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The prediction of university freshman performance on the basis of high school achievement in British.. 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 this 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 relationship at the University of B r i t i s h Columbia between high school achieve- ment, as represented by grade twelve results, and university per- formance, as represented by f i r s t year standing. The aim of the work was to provide counsellors, both at the University of Bri t i s h Columbia and in the secondary schools of this province with pre- dictive information for use i n counselling. The high school variables used were letter grade aver- age, percentage average, standing at f i r s t attempt, recommendation, number of Departmental examinations written, and major subjects taken. The criterion of university performance used was f i r s t \ year standing in 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 chosen had completed their f i n a l year i n a public high school i n Bri t i s h Columbia, were not repeating any f i r s t year uni- versity courses, and had had an uninterrupted secondary education. They had registered for at least fifteen units of course work, which included English 100-101, Mathematics 100 or 101, a foreign language, a science, and an elective. Results of this 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 this study was reviewed. By use of the Chi-Square technique and of a method of partitioning Chi-Square, i t was determined whether the difference in freshman performance was significant among the students grouped according to the various high school variables, and where the d i f - ference lay. Contingency coefficients were calculated to show the degree of relationship between the variables and the criterion. Most of the results of the investigation were i n agree- ment with those reported by other authors who had conducted simi- lar studies. It was found that there i s a high positive relation- ship between freshman standing and grade twelve average, whether letter grade or percentage, that students who complete University Entrance standing at f i r s t attempt perform at a higher level at university than students who are required to make more than one attempt, that recommended students are better academic risks 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. Contrary to most studies, and agreeing rather with the exceptions, i t was found that there is some relationship between major subjects taken i n high school and freshman standing. Stu- dents who have included i n their high school programmes Mathe- matics, Science, English, and Social Studies as majors are less l i k e l y to f a i l at university than students who take Mathematics and Science majors but omit English and Social Studies majors. Students who have taken a high school foreigh language major are more successful i n f i r s t year university than those who omit a foreign language major. A word of caution was included regarding the impossi- b i l i t y of perfect prediction for a l l students owing to the unre- l i a b i l i t y of marks, to individual differences, and to personal problems, adjustment and growth. Within the specified limitations of the results, the study indicated that high school achievement could be used effectively i n prediction of performance at univer- sit y . A number of suggestions for further study were mentioned, the most strongly recommended of which were a study of the possi- b i l i t y of using a prediction formula including both high school achievement records and aptitude test results, and an investiga- tion of capable students who do not proceed to university. In presenting 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 the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that 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 reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e . 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 f i n a n c i a l g a i n s h a l l not be allowed, without my w r i t t e n permission. Department of The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date ACKNOWLEDGEMENTS The writer wishes to express her sincere appreciation to Mr. J.F. McLean, Director of Student and Personnel Services, for making i t possible to conduct this study; to Mr. J.E.A. Parnall, Registrar, for permission to use high school transcripts; to 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 concerning s t a t i s t i c a l technique. For guidance and encouragement received during the entire investigation, the writer i s sin- cerely grateful to Dr. H.L. Stein, Supervisor of Graduate Studies, Faculty of Education. TABLE OF CONTENTS CHAPTER ?AGE I INTRODUCTION AND BACKGROUND OF THE PROBLEM 1 A The Problem and Justification for Investigation • 1 1 . General 1 2 . Specific 1 B Definition of Students Used i n Study 5 C Sources of Data 6 D Assumptions 6 E Limitations of Study 7 II REVIEW OF THE LITERATURE 10 A Introduction 10 B High School Marks, Average and Rank 11 C Recommendations •• 16 D High School Repeaters • 18 E High School Subjects 19 F R e l i a b i l i t y of Criteria 19 G Conclusions • 20 III METHODS OF INVESTIGATION 22 A Data Gathering Techniques • 22 1 . High School Records 22 2 . University Standing 2k B S t a t i s t i c a l Methods 25 1 . Averages and Standing at First Attempt 25 2 . Accreditation 26 3 . Majors 27 i i CHAPTER PAGE IV ANALYSIS OP THE DATA 29 A Averages and Standing at First Attempt 29 1. Letter Grade Average 29 2. Percentage Average 3^ 3. Standing at Fi r s t Attempt 39 B Accreditati.on h-2 1. Recommended and Non-Recommended Students *+5 2. Number of Departmental Examinations Written . **7 3 . Majors ., 51 V CONCLUSIONS, IMPLICATIONS AND RECOMMENDATIONS FOR FURTHER STUDY ... 60 A Conclusions 60 1* General 60 2. Specific 60 B Implications 63 C Recommendations for Further Study ........... 65 VI SUMMARY OF THE PRESENT STUDY 67 BIBLIOGRAPHY 70 APPENDIX A 75 APPENDIX B 76 i i i LIST OF TABLES TABLE PAGE I Frequencies of University Freshman Standing Based on Letter Grade Average 29 II Frequencies (Percentages in Parentheses) of University Freshman Standing Based on High School Letter Grade Average (Small Frequencies Combined) 30 III Frequencies of University Freshman Standing Based oni:High School Letter Grade Average (Reduced to 3 by 3 Contingency Table) 32 IV Frequencies of University Freshman Standing Based on High School Percentage Average Resulting From Departmental Examinations 3*+ V Frequencies (Percentages in-Parentheses) of University Freshman Standing Based on High School Percentage Average (Small Frequencies Combined) . 