f i c i e n t s were calculated to show the degree of r e l a t i o n s h i p between the variables and the c r i t e r i o n . Most of the results of the investigation were i n agreement with those reported by other authors who had conducted similar studies. I t was found that there i s a high positive r e l a t i o n ship between freshman standing and grade twelve average, whether l e t t e r grade or percentage, that students who complete University Entrance standing at f i r s t attempt perform at a higher l e v e l at u n i v e r s i t y than students who are required to make more than one attempt, that recommended students are better academic r i s k s than  non-recommended students, and that students who are required to write three or more Departmental examinations are more l i k e l y to f a i l at u n i v e r s i t y than students who write just one or two examinations. Contrary to most studies, and agreeing rather with the exceptions, i t was found that there i s some r e l a t i o n s h i p between major subjects taken i n high school and freshman standing. Students who have included i n t h e i r high school programmes Mathematics, Science, E n g l i s h , and S o c i a l Studies as majors are less l i k e l y to f a i l at u n i v e r s i t y than students who take Mathematics and Science majors but omit English and S o c i a l Studies majors. Students who have taken a high school foreigh language major are more successful i n f i r s t year u n i v e r s i t y than those who omit a foreign language major. A word of caution was included regarding the impossib i l i t y of perfect p r e d i c t i o n for a l l students owing to the unrel i a b i l i t y of marks, to i n d i v i d u a l d i f f e r e n c e s , and to personal problems, adjustment and growth. Within the specified l i m i t a t i o n s of the r e s u l t s , the study indicated that high school achievement could be used e f f e c t i v e l y i n p r e d i c t i o n of performance at university. A number of suggestions f o r further study were mentioned, the most strongly recommended of which were a study of the p o s s i b i l i t y of using a p r e d i c t i o n formula including both high school achievement records and aptitude test r e s u l t s , and an i n v e s t i g a t i o n of capable students who do not proceed to u n i v e r s i t y .  In p r e s e n t i n g the  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  r e q u i r e m e n t s f o r an advanced degree at the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and agree t h a t p e r m i s s i o n f o r e x t e n s i v e for  s c h o l a r l y purposes may  study.  I further  copying of t h i s  be g r a n t e d by the Head o f  Department o r by h i s r e p r e s e n t a t i v e .  Department  be allowed, w i t h o u t my w r i t t e n  of  The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver 8, Canada. Date  my  I t i s understood  that copying or p u b l i c a t i o n of t h i s t h e s i s f o r g a i n s h a l l not  thesis  financial  permission.  ACKNOWLEDGEMENTS  The writer wishes to express her sincere appreciation to Mr. J.F. McLean, Director of Student and Personnel Services, f o r making i t possible to conduct t h i s study; t o Mr. J.E.A. P a r n a l l , Registrar, for permission to use high school t r a n s c r i p t s ; t o Mr. H.M. Evans, Registrar, B r i t i s h Columbia Department of Education^ for sending information regarding accreditation, and to Dr. R.W.B. Jackson, Director, Department of Educational Research, Ontario College of Education, for valuable suggestions statistical  concerning  technique.  For guidance and encouragement received during the entire i n v e s t i g a t i o n , the writer i s s i n cerely g r a t e f u l to Dr. H.L. Stein, Supervisor of Graduate Studies, Faculty of Education.  TABLE OF CONTENTS CHAPTER I  II  III  ?AGE INTRODUCTION AND BACKGROUND OF THE PROBLEM  1  A  The Problem and J u s t i f i c a t i o n f o r Investigation • 1. General 2. Specific  1 1 1  B  D e f i n i t i o n of Students Used i n Study  5  C  Sources of Data  6  D  Assumptions  6  E  Limitations of Study  7 10  REVIEW OF THE LITERATURE A  Introduction  10  B  High School Marks, Average and Rank  11  C  Recommendations  D  High School Repeaters  E  High School Subjects  19  F  R e l i a b i l i t y of C r i t e r i a  19  G  Conclusions  •• 16 • 18  •  METHODS OF INVESTIGATION A  Data Gathering Techniques 1 . High School Records 2. University Standing  B  S t a t i s t i c a l Methods 1 . Averages and Standing at F i r s t Attempt 2 . Accreditation 3 . Majors  20 22 • 22 22 2k 25 25 26 27  ii CHAPTER IV  V  VI  PAGE ANALYSIS OP THE DATA  29 29 29 3^ 39  A  Averages and Standing at F i r s t Attempt 1. Letter Grade Average 2. Percentage Average 3 . Standing at F i r s t Attempt  B  Accreditati.on 1. Recommended and Non-Recommended Students 2. Number of Departmental Examinations Written 3 . Majors .,  . **7 51  CONCLUSIONS, IMPLICATIONS AND RECOMMENDATIONS FOR FURTHER STUDY ...  60  h-2 *+5  A  Conclusions 1* General 2. Specific  60 60 60  B  Implications  63  C  Recommendations f o r Further Study ........... 65  SUMMARY OF THE PRESENT STUDY  67  BIBLIOGRAPHY  70  APPENDIX A  75  APPENDIX B  76  iii LIST OF TABLES TABLE I II  III  IV  V  VI  VII  VIII . IX  X  XI  PAGE Frequencies of University Freshman Standing Based on Letter Grade Average  29  Frequencies (Percentages i n Parentheses) of University Freshman Standing Based on High School Letter Grade Average (Small Frequencies Combined)  30  Frequencies of University Freshman Standing Based oni:High School Letter Grade Average (Reduced to 3 by 3 Contingency Table)  32  Frequencies of University Freshman Standing Based on High School Percentage Average Resulting From Departmental Examinations  3*+  Frequencies (Percentages in-Parentheses) of University Freshman Standing Based on High School Percentage Average (Small Frequencies Combined) .  35  Frequencies of University Freshman Standing Based on High School Percentage Average (Reduced to 3 by 3 Contingency Table)  36  Departmental Examination Means and Standard Deviations of Students Grouped According to F i r s t Year University Standing  38  Frequencies of University Freshman Standing Based on F i r s t Attempt and on Repetition  *+0  Frequencies (Percentages i n Parentheses) of University Freshman Standing Based on F i r s t Attempt and on Repetition (Small Frequencies Combined) Frequencies of University Freshman Standing Based on Grade Twelve Status with Respect to Accreditation Frequencies (Percentages i n Parentheses) of University Freshman Standing Based on Grade Twelve Status with Respect to Accreditation (Small Frequencies Combined)  M-O  *+3  ^  iv TABLE XII  XIII XIV  XV XVI  XVII  XVIII  XLX  PAGE Frequencies (Percentages i n Parentheses) of University Freshman Standing Based on Recommendation and Non-Recommendation (Small Frequencies Combined)  h5  Frequencies of University Freshman Standing Based on Number of Departmental Examinations Written .. h8 Frequencies (Percentages i n Parentheses) of University Freshman Standing Based on Number of Departmental Examinations Written (Small Frequencies Combined)  ^9  Frequencies of University Freshman Standing Based on High School Majors , •  52  Frequencies (Percentages i n Parentheses) of University Freshman Standing Based on Majors (Small Frequencies Combined)  53  Frequencies of University Freshman Standing Based on High School Majors (Reduced to 3 by 3 Contingency Table)  5^  Frequencies of University Freshman Standing Based on Having a High School Foreign Language Major and not Having One 56 Frequencies (Percentages i n Parentheses) of University Freshman Standing Based on Having a High School Foreign Language Major and not Having One (Small Frequencies Combined) ........  57  CHAPTER I INTRODUCTION AND BACKGROUND OF THE PROBLEM  A  The Problem and J u s t i f i c a t i o n f o r Investigation 1.  General This study i s an investigation of the r e l a t i o n s h i p be-  tween achievement i n high school and performance at university, i n order to determine how well u n i v e r s i t y  success can be predicted  from high school records. Grade twelve records were used to represent high school achievement because i t i s i n grade twelve that the f i n a l requirements f o r university entrance are completed.  In view of the com-  paratively high f a i l u r e rate i n the f i r s t year at university and consequent enrolment a t t r i t i o n , f i r s t year standing was used to represent u n i v e r s i t y performance. 2.  Specific Who should go to university?  This i s a v i t a l question  for a l l concerned with education. To send a poor student to univ e r s i t y i s a c o s t l y and unprofitable proposition from the taxpayer' point of view.  A t t r i t i o n presents a problem f o r the administrators  making i t d i f f i c u l t to budget accurately.  From the i n d i v i d u a l  student's point of view i t i s not only c o s t l y and time consuming but also distressing to f a i l . S c i e n t i f i c and i n d u s t r i a l progress has led t o a society which demands more t r a i n i n g i n both technical and s o c i a l s k i l l s .  2  The revolution which has taken place as a r e s u l t of mass education must be appreciated. More people are spending more time i n school. The greater the number of individuals receiving secondary education the greater the number entering u n i v e r s i t y .  U n i v e r s i t y attendance  i s no longer the privilege of the few. According to Conway and Brown ( 1 ^ ) , the percentage of students i n B r i t i s h Columbia remaining i n school to the beginning of grade twelve has increased from 3 5 P©£ cent i n 19^7 t o **5 per cent i n 1 9 5 6 .  Approximately two-thirds of the grade twelve students  are enrolled i n the u n i v e r s i t y programme.  With a f a i l u r e rate of  15 per cent i n grade twelve, i t i s e a s i l y seen that 2 5 per cent of the o r i g i n a l f i r s t grade population ultimately obtain u n i v e r s i t y entrance.  As a t t r i t i o n decreases, a change i n standards i s Inevi-  tably the r e s u l t ; u n i v e r s i t y candidates are drawn from a poorer group.  Are a l l of these candidates capable of u n i v e r s i t y work? The f a i l u r e rate i n f i r s t year suggests that many students  are entering u n i v e r s i t y who do not p r o f i t from the opportunities offered.  The c r i t i c a l aspect of the s i t u a t i o n i s that these students  have, nevertheless, successfully completed the u n i v e r s i t y entrance requirements.  Are there, then, borderline cases who should be d i s -  couraged from going to u n i v e r s i t y where they must compete with more and better students?  I f so, where i s the l i n e to be drawn between  poor students and p o t e n t i a l l y successful ones? C r i t i c i s m abounds. Some c r i t i c s suggest r a i s i n g admission requirements, s i f t i n g the applicants and r e j e c t i n g the u n f i t .  The  opposing theory i s to permit a l l to enter u n i v e r s i t y where the pro-  3  grammes offered would be broadened t o suit various l e v e l s of a b i l i t y i n the same way as secondary c u r r i c u l a have been broadened i n recent years. There are c r i t i c s also of the system of accreditation i n t h i s province.  They advocate that standardized entrance examina-  tions be written by a l l those who wish to enter u n i v e r s i t y . f e e l that "recommendation  11  Others  i s an adequate means of s e l e c t i o n .  The main j u s t i f i c a t i o n f o r t h i s study l i e s however, not i n administrative decisions but i n the p r a c t i c a l and functional aspects connected with i n d i v i d u a l counselling.  Teachers and coun-  s e l l o r s , both i n the secondary school and at the u n i v e r s i t y are better equipped to guide students i f they have some f a c t u a l and s t a t i s t i c a l evidence.  A counsellor may be s a t i s f i e d with his pre-  d i c t i o n of a p a r t i c u l a r student's success but he must be able to impress facts on the student and perhaps the parents. There are two sides to t h i s problem.  One i s the i n s i s -  tence of a student on going to u n i v e r s i t y when he has l i t t l e or no chance f o r success; the other i s the hesitancy of a capable youth who could p r o f i t from further education but who lacks confidence to attempt u n i v e r s i t y work.  To counsel e f f e c t i v e l y , both i n helping  the student to lower his vocational aim and to follow more suitable pursuits i n which he may be happier and more successful, and In encouraging the student to develop his academic p o t e n t i a l i t i e s by proceeding to u n i v e r s i t y , i t i s necessary to have objective evidence. How can t h i s evidence be obtained, success be predicted?  How and how w e l l can  Is the high school record a good predictor?  If S p e c i f i c a l l y , the writer w i l l attempt to answer the f o l lowing questions: (a)  Is there a difference i n f i r s t year standing among stu-  dents grouped according to t h e i r grade twelve l e t t e r grade average? (b)  Is there a difference i n f i r s t year standing among the  students, who wrote three or more Departmental  examinations,  grouped according to t h e i r percentage average? (c)  Is there a difference i n f i r s t year standing between the  students who passed at f i r s t attempt and those who were required to write one supplemental or more and/or t o repeat one subject or more? (d)  Of the students who attended accredited high schools, do  students who were recommended i n a l l subjects d i f f e r i n f i r s t  year  standing from students who were not recommended i n a l l subjects? (e)  Is there a r e l a t i o n s h i p between the number of Departmen-  t a l examinations that a student i s required to write and h i s f i r s t year  standing? (f)  Is there a difference i n f i r s t year standing according to  majors taken i n high school?  The following groupings of majors are  considered: (1)  including Mathematics and Science but excluding English and S o c i a l Studies;  (2)  Including E n g l i s h and S o c i a l Studies but excluding Mathematics and Science;  (3)  including Mathematics, Science, E n g l i s h and S o c i a l Studies;  5  (*+) (g)  a l l other combinations of subjects,  Is there a difference i n f i r s t year performance between  students who had a f o r e i g n language major i n high school and those who d i d not? B  D e f i n i t i o n of Students Used i n Study To eliminate extraneous variables and i n order t o obtain  as homogeneous a group as possible, c e r t a i n delimiting factors were observed. The study was limited to students i n f i r s t year i n the Faculty of Arts and Science during the 1 9 5 7 - 5 8 session. Freshman i n other f a c u l t i e s were excluded.  Of the 1 8 8 3 students i n f i r s t  year of Arts and Science, 737 were chosen according to the following factors. Only the students who had an uninterrupted education were considered.  Students who were out of school f o r a year or  more a f t e r completing grade twelve were excluded.  Likewise ex-  cluded were students who l e f t school prior to completing grade twelve, returning l a t e r to complete high school. Those, however, who took grade twelve i n 1 9 5 5 - 5 6 but who repeated courses or were making up University Programme requirements i n 1 9 5 6 - 5 7 were i n cluded, unless they completed, i n addition, any senior matriculat i o n subjects during that year, i n which case they were excluded. Only the students who attended a public secondary school i n B r i t i s h Columbia during t h e i r f i n a l year were considered. No students who were repeating f i r s t year A r t s , or a part thereof, whether taken previously at U.B.C., V i c t o r i a College, or  6 as Senior Matriculation, were included. Only the students who registered f o r at least f i f t e e n units were included.  The course taken included E n g l i s h 100 -  101,  Mathematics 100 or 1 0 1 , a foreign language, a science, and an e l e c t i v e , whether an additional science or a non-science. C  Sources of Data The delimiting factors were found on students' R e g i s t r a -  t i o n cards. A l i s t of accredited schools was k i n d l y supplied by Mr. H.M.  Evans, Department of Education, V i c t o r i a . Students' high school progress, majors and  performance  were obtained from transcripts f i l e d i n the U.B.C. Registrar's Office.  From these t r a n s c r i p t s , averages were computed. Students' f i r s t year standing, as determined  by A p r i l  results were obtained from the Registrar's O f f i c e . Counselling f i l e s were used as a supplement when necessary, and c i t y schools were contacted about questionable cases. D  Assumptions The v a l i d i t y of t h i s study depends on the c r i t e r i a used.  In t h i s connection i t was necessary to make a number of assumptions . It was necessary to assume that the c r i t e r i o n of l e t t e r grades i s a r e l i a b l e one} that i s , that the same l e t t e r grades from d i f f e r e n t schools have the same meaning.  This Is an unsupported  assumption because there i s no objective data to support i t .  7 However, since the pattern of l e t t e r grades i s strongly suggested by the Department of Education and since most schools apparently conform to t h i s pattern, the assumption has some j u s t i f i c a t i o n . In addition to the use of l e t t e r grade averages, percentage averages from Departmental examinations were used with the assumption that they would provide a more r e l i a b l e c r i t e r i o n .  The  marks from Departmental examinations and consequent averages are based on standardized examinations with standardized marking.  In  addition, the scaling technique employed by the Department of Education reportedly makes the results more r e l i a b l e .  Conway ( 1 3 )  and Conway and Brown (Ih) give a detailed account of the methods employed  i n scaling. It was also necessary to assume that the marking of exam-  inations at u n i v e r s i t y and therefore the f i n a l standing i s r e l i a b l e . This i s done with reservation i n view of the lack of objective data to support i t . Because transcripts do not supply information regarding reasons f o r writing Departmental examinations, and because i t was impossible to contact each student who wrote them, i t was assumed that the students who wrote four or more examinations, whose high school record prior to grade twelve was good, and whose Department a l examinations were high, wrote a l l examinations i n order t o be e l i g i b l e to win a scholarship. cent average or better was used.  In order to define "high", 65 per The cases i n which a student was  required to write perhaps one examination and wrote the rest f o r scholarship purposes, or for practice, would be too few to contaminate the data s u f f i c i e n t l y to invalidate  it.  8  Because i t was impossible t o contact each student or each school, i t was assumed that, aside from the students who wrote Departmental examinations f o r scholarship purposes, the students who wrote one examination or more did so because their work during the year was below a C M  recommended.  M  l e v e l and they were therefore not  This assumption was made with some misgiving, be-  cause there i s evidence to indicate that on occasion a student or even a whole class i s required to write an examination, or examinations, f o r d i s c i p l i n a r y reasons.  On occasion, too, a student  i s required to write because of poor attendance.  Schools vary i n  t h e i r regulations regarding required attendance.  Since i t was im-  possible to determine and eliminate a l l of these cases, the assumptions had to be made. However, an attempt was made to check the questionable cases, through reference to Counselling f i l e s , contact with c i t y schools by telephone, and with i n d i v i d u a l students by telephone and letter • E  Limitations of Study The r e s u l t s , that i s , the predictive value of t h i s t h e s i s ,  can apply only to f i r s t year Arts and Science students whose high school background and programmes at u n i v e r s i t y are comparable to those of the students used as the sample i n t h i s study as defined earlier. It i s recognized that f i r s t year performance f e c t l y representative of academic success or f a i l u r e .  i s not perIt i s l i k e l y  9  that some students of limited academic a b i l i t y might s a t i s f a c t o r i l y complete f i r s t year but due to the e f f o r t involved, decide against continuing.  On the other hand, because of adjustment  problems,  some students who have d i f f i c u l t i e s i n f i r s t year might eventually graduate. The v a l i d i t y of the r e s u l t s depend on the r e l i a b i l i t y of the c r i t e r i a used.  As seen e a r l i e r , f o r the purposes of t h i s study  t h i s r e l i a b i l i t y i s assumed.  I t i s , however, questionable.  In i n d i v i d u a l counselling, knowledge of high school background alone i s not s u f f i c i e n t to predict success.  I t should be  considered together with an evaluation of aptitude test r e s u l t s , of the kind used by the University of B r i t i s h Columbia Counselling Department, and with,other data supplied by the student about himself.  CHAPTER I I REVIEW OF LITERATURE  A  Introduction The i n v e s t i g a t i o n of academic p r e d i c t i o n i s one of the  most popular of educational studies.  The number of journal ar-  t i c l e s and books on the subject i s very large, e s p e c i a l l y since the 1 9 3 0 s during which time there was an increased interest i n 1  these matters.  The subject has been studied with various methods  and from various points of view.  Investigations include predic-  t i o n with such variables as high school performance, standard achievement t e s t s , i n t e l l i g e n c e as measured by a single test or a battery of t e s t s , s o c i a l and economic data, personal data, i n terest and motivation, and combinations of v a r i a b l e s . Studies show that i t i s impossible to predict p e r f e c t l y the achievement of a l l entrants, and that there are cases of success or f a i l u r e that cannot be discovered u n t i l the student has t r i e d t o do u n i v e r s i t y work.  As T r l b i l c o c k (M-6,p.5*+6) says;  "While i t i s wasteful and otherwise undesirable to have the u n f i t i n c o l l e g e , i t i s also wasteful and otherwise undesirable to keep the f i t out of c o l l e g e . For many students there i s no adequate test of f i t n e s s except the a c t u a l attempt t o carry college work." However, there i s no doubt that i t i s an advantage t o both the u n i v e r s i t y and the students to evaluate as accurately as possible the students  1  chances of success or f a i l u r e i n u n i v e r s i t y work. Much work has been done on the evaluation of the e f f i c i e n c y  of high school performance as a predictor of u n i v e r s i t y success.  One  11  of the arguments i n favour of using such a predictor i s that i t i s an economical one.  The administration of i n t e l l i g e n c e and  titude tests i s comparatively c o s t l y .  ap-  High school records are  r e l a t i v e l y e a s i l y obtainable; they require a minimum of time, e f f o r t and expense to put into p r a c t i c a l use.  Above a l l , i t i s  generally agreed by authors i n the f i e l d that high school performance i s the best single c r i t e r i o n of university success.  Whether  used alone, or combined with other variables, such as academic aptitude test r e s u l t s to give a more sensitive method of prediction, high school performance should always be considered i n prognosis. The reason f o r the e f f i c i e n c y of high school marks i n p r e d i c t i o n i s a p t l y explained by Travers (*+5» p . 1 5 5 ) . "The value of high school grades f o r predictive purposes i s undoubtedly a r e s u l t of the f a c t that they represent a combination of a b i l i t y and motivational factors operating i n much the same way as they w i l l operate i n c o l l e g e . The advantages of these circumstances seem to outweigh the factors that tend to reduce the v a l i d i t y of high school grades." B  High School Marks. Average, and Rank Symonds (^^p.MfO) writes: "Of a l l the indices of a b i l i t y to do college work, marks i n the high school courses are the most s i g n i f i c a n t . They are also the easiest f o r a college to obtain. Colleges should use the quality of work done i n high school as the f i r s t index of college ability." The predictive value of high school averages i s demon-  strated by Stone (k$) who,  i n using as variables high school grade-  point average, scholastic aptitude as measured by the American Council on Education Psychological Examinations,  and achievement  12  t e s t s , concluded that, although multiple correlations prove more e f f i c i e n t , the most e f f i c i e n t single predictor of success at u n i v e r s i t y was the high school grade-point  average.  In a similar study, Drake and Henmon ( 2 0 ) used as v a r i ables, high school rank, the A.C.E. Psychological Examinations, the Henmon-Nelson test of mental a b i l i t y and the Co-operative English t e s t .  Using various combinations  found that the combinations  of the v a r i a b l e s , they  containing high school rank were more  e f f e c t i v e than any other combination, and that the best single variable f o r prediction was high school rank. Emme ( 2 2 ) , i n h i s review of studies carried out i n the late 1 9 3 0 * s concluded from h i s data that the best method of f o r e casting college success i s to use a formula including a combinat i o n of variables but that the best single c r i t e r i o n i s rank i n high school graduating c l a s s . S i m i l a r l y , Harris ( 2 8 ) , i n h i s review, concluded that although a combination of i n t e l l i g e n c e rating and high school achievement gives a higher c o r r e l a t i o n with college marks than either alone, high school grades alone show a higher c o r r e l a t i o n than i n t e l l i g e n c e r a t i n g alone. F r o e l i c h ( 2 5 ) » i n covering a l l the Wisconsin research done from 1909 to 19^1> came to the conclusion that a combination of high school achievement rating and i n t e l l i g e n c e r a t i n g increases the predictive e f f i c i e n c y of any single index, but that high school rank i s the best single c r i t e r i o n f o r predicting u n i v e r s i t y  success.  Combinations produced multiple c o r r e l a t i o n c o e f f i c i e n t s  approaching  .70.  tween . 5 0 and  High school rank alone yielded c o e f f i c i e n t s be-  .60.  Byrns (10), divided students i n t o four groups according to t h e i r p o s i t i o n i n high school and compared them with t h e i r average grades i n f i r s t year college. She then reversed t h i s process, d i v i d i n g freshmen into four groups according to college achievement and compared them with t h e i r high school rank.  Her  conclusions were that there i s a tendency for students who rank high i n high school to rank high i n college, and f o r students rank low i n high school to rank low i n c o l l e g e .  who  She added that,  since a considerable number of above-average students i n high school ranked low i n college, while very few poorer students i n high school reached the average l e v e l i n college, one can therefore be more c e r t a i n that low high school average guarantees c o l lege f a i l u r e than good high school average guarantees college success . Dearborn (18,p. 192), as e a r l y as 1909* concluded that " I f a p u p i l has stood i n the f i r s t quarter of a large class through high school, the chances are four out of f i v e that he w i l l not f a l l below the f i r s t half of his class i n university....The chances are but one i n f i v e that the student••.who has been i n the lowest quarter of his class w i l l r i s e above the median or average of the freshman class at university, and the chances that he w i l l prove a superior student at the u n i v e r s i t y are slim indeed." Forty years l a t e r , i n 19*+9 Dearborn said "...rank i n school performance i s s t i l l one of the best c r i t e r i a for predicting success i n college."  Ik Adams ( 1 ) , Samenfeld (37),  Schmitz (39),  Weintraub and S a l l e y  (^9),  and Frederickson and Schrader (2*f), i n their sep-  arate studies a l l agreed that high school achievement i s the most e f f i c i e n t single instrument f o r predicting u n i v e r s i t y  performance.  Canadian studies on t h i s subject are few, but they agree with the American findings.  The Alberta Progress Report (2,p.6*)>  concluded, "The findings so f a r indicate that the best single predictor of success at the University of Alberta i s the grade twelve average." school  They found a higher c o r r e l a t i o n between high  average and u n i v e r s i t y average (r=.56) than between high  school average and scholastic a b i l i t y tests (r =  A7).  In Ontario, the Atkinson Study of U t i l i z a t i o n of Student Resources  (*+) found that, i n terms of goal alone, the students who  planned to go to university had d e f i n i t e l y higher averages than others.  The study has not yet progressed s u f f i c i e n t l y f a r to i n d i -  cate prediction of success. In B r i t i s h Columbia, Wallace ( W  - found  significantly  high correlations between University Entrance examination r e s u l t s and average marks at V i c t o r i a College (r = between .71 and ,7k-). However, he stated, "There i s no passing university entrance average mark below which i t i s possible to say that students obtaining such average should not attempt f i r s t year college. At least one i n three students obtaining even the lowest passing university entrance average" (less than 53 per cent) "can succeed i n f i r s t year college. Very l i k e l y some of the u n i v e r s i t y entrance candidates who f a i l e d could, i f given the opportunity, pass f i r s t year at V i c t o r i a College." 36  » This i s a much higher passing rate than found i n the present study.  15  Authors i n t h i s area show that there i s a s i g n i f i c a n t positive c o r r e l a t i o n between high school average and college standing.  Garrett (27>p.93)j  concluded that, "Among a l l the f a c -  tors contributing t o production of scholastic success i n college, the student's average grade i n high school continues t o show the highest c o r r e l a t i o n with l a t e r college scholarship average."  In  examining thirty-two c o e f f i c i e n t s of c o r r e l a t i o n he found that they ranged from .29 t o . 8 3 .  S i m i l a r l y , Wagner (*+7)> i n h i s sur-  vey of forty-seven investigations, including two of his own, found c o r r e l a t i o n c o e f f i c i e n t s ranging from . 2 8 to . 8 6 .  Seyler  (*+0) calculated a c o r r e l a t i o n of . 6 0 . Dressel ( 2 1 ) calculated one of . 5 2 ; and Butsch (9) found correlations ranging between ,h7 and . 6 0 . Among the highest correlations recorded i n journals are those of Ashmore ( 3 ) which range between . 8 3 and . 8 9 . Among the numerous studies, only two disagree with the above conclusions.  Bou and S t o v a l l ( 5 ) » came to the conclusion  that although there i s a positive c o r r e l a t i o n between high school and college marks, the c o r r e l a t i o n i s so low that high school i n dex i s not a very r e l i a b l e c r i t e r i o n f o r selecting college students.  Since they also concluded that marks d i f f e r e d i n meaning  from one high school t o another, p a r t i c u l a r l y with respect to size of school, i t may be that Puerto Rico i s p a r t i c u l a r l y lacking i n standardization.  The other disagreeing conclusion i s that of the  Parkyn Report (33)> as reported i n The Christchurch Press, which stated that there i s no r e l a t i o n between standard of U n i v e r s i t y Entrance examinations and standard of f i r s t year University r e s u l t s .  16  The a r t i c l e reported that causes of f a i l u r e are discoverable only i n university.  Since t h i s i s just a newspaper a r t i c l e , and the  quotation may be taken out of context, i t i s d i f f i c u l t t o appraise its reliability. C  Rec ommendations With regard t o recommendation, that i s , the promotion by  accredited schools of students without writing formal examinations, few investigations have been conducted on the comparative  success  at u n i v e r s i t y of recommended and non-recommended students as defined i n t h i s province.  Brown and Nemzek ( 8 ) , however, i n a system  f a i r l y similar to the one used i n t h i s province, found a s i g n i f i cant difference i n terms of mean performance  of the two groups,  but concluded that although recommendation i s v a l i d for group d i f f e r e n t i a t i o n , i t i s not s a t i s f a c t o r y f o r i n d i v i d u a l purposes.  The  authors f e e l that the numbers of those recommended who are not succ e s s f u l and of those not recommended who are successful are so large that i f t h i s system i s to be used as a method of s e l e c t i o n , i t should be examined f o r improvement. In the l o c a l study mentioned e a r l i e r , Wallace (M^p.Sl) stated that the accreditation system i n t h i s province i s a s a t i s factory one f o r selecting students capable of doing college work. He found that; (1)  " I f a student i s recommended by an accredited school i n f i v e or a l l s i x of the compulsory u n i v e r s i t y entrance subjects, his chances of passing f i r s t year at V i c t o r i a College are 98*+ i n one thousand."  !7 (2)  " I f a student i s recommended i n four of the compulsory u n i v e r s i t y entrance subjects, and has t o write the other two, h i s chances of passing f i r s t year are 865 i n one thousand."  (3)  " I f a student i s recommended i n three of the compulsory university entrance subjects and has t o write the other three, his chances of passing f i r s t year college are 8kO i n one thousand." 36  Because recommendation i s on the basis of performance throughout  the year as rated by each of the students' teachers,  i t i s at least p a r t i a l l y a subjective evaluation.  In t h i s con-  nection i t i s interesting to note the results of an investigation by Prescott & Garretson (3*+), who distributed rating sheets to the teachers of a l l grade twelve students i n four c i t i e s i n A r i z o n a . The r a t i n g sheets included t h i r t e e n t r a i t s :  a b i l i t y to learn,  memory, persistence, habits of studiousness, conscientiousness, accuracy, desire to excel, a b i l i t y t o do independent work, a b i l i t y to budget time, a d a p t a b i l i t y , s o c i a l maturity, c u l t u r a l background and health.  At the bottom of the sheet was included a request f o r  an estimate of the pupils' probable success i n college.  An a r i t h -  metic average of a l l r a t i n g was calculated and then correlated with f i r s t semester marks at college.  The authors found a c o r r e l a t i o n  x The very high passing rate of recommended students reported by Wallace i s at least i n part due to a d i f f e r e n t recommendation p o l i c y . At the time of his study a student was required to obtain C+ i n a subject i n order to be recommended i n i t , although i f grades of C and C- were compensated by correspondingly high grades i n other subjects, a student could be recommended i n the subjects with the lower grades. Since that time the required grade f o r recommendation has been lowered to C.  18 c o e f f i c i e n t higher than one between college marks and mental a b i l i t y test score.  They added that any other variable added to the rating  increased the c o r r e l a t i o n so l i t t l e that i t did not j u s t i f y the added e f f o r t or expense. D  High School Repeaters L i t t l e work has been done on high school repeaters  their success at college.  and  I t i s believed by some educators that a  student gains by repeating high school courses because the review involved r e s u l t s i n a better foundation for subsequent u n i v e r s i t y work.  Sarbaugh (38,p.l78) discovered that analysis of data r e -  garding repeaters negated this p o s s i b i l i t y .  " I t appears, then,  that not only do enforced r e p e t i t i o n s of high school courses r e f l e c t an absence of college aptitude as measured by the ACE and a lower l e v e l of high school achievement as indicated by Regents average, but they also tend to presage i n f e r i o r achievement on the college l e v e l . " C o f f i e l d and Blommers (12) investigated t h i s problem i n the elementary school, with the conclusion that there i s very l i t t l e , i f any evidence to indicate that eventual mastery of school work i s enhanced by r e p e t i t i o n .  In qualifying t h e i r  they stated that a slow learner who  repeats eventually does no  better than an equally slow learner who this conclusion was  conclusion  does not repeat.  Although  based on younger learners, i t seems reasonable  to assume that i t would apply also to the students i n the f i n a l year of secondary school.  O • o  19  E  High School  Subjects  It i s a common practice among u n i v e r s i t i e s to demand the f u l f i l l m e n t of c e r t a i n subject requirements by t h e i r entrants. The majority of studies dealing with the r e l a t i o n s h i p between subjects taken i n high school and performance at u n i v e r s i t y add up to the conclusion as stated by Harris ( 2 8 ) , that no subject or combination of subjects has any noticeable bearing on college performance.  Douglass ( 1 9 ) ,  Rogers ( 3 5 ) , and Sorenson (*+2), i n t h e i r  separate studies concluded  that a pattern of subjects taken i n  high school bears no r e l a t i o n s h i p to u n i v e r s i t y success. to Darley ( 1 7 ) ,  According  patterns of high school subjects are less v a l i d  as p r e d i c t o r s : of college achievement than high school achievement and a measure of a b i l i t y . Garrett ( 2 7 )  concluded  that the b e l i e f that any p a r t i c u -  l a r pattern of secondary school subjects, e s p e c i a l l y f o r e i g n l a n guage, influences college success has been repudiated by most studies. However, there are a few exceptions.  For example, Ross  ( 3 6 ) found a c o r r e l a t i o n between college grades and the number of s o c i a l or natural science units taken i n high school.  Ferguson ( 2 3 )  found a positive r e l a t i o n s h i p for L a t i n and a negative one f o r H i s tory.  Bovee and F r o e h l i c h ( 6 ) found a r e l a t i o n s h i p between the  number of language units i n high school and grades i n c o l l e g e . F  R e l i a b i l i t y of C r i t e r i a How  as c r i t e r i a ?  much dependence can be placed on marks or l e t t e r grades Crawford and Burnhams ( 1 5 , p . 6 5 ) voiced t h e i r concern  20 about the r e l i a b i l i t y of marks, "A major bane of educational  prog-  nosis i s the comparatively low dependence which can be placed upon such c r i t e r i a as marks, whether i n high school, college or graduate studies."  Symonds (M+ ,p.+26) agreed that college marks must be l  made more r e l i a b l e i f prediction i s t o be improved. (5)  Bou and S t o v a l l  offered the c r i t i c i s m that an A or B i n one school i s not  necessarily equivalent  t o an A or B i n another school.  Brigham s 1  statement (7»P»57) i s relevant here: "I think that everyone who has worked i n t h i s f i e l d i s becoming t i r e d of assuming that the c r i t e r i o n - the college - i s i n f a l l i b l e and that the sources of e v i dences derived from the school and the examinations are i n error. In many subjects of Instruction the methods of teaching and examining i n the college are so f a u l t y that a perfect instrument of p r e d i c t i o n could not correlate higher than .kO or .50 with the college r e s u l t . " G  Conclusions In summary, i t i s found that the most e f f i c i e n t method  of predicting u n i v e r s i t y success i s by the use of a prediction f o r mula including a number of variables, one of which should be the high school average. predictor.  High school average alone i s the best single  Correlations between high school average and university  performance are p o s i t i v e , ranging from .28 t o .89. Accrediting high schools t o permit them t o recommend s t u dents capable of doing university work, i s found t o be a s a t i s f a c tory system of s e l e c t i o n . Repetition of high school courses suggests i n f e r i o r u n i v e r s i t y achievement.  21 It i s generally found that there i s no r e l a t i o n s h i p between pattern of subjects i n high school and college success. However, there are a number of exceptions, showing a c e r t a i n amount of r e l a t i o n s h i p . Scholastic c r i t e r i a are found to be somewhat unreliable, hampering e f f e c t i v e predictions.  CHAPTER I I I METHODS OF INVESTIGATION  A  Data Gathering Techniques The sample of 737 students were chosen on the basis of  the delimiting factors stipulated e a r l i e r . out  for each student.  A card was then made  On each card was recorded the following i n  formation: (a)  name and r e g i s t r a t i o n number  (b)  high school attended and whether accredited  (c)  majors taken i n high school  (d)  subjects taken i n grade twelve and the mark f o r each  (e)  average l e t t e r grade and, where applicable, percentage average; whether recommended or not, and i f not, the number of Departmental examinations written.  (f)  whether Departmental examinations written f o r scholarship e l i g i b i l i t y  (g)  whether supplemental w r i t t e n or subjects repeated  (h)  f i r s t year university standing i n A p r i l  A sample card i s shown i n Appendix A 1.  High-School Records A l e t t e r grade average was calculated from each student  grade twelve mark.  F i r s t attempt marks were used.  In almost a l l  cases these were June marks, whether i n l e t t e r grade form or percentage form.  I f a student, however, took the course during the  23  summer or through correspondence, the f i r s t attempt mark recorded under August r e s u l t s was used. While most marks are i n l e t t e r grade form, many records include varying numbers of percentage marks which are r e s u l t s of Departmental examinations.  The l a t t e r were converted to l e t t e r  grades, using the Department of Education Scale: 86-100 = A 73-85  = B  66-72  = C+  58-65  = C  50-57  = C-  Failed = E To obtain o v e r - a l l average, the following equivalents were used: 5  A  =  B  = h  C+  = 3 =  2  C- =  1  E  0  C  =  The closest l e t t e r grade average was used.  Up t o and including . 5  was counted as the lower l e t t e r grade; over . 5 , as the upper one. For each student who wrote three or more Departmental examinations, a mean of the percentage marks was calculated. P r a c t i c a l l y a l l subjects are valued at f i v e units of credit each.  For English *+0, however, two marks are given, one f o r  language and one f o r l i t e r a t u r e , constituting f i v e u n i t s .  A mean  2k of the two marks was calculated and t h i s weighted mark was then pooled with the other marks to calculate the o v e r - a l l average, whether i n terms of l e t t e r grade or percentage.  In other cases,  where two or three subjects i n one f i e l d , such as I n d u s t r i a l A r t s , made up a t o t a l of f i v e units of c r e d i t the same weighting technique was used.  However, because the cases i n which a student took  just one subject carrying less than f i v e units were too few to contaminate the data, the mark f o r that subject was pooled with the rest without being weighted. In counting the number of Departmental examinations a student was required to write, English kO again presented a problem. However, because University Entrance standing i s not complete  until  both parts are passed, the writer decided to count i t as one Departamental examination whether one part or both were written. S i m i l a r l y , when determining whether a student was r e quired to write supplementals or to repeat subjects, i f but one part of English kO f e l l into that category i t was regarded as a whole. 2.  University Standing Freshman standing i s given on the basis of A p r i l r e s u l t s  and i n terms of: (a)  F i r s t Class Honours (80-100 per cent)  (b)  Second Class Honours (65-79 per cent)  (c)  Pass (50-6*+ per cent)  (d)  Supplemental ( f a i l u r e i n one to s i x units of c r e d i t , whether or not marks s u f f i c i e n t l y high i n those courses to write supplementals)  2  (e)  5  Failure ( f a i l u r e i n more than s i x units of c r e d i t , thus granted no c r e d i t )  (f)  Deferred (standing deferred)  (g)  Withdrew  (h)  Did not write exams It i s recognized that some of the students i n the Supp-  lemental category and i n the Deferred category may raise t h e i r standing upon writing  supplementals i n August.  However, f o r the  purposes of t h i s study A p r i l results alone were considered. B  S t a t i s t i c a l Methods Students were c l a s s i f i e d into groups according to grade  twelve achievement and the groups were then compared i n terms of freshman standing. To determine whether any s i g n i f i c a n t existed  difference  among the groups, Chi-Square technique was employed.  extension, to explore further where the difference  l a y , Kimball's  (29) formula f o r the p a r t i t i o n of Chi-Square was used. of t h i s method of p a r t i t i o n i s shown i n Appendix B. c o e f f i c i e n t s were calculated ship between the variables  As an  An example  Contingency  to determine the degree of r e l a t i o n -  and the c r i t e r i o n .  S p e c i f i c a l l y , Chi-Square, Kimball's p a r t i t i o n of C h i Square and contingency c o e f f i c i e n t s were calculated  i n the following  comparisons: 1.  Averages and Standing at F i r s t Attempt (a)  Groups based on l e t t e r grade averages, A, B, C+, C,  C- and E were compared i n terms of f i r s t year standing.  26  (b) examinations  The students who wrote three or more Departmental ( i ) because they attended non-accredited school, ( i i ) because they were not recommended although a t tending accredited schools, ( i i i ) because they wished to write f o r scholarship e l i g i b i l i t y , were grouped according to percen-  tage average i n June, and compared i n terms of f i r s t year standing. The groups were divided as follows: Group 1  8 0 to 9 ^ per cent  Group 2  6 5 to 79 per cent  Group 3  50 to 6^- per cent  Group k  Below 50 per cent  In t h i s problem, i n addition to the use of the Chi-Square technique, t-tests were used to test differences between means of adjacent groups. (c)  A l l students were c l a s s i f i e d as either ( i ) those who had a clear pass at f i r s t  attempt  through recommendation or by writing Departmental examinations, or ( i i ) those who were required to write one supplemental or more and/or to repeat one subject or more.  Their standing i n f i r s t yearwas then  compared. 2. ,  Accreditation Schools i n B r i t i s h Columbia are accredited by the Depart-  ment of Education on the basis of a number of f a c t o r s .  I f a school  27 i s accredited, the p r i n c i p a l and s t a f f have the authority to r e commend students on the University Programme whose l e t t e r grade standing i n a given subject i s C or higher. ted  Thus they are promo-  i n some or a l l subjects without being required to write De-  partmental  examinations. (a)  Of the students who attended accredited schools,  the students who were recommended i n a l l subjects were compared with those who were required to write one Departmental examination or more, i n terms of f i r s t year standing. (b)  The non-recommended students were grouped according  to the number of examinations  they were required to write, and ob-  served i n r e l a t i o n to f i r s t year standing. 3.  Majors In order to obtain U n i v e r s i t y Entrance standing i n B r i t i s h  Columbia, students must obtain c r e d i t i n required courses: four years of E n g l i s h , three years of S o c i a l Studies, two years of general Science, two years of a f o r e i g n language and three years of Health and Personal Development.  In a d d i t i o n , they must obtain credit  i n at least seven optional courses, at least three of which must be taken at an advanced l e v e l , such as a f i f t h year of E n g l i s h , (English 91) or two a d d i t i o n a l years of a f o r e i g n language (91 and 92).  Other possible advanced electives are S o c i a l Studies, Mathe-  matics, Science, Commerce, I n d u s t r i a l Arts, Home Economics. advanced electives are commonly c a l l e d Majors.  These  28 (a)  Students were grouped according to what majors they  completed i n high school: (i)  those completing majors which included Mathematics and Science but excluded E n g l i s h and S o c i a l Studies,  (ii)  those completing majors which included E n g l i s h and S o c i a l Studies but excluded Mathematics and Science,  (iii)  those completing English, S o c i a l Studies, Mathematics and Science majors, and  (iv)  those completing some of the above majors and others i n various combinations  other than ( i ) ,  ( i i ) , or ( i i i ) . Marks disregarded, the groups were then compared i n terms of f i r s t year standing. (b)  Students were c l a s s i f i e d according to whether they  had or had not a foreign language major.  Marks disregarded again,  the two groups were compared i n terms of f i r s t year standing.  CHAPTER IV ANALYSIS OF THE DATA In accordance with the outline i n the previous chapter, the following sections give i n d e t a i l the results of the s t a t i s t i cal A  analysis. Averages and Standing at F i r s t Attempt 1.  Letter Grade Average Considering high school l e t t e r grade averages  first,  Table I shows the d i s t r i b u t i o n of these averages with corresponding  f i r s t year u n i v e r s i t y standing. TABLE I FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL LETTER GRADE AVERAGE  Grade 12 Letter F i r s t Second Pass Supp.Fail DeGrade With-Did not Totals Average Class Class ferred drew -V/rite 20 2 1 2 A 3k 9 100 h B 1 211 32 15 ^9 7 3 1 6 C+ 56 9*f 37 63 3 13 273 C 172 2 . 2 76 57 15 17 3  5  CE Totals  36  IhQ  110  207  29 3 171  9  6 1  3  **3  ±3  13  737  x The four who f a i l e d at f i r s t attempt subsequently wrote supplementals or repeated subjects and obtained University Entrance Standing. Examination of t h i s table alone would lead to the conclusion that u n i v e r s i t y standing i s not independent l e t t e r grade average.  of high school  In  order to eliminate small frequencies, Table I I was  obtained by combining  on the one hand students with no credit at  university and on the other hand students with C- and E averages i n high school. TABLE I I FREQUENCIES (PERCENTAGES IN PARENTHESES) GF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL LETTER GRADE AVERAGE (SMALL FREQUENCIES -COMBINED) F i r s t Year U n i v e r s i t y Standing Grade 12 Letter Grade Average  First Class  Second Class  A  20 (58.82)  9 (26.1+7)  B  15 ( 7.11)  100 (^7.39)  32 (15.17)  (  37 (13.55)  63 (23.08)  ( 1?16)  15 ( 8.72)  C+  (JO  ^37)  C  (*)  36  ( h.QQ) (20.08)  00  00.  C-,E Totals  No Credit  Pass  110 Q1+.92)  Totals  (%)  3k  2 ( 5.88)  3 ( 8.82)  ( ^.61)  k-9  15 ( 7.11)  211 (28.63)  9k  (3^3)  78 (28.57)  273 (37.01+)  57 (33.1*0  98 (56.98)  172 (23.3*+)  5 (10.61+)  (89.36)  207 (28.09)  236 (32.02)  (23.22)  1+2  k?  ( 6.38) 737  From t h i s table i t can be seen that only about 1+0 per cent of the sample of students completed dit  f i r s t year with f u l l c r e -  i n A p r i l , 28 per cent obtained p a r t i a l c r e d i t , and 32 per cent  obtained no c r e d i t .  Of the students with A average, about 8 5 per  31  cent obtained f u l l c r e d i t , and t h i s was done at honours l e v e l .  Of  the B students almost 7 0 per cent obtained f u l l c r e d i t ; of the C+ students only about 37 per cent obtained f u l l c r e d i t .  Less than  nine per cent of the C students obtained f u l l c r e d i t , and none of the C- and E students did so. ter  Less than ten per cent of the l a t -  group obtained p a r t i a l c r e d i t . These are but a few of the many comparisons that can be  made from the table alone.  A l l show a positive c o r r e l a t i o n , de-  s c r i p t i v e l y speaking, between high school l e t t e r grade average and university standing. S t a t i s t i c a l l y , testing the n u l l hypothesis that univers i t y standing i s independent a Chi-Square  of high school l e t t e r grade average,  of 528.1*+ with 16 degrees of freedom was  This value i s very highly s i g n i f i c a n t ( P ^ . 0 0 1 ) . thesis was  calculated.  The n u l l hypo-  therefore rejected i n favour of the a l t e r n a t i v e hypo-  thesis that there i s a difference among the groups i n a positive d i r e c t i o n ; that i s , that there i s a positive association between high school l e t t e r grade average and freshman standing.  To ascer-  t a i n the degree of r e l a t i o n s h i p , a contingency c o e f f i c i e n t  was  calculated, C = . 6 5 , which indicates a high c o r r e l a t i o n . * To eliminate the c e l l s with small expected f r e q u e n c i e s ,  SK  and i n order to obtain a 3 by 3 table for the p a r t i t i o n of C h i Square, categories were combined further to produce Table I I I . x /  Maximum value of C i n a 5 by 5 table i s \89h  (26,p.390).  SH In Table II there were two c e l l s with expected frequencies of less than 5 , and one c e l l with expected frequency of 5 . 0 7 . Although the majority of s t a t i s t i c i a n s would not approve, according to Cochran ( 1 1 ) , the number of small c e l l s i s not out of proportion.  32  TABLE I I I FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL LETTER GRADE AVERAGE (REDUCED TO 3 BY 3 CONTINGENCY TABLE) Grade 12 Letter Grade Average  Full Credit  Supp.  No Credit  Totals  A, B  176  51  18  2h$  C+  101  9^  78  273  17  62  l*fO  219  236  737  C, C—j E  29h  Totals  Combining categories Chi-Square t o 2 ^ 5 . 6 6 .  207  caused some loss of power, reducing  The reduced value, with four degrees of f r e e -  dom, i s s t i l l very highly s i g n i f i c a n t ( P / . 0 0 1 ) . P a r t i t i o n i n g the above Chi-Square i n t o i t s components, values were calculated t o be: Chi-Square ( 1 ) = 3 9 . 2 6 (difference between A, B group and C+ group i n terms of obtaining  f u l l c r e d i t or just p a r t i a l  credit). Chi-Square ( 2 ) = 2 6 . 7 2 (difference between A, B group and C+ group i n terms of obtaining  some c r e d i t or no c r e d i t at a l l ) .  Chi-Square ( 3 ) = 33»98 (difference between A, B, C+ groups combined and C, C-, E groups combined i n terms of obtaining f u l l c r e d i t or just p a r t i a l c r e d i t ) . Chi-Square (U-) = lk-5.71 (difference between A, B, C+ groups combined and C, C-, E groups combined i n terms of obtaining t  some c r e d i t or no credit at a l l ) .  33  Each single degree of freedom Chi-Square i s s i g n i f i c a n t at .001 l e v e l of confidence indicating that each component contributed to making the t o t a l Chi-Square s i g n i f i c a n t .  Chi-Square (h) provided  most of the contribution. Prom these s t a t i s t i c s the following conclusions can be made. a.  There i s a s i g n i f i c a n t difference,  i n favour of the  A, B group, between the performance of the A, B group and the C+ group i n terms of obtaining f u l l credit i n f i r s t year or just p a r t i a l c r e d i t . b.  There i s a s i g n i f i c a n t difference,  i n favour of the  A, B group, between the performance of the A, B group and the C+ group i n terms of obtaining some credit ( f u l l or p a r t i a l ) or no c r e d i t at a l l . c.  There i s a s i g n i f i c a n t difference,  i n favour of the  A, B, C+ groups combined, between the performance of t h i s combined group and the C, C-, E groups combined i n terms of obtaining f u l l credit or just p a r t i a l credit. d.  There i s a s i g n i f i c a n t difference,  i n favour of the  A, B, C+ groups combined, between the performance of t h i s combined group and that of the C, C-, E groups combined i n terms of obtaining some c r e d i t ( f u l l or p a r t i a l ) or no credit at a l l . More than half (about 59 per cent) of the t o t a l v a r i a t i o n was contributed by t h i s category.  3k  2.  Percentage Average Considering only the students who wrote three or more  Departmental examinations, Table IV shows the d i s t r i b u t i o n of the grouped percentage averages with corresponding f i r s t year univers i t y standing. TABLE IV FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL PERCENTAGE AVERAGE RESULTING FROM DEPARTMENTAL EXAMINATIONS F i r s t Year University Standing Grade 12 Percentage F i r s t Second Pass Supp. F a i l DeWith- Did not Totals Average Class Class ferred drew Write 80-91$  29  27  2  2  65-79^  2  28  16  15  2  1  5  25  ^9  2  12  50-61$  Below 50% Totals  31  56  23  61  1  63  1  1  68  11  3  9**  h  1  19  17  5  2h2  3  3  s  H These students subsequently wrote supplementals or repeated subjects and obtained University Entrance standing. As before, observation of the table alone would lead one to conclude that there i s a positive relationship between high school percentage average and freshman standing. In Table V the groups with no credit are combined, and the r e l a t i v e proportions are shown i n terms of percentages.  35 TABLE V FREQUENCIES (PERCENTAGES IN PARENTHESES) OF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL PERCENTAGE AVERAGE (SMALL FREQUENCIES COMBINED) F i r s t Year University Standing Grade 12 Percentage • Average  First Class (JO.  Second Class (50  Pass  Supp.  (50  (JO  80-9k$  29 27 (k7.5k) (Mf.26)  ( 3?28)  (3.28)  (1.6k  65-79$  28 ( k l.l8) ( 2?9k)  16 (23.53)  15 (22.06)  50-6U$  1 1.06)  5 5.32)  25 (26.60)  7 (10.29) 63 (67.02)  (10*53)  17 (8if.if7)  (18.18)  88 (36.36)  (  (  Below 50$ 56 31 (12.81) (23.1k)  Totals  23 ( 9.50)  Totals  No Credit (JO )  (JO 61 (25.21) 68 (28.10) 9k (38.8k) (  7.85 2k2  About 95 per cent of the top group (80-9^$ average) obtained f u l l c r e d i t .  Approximately 68 p er cent of the next group  (65-79$ average) obtained f u l l c r e d i t ; only about s i x per cent of the next group (50-6^$ average) did so, and none of the bottom group passed. S t a t i s t i c a l l y , the null.hypothesis was again rejected. The calculated Chi-Square of 227.01, with twelve degrees of freedom, i s highly  significant (P/.001).  A high degree of relationship i s  shown by a contingency c o e f f i c i e n t of  .70.  To eliminate c e l l s with small expected frequencies,* and i n order to obtain a 3 by 3 table for the p a r t i t i o n of Chi-Square,  H In Table V there were four c e l l s with expected frequencies of less than 5. In view of this comparatively high proportion of small c e l l s Chi-Square was computed with reservation. The following Chi-Square, with four degrees of freedom provides a more s a t i s factory measure.  36  categories were further combined to produce Table VI. TABLE VI FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL PERCENTAGE AVERAGE (REDUCED TO 3 BY 3 CONTINGENCY TABLE) F i r s t Year University Standing Grade 12 Percentage Average  Full Credit  Supp.  80-9^  58  2  1  61  65-79%  ^6  15  7  68  6  27  80  113  88  2*+2  Below  6%  No Credit  110  Totals  Loss of power was again evident. grees of freedom was  Chi-Square with four de-  calculated to be 1 6 0 . 2 9 .  reduced value i s s t i l l highly s i g n i f i c a n t P a r t i t i o n i n g t h i s Chi-Square  Totals  Nevertheless, t h i s  (P/.001).  into i t s component single de-  gree of freedom Chi-Squares, the following values were calculated: Chi-Square  (1)  = 11.18  (difference between students with aver-  ages of 8 0 - 9 ^ per cent and those with averages of 6 5 - 7 9 per cent i n terms of obtaining f u l l credit or just p a r t i a l c r e d i t ) . Chi-Square  ( 2 ) = 1.0** (difference between students with aver-  ages of 80-9*+ per cent and those with averages of 6 5 - 7 9 per cent i n terms of obtaining some c r e d i t or no credit at a l l ) . Chi-Square  ( 3 ) = 3 9 . ^ 7 (difference between students with aver-  ages of 65-9*+ per cent and those with averages below 6 5 per cent i n terms of obtaining f u l l c r e d i t or just p a r t i a l c r e d i t ) .  37  Chi-Square  (h) = 1 0 9 . 3 7 (difference between students with  averages of 65-9 *- per cent and those with averages below 1  65 per cent i n terms of obtaining some c r e d i t or no c r e d i t at a l l ) . One of these values, Chi-Square  ( 2 ) , i s i n s i g n i f i c a n t and c o n t r i -  buted v i r t u a l l y nothing t o the t o t a l v a r i a t i o n .  The other three  are s i g n i f i c a n t at . 0 0 1 l e v e l of confidence. Prom the foregoing s t a t i s t i c s the following conclusions can be made. a.  There i s a s i g n i f i c a n t difference i n freshman standing between the students with grade twelve  averages  of 80-9*+ per cent and those with averages of 6 5 - 7 9 per cent i n terms of obtaining f u l l c r e d i t or oust partial credit.  This category contributed about  seven per cent to the t o t a l v a r i a t i o n . b.  There i s no s i g n i f i c a n t difference i n freshman standing between the students with grade twelve  averages  of 80-9*+ per cent and those with averages of 6 5 - 7 9 per cent i n terms of obtaining some c r e d i t ( f u l l or p a r t i a l ) or no credit at a l l . c.  There i s a s i g n i f i c a n t difference i n freshman standing between students with grade twelve averages of 6 5 - 9 ^ per cent and those with averages below 6 5 per cent i n terms of obtaining f u l l c r e d i t or just p a r t i a l credit.  This category contributed about 2 5 per cent  to the t o t a l v a r i a t i o n .  d.  The most s i g n i f i c a n t difference i n freshman standing  l i e s between students with grade twelve  averages  of 6 5 - 9 ^ per cent and those with averages below 6 5 per cent i n terms of obtaining some c r e d i t ( f u l l or p a r t i a l ) or no credit at a l l .  This category c o n t r i -  buted about 68 per cent of the t o t a l v a r i a t i o n . The difference, i n every case, i s i n favour of the group with the higher averages. Table VII shows the grade twelve means and standard deviations of the students grouped according to freshman standing. A steady decrease i n mean value i s noticeable as standing drops. TABLE VII DEPARTMENTAL EXAMINATION MEANS AND STANDARD DEVIATIONS OF STUDENTS GROUPED ACCORDING TO .FIRST YEAR UNIVERSITY STANDING . F i r s t Year University Standing Means and Standard Deviations Derived from Grade 1 2 Departmental Exams  First Class  Second Class  Pass  Supp.  No Credit  Mean  81+.68  78.1+1  69.78  63.07  5^.57  Standard Deviation  >.10  5.69  6.67  10.08  7.72  31  56  23  Number  ¥+  88  Adjacent means were tested with t - t e s t s , and thefollow ing values were calculated: a.  Between f i r s t and second class honours standing: t d.f.  = 5.hO = 85  39  b.  Between second class honours and pass standing: t = 5.82 d.f. = 77  c.  Between pass and supplemental t  =  d.f. = d.  3.26 55.7  standing:  s  Between supplemental and f a i l standing: t = 5.^2 d.f. = 130  A l l t values but the t h i r d one are s i g n i f i c a n t at . 0 0 1 l e v e l of confidence, and the t h i r d one i s s i g n i f i c a n t at . 0 1 l e v e l of c o n f i dence.  These r e s u l t s substantiate the preceding conclusion that  freshman standing i s not independent of high school percentage average. 3.  Standing at F i r s t Attempt Comparing next the students who  passed a l l subjects at  f i r s t attempt with those who wrote Department of Education supplementals and/or repeated grade twelve subjects, Table VIII shows their d i s t r i b u t i o n with corresponding f i r s t year university  ^  standing.  x Variances of these two groups were not homogeneous and therefore Welch's ( 5 0 ) approximation was used.  ko TABLE VIII FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON FIRST ATTEMPT AND ON REPETITION F i r s t Year University Standing Grade 12 Performance  F i r s t Second Class Class Pass Supp. F a i l  Passed at First Attempt  36  1^8  109  198  133  8  28  9  669  1  9  38  1  15  k  68  110  207  171  9  k3  13  737  Wrote Supps. and/or Repeated Subjects 36  Totals  1^8  DeWith- Did not ferred drew Write Totals  In Table IX the groups with no credit have been combined and the r e l a t i v e proportions i n terms of percentages are shown. TABLE IX FREQUENCIES (PERCENTAGES IN PARENTHESES) OF UNIVERSITY FRESHMAN STANDING BASED ON FIRST ATTEMPT AND ON REPETITION (SMALL FREQUENCIES COMBINED) F i r s t Year U n i v e r s i t y Standing Grade 12 Performance  First Class  Second Class  36 ( 5.38)  l*f8 (22.12)  (%)  at F i r s t Attempt  Wrote Supps. and/or Repeated Subjects Totals 36  (%)  1^8  Pass  Supp.  (%)  (%)  No Credit  Totals  (%)  (%)  109 (16.29)  198 (29.60)  178 (26.6l)  669 (90.77)  1 ( l.*f7) 110  9 (13>2*0 207  58 (85.29) 236  68 ( 9.23) 737  1+1 It i s interesting to note that of the t o t a l sample of 737 students, only about nine per cent entered u n i v e r s i t y after having had to make more than one attempt at passing a subject or subjects.  Of t h i s group of 68 students, only one student  f i r s t year university.  passed  I t i s obvious from the table alone that  students who make more than one attempt at completing  university  entrance standing i n high school are poorer students at u n i v e r s i t y . S t a t i s t i c a l l y , the table, with four degrees of freedom yielded a Chi-Square of 100.10 which i s highly s i g n i f i c a n t (P^.001), indicating that the two groups d i f f e r i n freshman standing.  The  degree of r e l a t i o n s h i p , C = .35* i s not as high as would be expected due to the fact that only one of the categories contributed to the t o t a l v a r i a t i o n , as i s seen below. In the p a r t i t i o n of the t o t a l , the only single degree of freedom Chi-Square of significance was calculated i n comparing the two groups i n terms of whether they obtained some credit ( f u l l or p a r t i a l ) or no credit at a l l .  I t s value, 97.67, i s about 97 per  cent of the t o t a l v a r i a t i o n and i s s i g n i f i c a n t at .001 l e v e l of confidence.  I t was not possible to p a r t i t i o n the t o t a l further i n the  usual manner i n view of the c e l l s with frequencies of zero and one.  36  x Maximum values f o r C i n a rectangular table are not known (32,p.182), but are less than 1.00, as i n square tables, approaching 1.00 only as the number of c e l l s approaches i n f i n i t y . x x The very fact that there are no cases of students who made more than one attempt at completing u n i v e r s i t y entrance standing i n the upper categories i s indicative of a difference i n performance.  1+2 However, using Kimball's method i n reverse, a Chi-Square  of 53»88,  s i g n i f i c a n t at .001 l e v e l of confidence, was calculated i n comparing the two groups i n terms of whether they obtained p a r t i a l credit or no credit at a l l . It may be concluded that students who enter u n i v e r s i t y with successful f i r s t attempts at completing u n i v e r s i t y entrance standing obtain a higher freshman standing than those who are r e quired to write supplementals and/or to repeat subjects. B.  Accreditation Table X shows the d i s t r i b u t i o n , with corresponding univer-  s i t y standing, of students who attended non-accredited schools, s t u dents who attended accredited schools and who were recommended i n a l l subjects and therefore did not write Departmental those who were recommended but wrote Departmental scholarship e l i g i b i l i t y ,  examinations,  examinations f o r  and those who were not recommended.  k3  TABLE X FREQUENCIES GF UNIVERSITY FRESHMAN STANDING BASED ON GRADE TWELVE STATUS WITH RESPECT TO ACCREDITATION Grade 12 Status  F i r s t Year University Standing F i r s t Second DeWith- Did not Class Class Pass Supp.Fail ferred drew Write Totals  From NonAccredited Schools  3  6  3  10  6  3  Recommended, did not write  5  82  70  100  37  8  309  28  k9  16  16  2  2  2  115  9  18  81  125  3  30  l*f6  107  2 0 7 170  8  Recommended, wrote f o r Scholarship Not Recommended Totals  36  k3  1  32  8  27k  13  730*  x T o t a l number has been reduced by seven students who wrote departm e n t a l f o r a v a r i e t y of reasons other than the usual one and therefore could not be f i t t e d into any of the categories i n the t a b l e . In Table XI the students obtaining no c r e d i t have been combined and the r e l a t i v e proportions i n terms of percentages are given. The proportion of students attending non-accredited was too small to perform any s t a t i s t i c a l a n a l y s i s .  schools  However, i t can  be seen that the proportions of these students i n the categories pertaining to u n i v e r s i t y standing do not d i f f e r g r e a t l y from the t o t a l proportions.  The proportion of f i r s t c l a s s standings i s some-  what higher f o r the group from non-accredited  schools, and the pro-  portion of pass standings i s somewhat lower, but the proportion of f a i l u r e s i s almost i d e n t i c a l .  The proportion of students from non-  accredited schools obtaining f u l l c r e d i t i s also almost  identical  with the proportion of students from accredited schools who obtained f u l l credit. TABLE XI FREQUENCIES (PERCENTAGES IN PARENTHESES) OF UNIVERSITY FRESHMAN STANDING BASED ON GRADE TWELVE STATUS WITH RESPECT TO ACCREDITATION (SMALL FREQUENCIES COMBINED) Grade 12 Status  F i r s t Year U n i v e r s i t y Standing First Class  From NonAccredited  3  Schools  Recommended Did Not  Write  Recommended Wrote f o r  Scholarship  ST  Pass  6  3  10  No Credit  10  Totals CD 32  ( 9.37)  (18.75) ( 9.37)  5 ( 1.62)  82 70 100 52 309 (26.5*0 (22.65) (32.36) (16.83) (^2.33)  28  *+9  16  9 ( 3.28)  18 ( 6.57)  (31.25) (31.25) ( *f.38)  16  6  (2*+.35) (^2.6l) (13.91) (13.91) ( 5.22)  Not Recommended Totals  Second Class  36 ( ^.93)  lh6 107 (20.00) ( H K 6 6 )  115  (15.75)  166 27^ (29.56) (60.58) (37.53) 81  207 23^ (28.36) (32.05)  730  As would be expected, the students who were recommended but wrote Departmental examinations the best students at u n i v e r s i t y .  f o r scholarship e l i g i b i l i t y were  Of t h i s group approximately 67 per  cent were honours students; a t o t a l of over 80 per cent obtained  k5 f u l l c r e d i t ; only about lk per cent had supplemental about f i v e per cent obtained-no  and only  credit.  The l a t t e r 19 per cent might w e l l be considered excep t i o n s , but should be noted.  Even the best students from high  school f a i l sometimes and may have supplemental  at u n i v e r s i t y .  S i m i l a r l y , i t must be noted that about three per cent of the students who were not recommended achieved second class honours and about s i x per cent passed.  These are small proportions, unques-  tionably, but they do e x i s t . 1.  Recommended and Non-recommended Subjects In order to test the difference i n freshman standing be-  tween the recommended and the non-recommended students, the  non-  accredited group was eliminated, producing Table XII, i n which the two recommended groups were combined. TABLE XII FREQUENCIES (PERCENTAGES IN PARENTHESES) OF UNIVERSITY FRESHMAN STANDING BASED ON RECOMMENDATION AND NON-RECOMMENDATION " (SMALL FREQUENCIES COMBINED) Grade 12 Standing  Recommended  F i r s t Year University Standing First Class  33 ( 7.78)  Not Recommended Totals  _____  33  < k.73)  Second Class  No Credit  Pass  Totals  131 86 116 58 k2k (30.90) (20.28) (27.36) (13.68) (60.7^5) 9 ( 3.29)  18 ( 6.57)  IkO  10lf  81 166 27k (29.56) (60.58) (39.255) 197  22k  (20.06) (1^.90) (28.22) (32.09)  698  k6 This table alone shows that recommended students perform at a higher l e v e l at university.  Almost 59 per cent of t h i s group  obtained f u l l c r e d i t , as contrasted with ten per cent of the nonrecommended group.  Less than lk per cent of the recommended group  as opposed to over 60 per cent of the non-recommended group obtained no c r e d i t . Table XII with four degrees of freedom yielded a Chi-Square of 219.10, which i s highly s i g n i f i c a n t (P^.001), and a contingency c o e f f i c i e n t of .*+9.  The l a t t e r shows a positive and reasonably high  c o r r e l a t i o n , i n spite of the lack of contribution of one of the categories as explained below. In the p a r t i t i o n of Chi-Square, the following single degree of freedom Chi-Squares were calculated: Chi-Square (1) = ,k6* (difference between recommended and nonrecommended students i n terms of obtaining f i r s t  or second  class honours standing). Chi-Square (2) = 3*99 (difference between the two groups i n terms of obtaining honours standing or just a pass standing) . Chi-Square (3) = **7«5l (difference between the two groups i n terms of obtaining f u l l c r e d i t or just p a r t i a l c r e d i t ) . Chi-Square (k) = 168.03 (difference between the two groups i n terms of obtaining some c r e d i t or no c r e d i t at a l l ) . Chi-Square (1) i s i n s i g n i f i c a n t and contributed v i r t u a l l y nothing to the t o t a l v a r i a t i o n . x  Chi-Square (2) i s s i g n i f i c a n t but only at  Small c e l l frequencies are involved i n t h i s Chi-Square  .05 l e v e l of confidence, contributing only somewhat to the t o t a l . Chi-Square (3) i s s i g n i f i c a n t (P^.001),  contributing about 20 per  cent to the t o t a l , and Chi-Square (*+) i s highly s i g n i f i c a n t  (P/.001),  contributing about 76 per cent to the t o t a l v a r i a t i o n . Thus i t may be concluded that recommended students achieve higher standing at university than do non-recommended s t u dents.  That i s : a.  There i s no s i g n i f i c a n t difference between the two groups i n terms of obtaining f i r s t or second class honours standing;*"  b.  There i s a difference between the two groups i n terms of obtaining honours or just a pass standing.  c.  There i s more difference between the two groups i n terms of obtaining f u l l credit or just p a r t i a l c r e d i t .  d.  Most of the difference i s i n terms of obtaining some credit ( f u l l or p a r t i a l ) or no credit at a l l .  In every case the difference i s i n favour of the recommended group.. 2.  Number of Departmental Examinations Written The 2?h non-recommended students were required t o write  from one t o s i x Departmental examinations. Table XIII gives the d i s t r i b u t i o n of the number of Departmental examinations written with the  r e l a t i v e u n i v e r s i t y standing.  This conclusion must be made with reservation due to the small c e l l frequencies involved.  U8  TABLE XIII FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON NUMBER OF DEPARTMENTAL EXAMINATIONS WRITTEN Number of F i r s t Year University Standing Departmentals Written With-Did not F i r s t Second DeClass Class Pass Supp. F a i l ferred drew Write  Totals  12  hi  kQ  2  12  2  126  2  h  23  22  1  6  2  58  3  1  10  28  5  1  k5  h  6  19  5 »  2 ,  32  5  1  6  1  1  9  2  1 8  27k  1  9  6 Totals  1 9  18  81  125  3  30  In Table XIV categories are combined to eliminate small c e l l s and proportions are given i n terms of percentages.  Propor-  tions alone suggest that students who are required to write fewer Departmental examinations do somewhat better at u n i v e r s i t y .  Ap-  proximately 52 per cent of the students writing one or two examinations f a i l e d to obtain any c r e d i t , while over 78 per cent of the students writing three or more examinations did so.  ROTABLE XIV FREQUENCIES (PERCENTAGES IN PARENTHESES,) OF UNIVERSITY FRESHMAN STANDING BASED ON NUMBER" OF DEPARTMENTAL EXAMINATIONS WRITTEN (SMALL FREQUENCIES COMBINED) Number of Departmentals Written  F i r s t Year University Standing No Credit  Totals  hi  (32.5^)  6h (50.79)  126 (M-5.98)  ( 6.90)  23 (39.65)  31 (53A5)  58 (21.17)  2 ( 2.22)  17  (18.89)  71 (78.89)  90 (32.85)  81  166 (60.58)  2?h  Full Credit  (%)  1  21 (16.67)  2  if  3 or more  27 ( 9.85)  Totals  Supp.  (%)  (29.56)  (%)  {%)  Table XIV with four degrees of freedom yielded a C h i Square of 2*f.06 which i s s i g n i f i c a n t at.001 l e v e l of confidence. The contingency c o e f f i c i e n t of .28 i s positive although not very high.  However, i t s lack of magnitude may be explained by two pre-  v a i l i n g conditions: 1.  the range of the t o t a l group i s extremely r e s t r i c t e d ; *  2.  two of the categories f a i l to contribute to the t o t a l variation.  In the p a r t i t i o n of the t o t a l v a r i a t i o n , the following single degree of freedom Chi-Squares were calculated:  x A high c o r r e l a t i o n cannot be found i n a r e s t r i c t e d range. Neidt and Ahmann (51,p.76).  Wert,  Chi-Square (1) = h.k6 (difference  between students who wrote  one Departmental examination and those who wrote two i n terms of obtaining f u l l credit or just p a r t i a l c r e d i t ) . Chi-Square (2) = .12 (difference  between students who wrote  one Departmental examination and those who wrote two i n terms of obtaining some credit or no credit at a l l ) . Chi-Square (3) = 1.69 (difference  between students who wrote  one or two Departmental examinations and those who wrote three or more i n terms of obtaining f u l l or p a r t i a l c r e d i t ) . Chi-Square (*+) = 18.81 (difference  between students who wrote  one or two Departmental examinations and those who wrote three or more i n terms of obtaining some credit or no credit  at a l l ) .  Chi-Square (1) i s s i g n i f i c a n t at .05 l e v e l of confidence and contributed about 18 per cent to the t o t a l v a r i a t i o n .  Chi-Squares (2)  and (3) are not s i g n i f i c a n t , while Chi-Square (h) i s s i g n i f i c a n t at .001 l e v e l of confidence and comprises about 72 per cent of the total variation. From these s t a t i s t i c s , i t may be concluded that: (a) There i s some difference  between the students who  wrote one Departmental examination and those who wrote two i n terms of obtaining f u l l credit or just partial credit.  The difference  students who wrote just one.  i s i n favour of the  (b)  There i s no difference between the same two groups i n terms of obtaining some credit ( f u l l or p a r t i a l ) or no credit at a l l .  (c)  There i s no difference between the students who wrote one or two Departmental examinations and those who wrote three or more i n terms of obtaining f u l l or p a r t i a l c r e d i t .  (d)  The greatest v a r i a t i o n l i e s between the students who wrote one or two Departmental examinations and those who wrote three or more, i n terms of obtaining some c r e d i t ( f u l l or p a r t i a l ) or no credit at a l l . The difference i s i n favour of those who wrote fewer Departmental examinations.  C.  Majors Table XV shows the d i s t r i b u t i o n of the students talcing  various combinations of major subjects with their r e l a t i v e f i r s t year standing.  52 TABLE XV FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL MAJORS High School Majors  F i r s t Year University Standing F i r s t Second DeWith Class Glass Pass Supp.Fail ferred drew  Did not Write Totals  Ma., Sc., Eng., Soc. St. Ma., Sc.  18  h2  21  kQ  25  3  5  1  163  h  20  22  38  *+6  1  V?  3  151  Eng., Soc. St. A l l other Combinations  2  h  2  3  3  12  82  65  118  97  5  20  9  H08  Totals  36  IkQ  110  207  171  9  ^3  13  737  1  It was the writer's intention, among other  15  comparisons,  to compare the freshman standing of the students who took Mathematics and Science as majors butwho omitted E n g l i s h and S o c i a l Studies from their programmes with the students who took English and S o c i a l Studies as majors but who omitted Mathematics and S c i ence. doned.  Owing to the small number of the l a t t e r the idea was abanThis group i s therefore combined i n Table XVI with the  group containing a l l other combinations  of majors.  A l l those with  no credit are also combined, and r e l a t i v e proportions are given i n terms of percentages.  TABLE XVI FREQUENCIES (PERCENTAGES IN PARENTHESES) OF UNIVERSITY FRESHMAN STANDING BASED ON MAJORS (SMALL FREQUENCIES COMBINED) High School Majors  F i r s t Year University Standing First Class  (JO  Ma., Sc., Eng., Soc. St. Ma., Sc. A l l other Combinations Totals  Second Class  (JO  Pass  Supp.  (JO  0 0  No Credit  (JO  Totals  (JO  18 k8 k2 21 3k 163 (11.0k) (25.77) (12.88) (29 M) (20.86) (22.12) k 20 22 (13.2k) (lk.57) ( 2.65)  67 151 (25.16) (Mf.37) (20.^9)  86 lk 67 ( 3.3D (20.33) (15.W  121 k23 (28.60) (31.91) (57.39)  36  1^8  110  207  236  737  From the proportions given i n Table XVI, i t i s evident that less than half as many students f a i l who took not only Mathe matics and Science but also English and S o c i a l Studies as majors. Table XVI, with eight degrees of freedom yielded a ChiSquare of 37.3k, which i s s i g n i f i c a n t at .001 l e v e l of confidence and a contingency c o e f f i c i e n t of .22, showing a positive correl a t i o n , although not a very high one. This again i s due partly t the fact that some of the categories contributed l i t t l e to the total variation. Combining categories further to produce a 3 by 3 table, (Table XVII), with four degrees of fieedom, resulted i n some loss  of power, y i e l d i n g a reduced Chi-Square of 21.l+6 which, neverthel e s s , i s s t i l l s i g n i f i c a n t at .001 l e v e l of confidence. TABLE XVII FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL MAJORS (REDUCED TO A 3 BY 3 CONTINGENCY TABLE) High School Majors  F i r s t Year University Standing Full Credit  Supp.  No Credit  Totals  Ma., Sc., Eng., Soc.St.  81  - ^8  3>+  163  Ma., Sc.  if6  38  67  151  A l l other Combinations  167  121  135  *+23  Totals  29*+  207  236  737  In the p a r t i t i o n of the l a t t e r Chi-Square the following single degree of freedom Chi-Squares were calculated: Chi-Square (1) = l.hO (difference between students with Engl i s h , S o c i a l Studies, Mathematics and Science majors and those with just Mathematics and Science majors i n terms of obtaining f u l l credit or just p a r t i a l c r e d i t ) . Chi-Square (2) = 19.91  (difference between students with Eng-  l i s h , S o c i a l Studies, Mathematics and Science majors and those with just Mathematics and Science majors i n terms of obtaining some c r e d i t or no c r e d i t at a l l ) .  Chi-Square (3) = . l * (difference between students with English, 1  S o c i a l Studies, Mathematics and Science majors combined with the students having just Mathematics and Science majors, and the students with any other combination of majors, i n terms of obtaining f u l l credit or just p a r t i a l credit. Chi-Square (*+) = .01 (difference between students with English,  S o c i a l Studies, Mathematics and Science majors com-  bined with the students having just Mathematics and Science majors and the students with any other combination of majors, i n terms of obtaining some c r e d i t or no c r e d i t at all). These results indicate that only one of the categories caused the t o t a l v a r i a t i o n to be s i g n i f i c a n t . at  Chi-Square (2) i s s i g n i f i c a n t  .001 l e v e l of confidence and comprises about 93 per cent of the  total variation.  That i s , the only difference of significance i s  between the group with English, S o c i a l Studies, Mathematics and Science majors and the group with just Mathematics and Science majors i n terms of obtaining some credit ( f u l l or p a r t i a l ) or no credit  at a l l .  There i s no difference between these two groups i n  terms of obtaining f u l l credit or just p a r t i a l c r e d i t .  There i s  also no difference, on any basis, between the combined group of students taking English, S o c i a l Studies, Mathematics and Science and just Mathematics and Science and the group taking a l l other combinations  of majors.  56 It may be concluded then that the students who have i n cluded i n their high school programmes both the sciences and the humanities as majors are somewhat better students at u n i v e r s i t y than the students who have taken the science majors without the humanities, i n that fewer of the former  fail.  Table XVIII shows the d i s t r i b u t i o n of students who had a foreign language major i n high school and students who did not, with corresponding freshman standing. TABLE XVIII FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON HAVING A HIGH SCHOOL FOREIGN LANGUAGE MAJOR AND NOT HAVING ONE High School Majors  F i r s t Year University Standing F i r s t Second DeWith Class Class Pass Supp.Fail ferred drew  Did not Write Totals  Foreign Lang .Major  21  65  32  15  83  78  18  h  1  3  191  153  5  ^2  10  5^6  No foreign Lang .Major Totals  160  36 1M-8 110 207 171 9 ^3 13 737 Again a l l those with no c r e d i t are combined i n Table XLX,  and r e l a t i v e proportions i n terms of percentages are given.  As can  be seen only about 26 per cent of the students took a foreign l a n guage major.  57 TABLE XIX FREQUENCIES (PERCENTAGES IN PARENTHESES) OF UNIVERSITY FRESHMAN STANDING BASED ON HAVING A HIGH SCHOOL FOREIGN LANGUAGE MAJOR AND NOT HAVING ONE (SMALL FREQUENCIES COMBINED) High School Majors  F i r s t Year University Standing First Class  00  Foreign Lang.Maj.  Second Class  (JO  Pass  Supp.  (JO  (JO  No Credit  (JO  Totals  (JO  26 1+7 191 65 21 32 (10.99) (3^.03) (16.75) (2k.61) (13.61) (25.92)  No Foreign Lang. Maj.  78 15 83 ( 2.75) (15.20) (llf.29) 36  Totals  IhQ  110  160 210 5k6 (29.30) (38.1+6) (7^.08) 207  236  737  From the proportions i n , t h i s table i t appears that the students who included a foreign language major i n their programmes achieve higher standing at u n i v e r s i t y .  About 61 per cent of stu-  dents with foreign language majors as contrasted with about 32 per cent of those with no foreign language major obtained f u l l c r e d i t . Less than 1*+ per cent of the former as contrasted with over 38 per cent of the l a t t e r obtained no c r e d i t . To test whether the difference i s s i g n i f i c a n t ,  Chi-Square  with four degrees of freedom was calculated to be 73.67. This value i s highly s i g n i f i c a n t (P/.001). The degree of r e l a t i o n s h i p i s moderately high, the contingency c o e f f i c i e n t being .30, with one of the categories making no contribution to the t o t a l v a r i a t i o n , as seen below.  In the p a r t i t i o n of the above Chi-Square, the following  single degree of freedom Chi-Squares were calculated: Chi-Square (1) = 3.13 (difference between students with a foreign language major and those without one i n terms of obtaining f i r s t or second class honours standing). Chi-Square (2) = 11.17  (difference between the two groups i n  terms of obtaining honours or just a pass standing). Chi-Square (3) = 19*22 (difference between the two groups i n terms of obtaining f u l l c r e d i t or just p a r t i a l c r e d i t ) . Chi-Square (k) = kO.lk (difference between the two groups i n terms of obtaining some c r e d i t or no credit-at a l l ) . The f i r s t of these four values i s i n s i g n i f i c a n t ; the other three are  s i g n i f i c a n t at .001 l e v e l of confidence. Chi-Square (k) con-  tributes more than half (5k per cent) to the t o t a l v a r i a t i o n . From these s t a t i s t i c s , i t may be concluded that: a.  There i s no s i g n i f i c a n t difference between students with a foreign language major from high school and those without one i n terms of obtaining f i r s t or second class honours standing.  b.  There i s a s i g n i f i c a n t difference between the two groups i n terms of obtaining honours or just a pass standing.  c.  There i s a s i g n i f i c a n t difference between the two groups i n terms of obtaining f u l l credit or just partial credit.  d.  The most s i g n i f i c a n t difference between the two groups i s i n terms of obtaining some c r e d i t  (full  or p a r t i a l ) or no credit at a l l . In each of the l a s t three cases above, the difference was i n f a vour of the group with a foreign language major.  CHAPTER V CONCLUSIONS, IMPLICATIONS, AND RECOMMENDATIONS FOR FURTHER STUDY  A  Conclusions 1.  General In keeping with other studies i n t h i s f i e l d , r e s u l t s  obtained i n t h i s study show that there i s a d e f i n i t e positive r e lationship between high school achievement and u n i v e r s i t y performance. Better students i n high school are better students at university. 2.  Specific From the s t a t i s t i c s employed, c e r t a i n s p e c i f i c conclu-  sions have been reached. (a)  There i s a high positive relationship between grade  twelve l e t t e r grade average and freshman standing.  Students with  a higher l e t t e r grade average have a better chance of achieving a higher standing at u n i v e r s i t y .  In p a r t i c u l a r , students with C+  average or better are less l i k e l y t o f a i l than students with C average or lower. (b)  There i s an equally high positive r e l a t i o n s h i p be-  tween grade twelve percentage average, r e s u l t i n g from Departmental examinations, and freshman standing, p a r t i c u l a r l y when the d i v i s i o n point i s at 65 per cent on one side and between pass and f a i l on the other.  That i s , the higher the percentage average a student  61 has on Departmental examinations, the better he does at u n i v e r s i t y , and i n p a r t i c u l a r , a student whose high school average i s over 65 per cent has a much better chance of passing at u n i v e r s i t y than one whose average i s below 65 per cent. (c)  Students who successfully pass a l l grade twelve  subjects at f i r s t attempt achieve a higher freshman standing than students who are required to write supplementals and/or to repeat subjects.  Repeaters are poorer academic r i s k s . (d)  Recommended students obtain higher f i r s t year stand-  ing than non-recommended students. The difference i s p a r t i c u l a r l y noticeable when the d i v i s i o n point i s between obtaining some credit and f a i l i n g .  That i s , there i s less chance of a recommended stu-  dent f a i l i n g than of a non-recommended student f a i l i n g . Although the number of students from non-accredited schools was too small f o r s t a t i s t i c a l comparison with those from accredited schools, i n proportions alone they do not d i f f e r i n standing from the students from accredited schools. (e)  In spite of a very r e s t r i c t e d range, there i s some  relationship between the number of Departmental examinations a student i s required to write and his freshman standing.  Students who  write three or more Departmental examinations are more l i k e l y to f a i l than are those who write just one or two. (f)  There i s some r e l a t i o n s h i p between major subjects  taken i n high school and subsequent freshman standing, but only i n a limited way.  Fewer of the students f a i l who include i n t h e i r  high school programmes both the humanities and the sciences as  62 majors (English, S o c i a l Studies, Mathematics, Science) than of those who take just the sciences (Mathematics and Science), omitting the humanities.  There i s no r e l a t i o n s h i p evident i n other  comparisons. (g)  Students who include a foreign language major i n  their high school programmes obtain a higher freshman standing than those with no foreign language major, except when the comparison i s made i n terms of f i r s t or second class honours standing, i n which case there i s no difference. The l a t t e r two conclusions are not i n agreement with the majority of studies which f i n d that u n i v e r s i t y success i s independent of previous pattern of subjects.  I t i s possible that students  who take a l l four of the more academic majors and those who take a f o r e i g n language major i n addition or i n l i e u of one of the other four are students with higher a b i l i t y , and are not necessarily better prepared f o r u n i v e r s i t y work as a r e s u l t of having taken these majors.  Students with higher academic a b i l i t y may choose to  take these majors or may be encouraged or counsellors.  to do so by t h e i r teachers  In any case, the s i t u a t i o n i s i n d i c a t i v e of a  higher degree of success, and cannot be overlooked. In conclusion, i t should be noted that although positive relationships are evident throughout the problems presented, they are by no means perfect.  Very few categories are incompatible with  successful f i r s t year standing or guarantee success. the tables alone reveals deviations.  A survey of  63 B  Implications It i s reasonable  to expect i n any educational system  that the better students i n high school have a good chance of being successful at u n i v e r s i t y , while the poorer students are l i k e l y to have d i f f i c u l t i e s .  Most of the findings of t h i s study, therefore,  confirm those of other i n v e s t i g a t i o n s , and are not unusual.  The  conclusions, however, regarding recommended and non-recommended students are most pertinent to B r i t i s h Columbia, and should therefore be emphasized.  They are important  not only i n p r e d i c t i o n  but also because they provide a strong argument i n favour of the system of recommendation used i n t h i s province. Also pertinent to t h i s province are the conclusions concerning high school majors, both the positive conclusion with r e gard to a foreign language major and the negative one with regard to the sciences.  The student's  choic:e and completion  of c e r t a i n  majors can be used i n prediction, regardless of whether academic a b i l i t y plays a part i n his choice. Keeping i n mind the l i m i t a t i o n s of t h i s study, i t may  be  said with a reasonable degree of conclusiveness that u n i v e r s i t y success can be predicted from high school records.  These records  should therefore be examined c a r e f u l l y by counsellors when discussing with students t h e i r future academic plans. Because i n d i v i d u a l p r e d i c t i o n cannot be as accurate as group prediction, some caution must be exercised i n the former. It should be kept i n mind that there w i l l always be exceptional cases that do more poorly or much better than expected because of growth and emotional f a c t o r s which cannot be measured or c o n t r o l l e d .  6k The remarks of Dr. J.A.B. McLeish (31,p.li+ and  p.l6)  are pertinent here: "The standing of the young high school graduate i n mat r i c u l a t i o n examinations i s obviously a selective factor of great importance. Authorities i n testing have underrated the predictive value of a student's high school record. But again i t i s not easy to s e t t l e upon a minimum cut-off percentage below which one can confidently predict that the incoming student would f a i l . " .... "The g i r l who appears rather immature at entrance may be just the one who w i l l mature most quickly i n the new climate of the u n i v e r s i t y . The boy who seemed to be thoroughly stable and ready for college work, i n the eyes of his former p r i n c i p a l , may have a rough and perhaps f a i l i n g f i r s t year i f he i s unable to contend with loneliness, or with an excess of college a c t i v i t i e s , or with the nagging worry of f i n a n c i a l problems. Perhaps the best that the u n i v e r s i t y can do i s to make ample room i n i t s admissions plans for the merely 'good , or at l e a s t , 'reasonably good , youngster at the gate, and then within the gate provide as ample counselling f a c i l i t i e s and f i n a n c i a l assistance as i t possibly can." 1  1  Not only do i n d i v i d u a l differences and personal problems interfere with perfect prediction, but also does the u n r e l i a b i l i t y of both school marks and u n i v e r s i t y marks. t i o n Dale (16,  In t h i s connec-  p.198) comments:  "Even i f a l l students have been c o r r e c t l y selected, not a l l w i l l pass. I t i s inherent i n the nature of examinations that some must f a i l . It i s also inherent i n the nature of man that some professors w i l l set a standard which i s higher than i t should be, just as others w i l l set a standard which i s too low." In conclusion, the writer f e e l s that i n spite of the hazards involved i n prediction, t h i s study provides  counsellors  with s t a t i s t i c a l and f a c t u a l evidence concerning high school records.  It i s hoped that this evidence, combined with information  gained from aptitude test results,» w i l l better prepare counx Luyendyk (30) and Shirran (^l) found that prediction of success can be made from r e s u l t s of c e r t a i n tests administered by the University of B r i t i s h Columbia Counselling Department.  65 s e l l o r s to predict students' performance at u n i v e r s i t y and to counsel effectively. The r e s u l t s of t h i s study may University administrators C  also be of interest to  for admissions purposes.  Recommendations for Further Study This study did not include students who  and/or foreign language i n f i r s t year. pre-Commerce students.  omit, a  science  These are, i n the main,  I t i s suggested that t h i s group be  studied  i n some similar fashion. The  importance of age,  sex, and other factors such as  t i v a t i o n , study habits, extra-curricular a c t i v i t i e s , and as factors i n academic performance should be  mo-  finances  studied.  In an attempt to evaluate more s a t i s f a c t o r i l y the  influ-  ence of c e r t a i n high school subjects on u n i v e r s i t y success further work might be done with the factor of i n t e l l i g e n c e controlled. It might be worthwhile also to investigate the comparative success of students with an interrupted education, that i s , those who  l e f t school for a year or more prior to entering  univer-  sity. An analysis of difference i n university performance  be-  tween r u r a l and urban school graduates would provide useful i n f o r mation, as would a study of difference between public and  private  school graduates. An i n v e s t i g a t i o n of the r e l i a b i l i t y of marking at  univer-  s i t y would be i n t e r e s t i n g . An investigation of the p o s s i b i l i t y of using a prediction formula including both high school achievement and aptitude test results would be most valuable.  66  Some research on the capable students who do not proceed to university, and the reasons for not doing so, would be very profitable.  In Ontario i t was found as reported by R.W.B. Jackson  i n a foreward to Report No. h of the Atkinson Study (k) that, "Of our most able i n some aspects of aptitude and achievement, for example, l i t t l e more than half go on to university; of our less able students, i t i s embarrassingly evident that too many do go on to university." If the same waste of human resources exists i n t h i s province, and there i s no reason to believe that B r i t i s h Columbia d i f f e r s from Ontario i n t h i s respect, the problem should be investigated and some attempt made to correct i t .  CHAPTER VI SUMMARY OF THE PRESENT STUDY  This investigation was designed to determine the r e l a tionship between high school achievement and u n i v e r s i t y performance with the primary purpose of providing information f o r couns e l l o r s which they could use i n predicting the success or f a i l u r e of university candidates. The high school variables used were l e t t e r grade average, percentage average, standing at f i r s t attempt,  recommendation,  number of Departmental examinations written, and major subjects taken.  The data regarding these variabiles were obtained from grade  twelve records.  The c r i t e r i o n of u n i v e r s i t y performance used was  f i r s t year standing i n A p r i l . A sample of 737 students was chosen from the Faculty of Arts and Science during the academic year of 1957-58.  The stu-  dents who were chosen had completed grade twelve i n a public secondary school i n B r i t i s h Columbia, were not repeating any f i r s t year u n i v e r s i t y courses, and had had an uninterrupted secondary education.  They had registered f o r at least f i f t e e n units of  course work, which included English 100-101, Mathematics 100 or 101, a foreign language, a science, and an e l e c t i v e . It was noted that the predictive value of t h i s i n v e s t i gation can adequately apply only to students whose high school background and u n i v e r s i t y programmes are comparable to those of the students used i n t h i s study.  Further l i m i t a t i o n s are imposed by  68 the necessity of making c e r t a i n assumptions regarding the r e l i a b i l i t y of high school records and u n i v e r s i t y marks. Literature which i s relevant to the areas investigated i n t h i s study was reviewed and conclusions were summarized. In order to determine whether the difference i n f r e s h man standing was  s i g n i f i c a n t among students grouped according to  the various high school variables, Chi-Square technique was ployed.  em-  To determine further where the difference lay, a method  of p a r t i t i o n i n g Chi-Square was  used.  Contingency  coefficients  were calculated to show the degree of relationship between the variables and the c r i t e r i o n . From these s t a t i s t i c s i t was found that there i s a high positive r e l a t i o n s h i p between f i r s t year u n i v e r s i t y standing and grade twelve average, whether i n l e t t e r grade or percentage  form,  and that students who achieve University Entrance standing at f i r s t attempt obtain a higher f i r s t year standing at u n i v e r s i t y than students who are required to write supplemental subjects.  and/or to repeat  It was a l s o found that recommended students perform at  a higher l e v e l at u n i v e r s i t y than non-recommended students, and that students who are required to write three or more Departmental examinations  are more l i k e l y to f a i l at university than students  who write just one or two examinations.  In a d d i t i o n , some r e l a -  tionship was found between major subjects taken i n high school and f i r s t year u n i v e r s i t y standing.  Students who  have included as  ma-  jors i n t h e i r high school programmes Mathematics, Science, E n g l i s h and S o c i a l Studies, are less l i k e l y to f a i l at u n i v e r s i t y than  69 students who take Mathematics and Science majors but who omit English and S o c i a l Studies majors.  Also, students who have taken  a high school foreign language major perform at a higher l e v e l at university than those who omit a foreign language major. It was concluded that, within specified l i m i t a t i o n s , the r e s u l t s indicated that high school records can be used e f f e c t i v e l y i n predicting u n i v e r s i t y performance.  I t was suggested  that some caution be exercised i n i n d i v i d u a l p r e d i c t i o n since i n d i v i d u a l differences make perfect prediction impossible.  For  more sensitive prediction, I t was further suggested that academic a b i l i t y test r e s u l t s be used to supplement high school  records.  70 BIBLIOGRAPHY  1.  Adams, F.J., "Predicting high school and college records from elementary school test data," Journal of Educational Psychology, v o l . 29, 1938, pp. 5 6 - 6 0 . '  2.  Alberta Progress Report. M a t r i c u l a t i o n Study Subcommittee February 1958? pp. 53.  3.  Ashmore, B., "High school teachers marks as indicators of college success," Journal of the American Association of College Registrars, v o l . 21, 1  19^6,  k.  pp. 219-230.  Atkinson Study of U t i l i z a t i o n of Student Resources. Department of Educational Research, Ontario College of Education, University of Toronto,  1957-58.  5.  Bou, I.R., and S t o v a l l , F.L., "A study of high school academic indices as a c r i t e r i o n f o r college admissions," Journal of Educational Research,  v o l . k l , 1950, pp. 309-320.  6.  Bovee, A.G., and Froehlich, G.J.. "Some observations on the relationship between mental a b i l i t y and achievement i n French," School Review, v o l .  53, 19^5, P P . 53^-537.  7.  Brigham, C.C., "Admission units and freshman placement," Educational Record, v o l . 15, 193k, pp. 57-67.  8.  Brown, A.H., and Nemzek, C.L., "A comparative study of the college success of recommended and nonrecommended students from one Detroit high school", Journal of S o c i a l Psychology, v o l . 20, 19M*, pp. 277-281.  9.  Butsch, R.L.G., "Improving prediction of academic success through d i f f e r e n t i a l weighting." Journal of Educational Psychology, v o l . 36, 1939,  pp. k01-k20.  ./  *  10.  Byrns, R., "Predicting college success by high school grades," Nations Schools, v o l . 10, No. 1, 1932, pp. 28-30.  11.  Cochran, W.G., "Some methods f o r strengthening the common chi-square t e s t s , " Biometrics, v o l . 10, No. k.  195k, pp. k i 7 - k 5 l .  71 12.  C o f f i e l d , W.H., and Blommers, P., "Effects of nonpromotion on educational achievement i n the elementary school", Journal of Educational Psychology, v o l . M-7, 1956, pp. 2 3 5 - 2 5 0 . :  13.  Conway, G.B., "Understandable standards: the scaling of University Entrance Examinations," Canadian Education, v o l . 1 1 , 1956, pp. 27-^1.  l*f.  Conway, C.B., and Brown, E.L., "The establishment of u n i v e r s i t y entrance standards i n required and optional subjects," Canadian Education, v o l . 11, 2 , 1956, pp. 17-30.  15.  Crawford, A.B., and Burnhams, P.S., Forecasting College Achievement. New Haven, Yale University Press, 19^6, pp. 2 9 1 .  16.  Dale, R.R., From School To University. London, Routledge and Kegan Paul L t d . , 195S PP» 58. 2  17.  Darley, J.G., "A study of c l i n i c a l prediction of student success or f a i l u r e i n professional t r a i n i n g , " Journal of Educational Psychology, v o l . 29, 193«, PP. 335-35^.  18.  Dearborn, W.F., "The student's background i n r e l a t i o n to school success", i n Donahue, W.T., et a l . The Measurement of Student Adjustment and Achievement. Ann Arbor, Michigan, University of Michigan Press, 19^9, PP. 191-199.  19.  Douglass, H.R., "Selecting good college r i s k s , " School and Society, v o l . 3 5 , 1932, pp. lkO-lk-7.  20.  Drake, L.E., and Henmon, V.A.C., "The prediction of scholarship i n the College of Letters and Science at the University of Wisconsin," School and Society, v o l . *+5, 1937, PP. 191-19 *. 1  21.  Dressel, P.L., "Effect of the high school on college grades," Journal of Educational Psychology, v o l . 3 0 , 1939, PP. 6 1 2 - 6 1 7 . \  22.  Emme, E.E., "Predicting college success," Journal of Higher Education, v o l . 1 3 , 19^2, pp. 263-267.  23.  Ferguson, G.O. J r . , "Some factors i n predicting college success," Sechool and Society,, v o l . 37, 1933, pp. 5 6 6 - 5 6 8 T  72 2h.  Fredericksen, N.O., and Schrader, W.B., "A.C.E. Psychological examination and hign school - standing as pred i c t o r s of college success." Journal of Applied Psychology, v o l . 36, 1952, pp. 261-265.  25.  Froehlich, G.J., "The prediction of academic success at the University of Wisconsin, 1909-19 »-1," B u l l e t i n of the University of Wisconsin. No. 235b, W l , pp. kh. I  26.  Garrett, H.E., S t a t i s t i c s i n Psychology and Education. Longmans, Green and Co., Toronto, 19 +6, pp. *+93. 1  27.  Garrett, H.F., "A review and interpretation of investigations of factors related to scholastic success i n colleges of arts and science and teachers colleges," Journal of Experimental Education^  v o l . 18, 19^9-50, pp. 91-138.  28.  Harris, D., "Factors a f f e c t i n g college grades; a review of the l i t e r a t u r e , " Psychological B u l l e t i n , v o l . 37, 19**0, PP. 125-166. -  29.  Kimball, A.W.,"Short-cut formulas f o r the exact p a r t i t i o n of Chi-Square i n contingency tables," Biometrics,  v o l . 10, 195^, PP. ^52-^58.  30.  Luyendyk, W.R., A study of the Predictive Value of the Battery of Psychological Tests Used by the Counselling Office of the University of B r i t i s h Columbia, unpublished Master's t h e s i s , University of B r i t i s h Columbia, B r i t i s h Columb i a , 1952, pp. 87.  31.  McLeish, J.A.B.,"Who should go t o college?" Saturday Night. September, 1956, pp. 13-16.  32.  McNemar, Q., Psychological S t a t i s t i c s . New York, John Wiley & Sons Ltd., 19^9, PP. 388.  33  Parkyn Report, Council of Educational Research, The C h r i s t church Press. New Zealand, June 13, 1958.  3^.  Prescott, A.C., and Garretson, O.K., "Teachers' estimates and success i n college," School Review, v o l .  *+8, 19^0, pp. 278-28*+.  35.  Rogers, H.W.,  "Success i n secondary school and college," School and Society, v o l . *+0, 193^, PP. 33^-336.  73 36.  Ross, F.C.,  37.  Samenfeld, H.W., "Predicting college achievement," Journal of Higher Education, v o l . 2k, 1953, pp. k32-k33.  38.  Sarbaugh, M.E., "The e f f e c t of r e p e t i t i o n of high school courses on college success," i n Studies i n A r t i c u l a t i o n of High School and College. University of Buffalo Studies, v o l . 9, 193k,  "A method of forecasting college success," School and Society, v o l . 3k, 1931, pp. 20-22.  pp. 1 7 k - l 8 3 .  39.  Schmitz, S.B.,  kO.  Seyler, E.C.,  kl.  Shirran, A.F., Six Years Later, unpublished report on students r e g i s t e r i n g i n f i r s t year Arts and Science at the University of B r i t i s h Columbia i n the academic year 1952-1953, Counselling Department, University of B r i t i s h Columbia, 1958, pp. 23.  k2.  Sorenson, H.,  "High School subjects as conditioners of c o l l e g i a t e success," Journal of Educational Research, v o l . 19, 1929, pp. 237-25k.  k3.  Stone, J.B.,  " D i f f e r e n t i a l prediction of academic success at Brigham Young University," Journal of Applied Psychology, v o l . 38, 195k, pp. 109-110.  *fk.  Symonds, P.M.,  Measurement i n Secondary Education^ New MacMillan Co., 1927, pp. 588.  k5.  Travers, R.M.W., " S i g n i f i c a n t research on the prediction of academic success," i n Donahue, W.T., et a l , The Measurement of Student Adjustment and Achievement, Ann Arbor, Michigan, University of Michigan Press, 19k9, pp. Ik7-190.  k6.  T r i b i l c o c k , W.E., "Many of the 'Lowest Third' of our graduates are college material," Clearing House. v o l . 12,  "Predicting success i n college: a study of various c r i t e r i a , " Journal of Educational Psychology, v o l . 28, 1937, PP. k65-k75.  "Value of rank i n high school graduating class for predicting freshman scholarship," Journal of the American Association of College Registrars, v o l . 15. 19^9. DP. 5-22.  1938,  k7.  Wagner, M.E.,  York,  pp. 5kk-5k6.  "A survey of the l i t e r a t u r e on college performance prediction," i n Studies i n A r t i c u l a t i o n of High School and College. University of Buffalo Studies, v o l . 9, 193k, pp. 19k-209.  7k  Wallace, R.T., The Effectiveness of the Methods of Selection for Admission to V i c t o r i a College* unpublished Master's thesis, University of B r i t i s h Columbia B r i t i s h Columbia, 19^7, pp. 91. Weintraub, R.G., and S a l l e y , R.E., "Graduating prospects of an entering freshman."^Journal of Educational Research, v o l . 39, 19*+5, PP» 116-126. Welch, B.L., "The generalization of 'Student's' problem when several d i f f e r e n t population variances are involved," Biometrika. v o l . 3k, 19k7, pp. 28-35. Wert, J.E., Neidt, CO., and Ahmann, J.S., S t a t i s t i c a l Methods i n Educational and Psychological Research, New York, Appleton-Century-Crofts, Inc. I9i?k, pp. k35.  APPENDIX A Sample of Card Used f o r Gathering Data  1.  Name 2.  Magee (A)  3.  Ma., Sc., Eng,  h.  Eng. ho Eng. 91 Ma. 91 Chem.91 Phys.91 Co. 10  R e g i s t r a t i o n No,  C C  57% 61%  C+ 59$ C  5.  C  6.  59%  7. 8.  1957  N.R. (3) S.R.  9.  Fail  1.  Year grade twelve completed  2.  School attended (A - Accredited, N.A. - not accredited)  3.  Majors completed  k.  Subjects taken i n grade twelve and marks  5.  Letter grade average  6.  Percentage average  7.  Scholarship (S.S.), Recommended (R) or Not Recommended (N.R.) and number of Departmentals written  8.  Supplementals written and/or subjects repeated (S.R.)  9.  F i r s t Year University Standing i n A p r i l .  76 APPENDIX B 2.  Sample of Kimball's Method f o r the P a r t i t i o n of Chi-Square, 3 by 3 Contingency Table*  High School Letter Grade Average  F i r s t Year University Standing F u l l Credit  Supp.  176  A, B  x  (b ) x  Totals  (a )  (A)  (b )  (b )  78  273  62  3  2  (B)  3  (c^  (c )  ihO <c >  219  • 29h  207  236  737  17  C, C-, E  (a ) 2  101  Totals  18  51  (a )  C+  No Credit  2  (n )  (n )  2  2  ABn2n  2  (N)  3  Chi-Square (1) = N[B(n a-|_ - n-ja ) - k{n h 2  (C)  3  2  -  1  n ] L  b )]  2  2  (A+B) (n +n ) x  2  = 737 [273(207x176 - 29^x51) - 2>+5( 207x101 - 29^x9^)3 (2*+5) (273) (29^) (207) (2^5+273) (29^+207)  2  = 39.26 Chi-Square (2) = N [ b ( a + a ) - a ( b - + b ) ] 2  3  ABn  1  3  2  3  L  2  2  (A+B) (n^ng)  = 737) [78(176+5D - 18(101+9^)] (2*+5) (273) (236) (2U,5+273) (29^+207) = 26.72 2  »  Reproduction of Table I I I , p. 32.  2  Chi-Square (3) = N [c (a +l3 ) - c ( a + b ) ] 2  2  1  1  1  2  2  2  Cn^CA+B) (n^rig) = (737)  2  [62(176+101) - 17(51+9*+)]  2  (219) (29k) (207) (2^5+273) (29^+207) = 33.98 Chi-Square (*f) = N [c^a-j+ag+b-j+b^ - U^+b^) ( c + c ) ] 1  2  2  Cn^ (A+B) (n-j+n ) 2  = 737 [1^0(176+51+101+9^)  - (18+78) (17+62)]  (219) (236) (2^5+273) (29^+207) = 1^-5.71  2  2.  Sample of Kimball's Method f o r the P a r t i t i o n of Chi-Square, 2 by 5 Contingency Table*  F i r s t Year University Standing Grade 12 Standing Recommended  First Class  Second Class  33  (a )  x  Not Recommended  0  58  k2k  (a )  18  ?  (A)  (b )  (b )  (bi,)  81  166  27k  iko  10k  197  22k  698  2  (»2?  Totals  (ak)  3  9  (b )  No Credit  116  (a )  2  x  Totals  86  131  (a )  Supp.  Pass  3  (n )  (n )  Chi-Square (1) = N [ a b 2  1  2  - a bi]  (n )  (i%)  3  2  (be;)  5  2  2  AB n^^ri-j+r^)  = (698J [33x9 - 131x0] 2  2  (k2k) (27k) (33) (IkO) (33+lkO) = .k6 Chi-Square (2) = N  2  [b (aj+a ) - a ( b + b ) ] 3  2  3  1  2  2  ABn (n +n ) ( n j + n ^ n^) 3  =  1  2  Cl8(33+13D - 86(0+9)] (k2k) (27k) (10k) (173) (277)  i 6 9 Q ) 2  = 3.99  x  Reproduction of Table XII, p. k5  2  (B)  CH)  79 Chi-Square (3) = N  2  Cbi .(a +a +a3) - Ai+Cb +b +b3)3  2  f  1  2  1  2  ABn^Cn-f^+n^) (n-j+n + n^+n^) 2  = (698) [81(33+131+86) - ll6(0+9+l8)] 2  2  (h2h) (2?h) (197) (33+1^+lOM-) (33+1^0+10^+197)  - = »+7.5l Chi-Square (h) = N  2  [b^(a +a +a +ai ) - a^b-j+b^b^+b^.) ] 1  2  3  f  ABn^n^+n^n^+nL,.) (nj+n + n^+n^+n^) 2  = (698) [166(366) 2  (h2h) (27^) (221+) = 168.03  58(108)]  (^l,.)  2  (698)  2  

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