35 VI Frequencies of University Freshman Standing Based on High School Percentage Average (Reduced to 3 by 3 Contingency Table) 36 VII Departmental Examination Means and Standard Devi- ations of Students Grouped According to F i r s t Year University Standing 38 VIII Frequencies of University Freshman Standing Based on First Attempt and on Repetition *+0 . IX Frequencies (Percentages i n Parentheses) of University Freshman Standing Based on First Attempt and on Repetition (Small Frequencies Combined) M-O X Frequencies of University Freshman Standing Based on Grade Twelve Status with Respect to Accreditation *+3 XI Frequencies (Percentages in Parentheses) of University Freshman Standing Based on Grade Twelve Status with Respect to Accreditation (Small Frequencies Combined) ^ iv TABLE PAGE XII Frequencies (Percentages i n Parentheses) of University Freshman Standing Based on Recommen- dation and Non-Recommendation (Small Frequencies Combined) h5 XIII Frequencies of University Freshman Standing Based on Number of Departmental Examinations Written .. h8 XIV Frequencies (Percentages in Parentheses) of University Freshman Standing Based on Number of Departmental Examinations Written (Small Frequencies Combined) ^9 XV Frequencies of University Freshman Standing Based on High School Majors , • 52 XVI Frequencies (Percentages i n Parentheses) of University Freshman Standing Based on Majors (Small Frequencies Combined) 53 XVII Frequencies of University Freshman Standing Based on High School Majors (Reduced to 3 by 3 Contingency Table) 5̂ XVIII Frequencies of University Freshman Standing Based on Having a High School Foreign Language Major and not Having One 56 XLX 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 Justification for Investigation 1. General This study i s an investigation of the relationship be- tween achievement i n high school and performance at university, i n order to determine how well university success can be predicted from high school records. Grade twelve records were used to represent high school achievement because i t is in grade twelve that the f i n a l require- ments for university entrance are completed. In view of the com- paratively high failure 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 university 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 uni- versity i s a costly and unprofitable proposition from the taxpayer' point of view. A t t r i t i o n presents a problem for the administrators making i t d i f f i c u l t to budget accurately. From the individual student's point of view i t is not only costly and time consuming but also distressing to f a i l . Scientific and industrial progress has led to a society which demands more training i n both technical and social s k i l l s . 2 The revolution which has taken place as a result 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 university. University attendance i s no longer the privilege of the few. According to Conway and Brown ( 1 ^ ) , the percentage of students i n Bri t i s h Columbia remaining i n school to the beginning of grade twelve has increased from 35 P©£ cent in 19^7 to **5 per cent i n 1 9 5 6 . Approximately two-thirds of the grade twelve students are enrolled in the university programme. With a failure rate of 15 per cent i n grade twelve, i t i s easily seen that 25 per cent of the original f i r s t grade population ultimately obtain university entrance. As a t t r i t i o n decreases, a change i n standards i s Inevi- tably the result; university candidates are drawn from a poorer group. Are a l l of these candidates capable of university work? The failure rate in f i r s t year suggests that many students are entering university who do not profit from the opportunities offered. The c r i t i c a l aspect of the situation i s that these students have, nevertheless, successfully completed the university entrance requirements. Are there, then, borderline cases who should be d i s - couraged from going to university where they must compete with more and better students? If so, where i s the line to be drawn between poor students and potentially successful ones? Criticism abounds. Some c r i t i c s suggest raising admission requirements, sifting the applicants and rejecting the unfit. The opposing theory i s to permit a l l to enter university where the pro- 3 grammes offered would be broadened to suit various levels of ab i l i t y i n the same way as secondary curricula have been broadened in recent years. There are c r i t i c s also of the system of accreditation i n this province. They advocate that standardized entrance examina- tions be written by a l l those who wish to enter university. Others fe e l that "recommendation11 i s an adequate means of selection. The main justification for this study l i e s however, not in administrative decisions but i n the practical and functional aspects connected with individual counselling. Teachers and coun- sellors, both in the secondary school and at the university are better equipped to guide students i f they have some factual and s t a t i s t i c a l evidence. A counsellor may be satisfied with his pre- diction of a particular student's success but he must be able to impress facts on the student and perhaps the parents. There are two sides to this problem. One i s the i n s i s - tence of a student on going to university when he has l i t t l e or no chance for success; the other is the hesitancy of a capable youth who could profit from further education but who lacks confidence to attempt university work. To counsel effectively, 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 en- couraging the student to develop his academic potentialities by proceeding to university, i t i s necessary to have objective evidence. How can this evidence be obtained, How and how well can success be predicted? Is the high school record a good predictor? If Specifically, 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 their grade twelve letter 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 their 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 to 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 differ 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 relationship between the number of Departmen- t a l examinations that a student i s required to write and his 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 Social Studies; ( 2 ) Including English and Social Studies but excluding Mathematics and Science; (3) including Mathematics, Science, English and Social Studies; 5 (*+) a l l other combinations of subjects, (g) Is there a difference in f i r s t year performance between students who had a foreign language major i n high school and those who did not? B Definition of Students Used i n Study To eliminate extraneous variables and i n order to obtain as homogeneous a group as possible, certain 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 1957-58 session. Freshman in other faculties were excluded. Of the 1883 students i n f i r s t year of Arts and Science, 737 were chosen according to the follow- ing factors. Only the students who had an uninterrupted education were considered. Students who were out of school for a year or more after completing grade twelve were excluded. Likewise ex- cluded were students who l e f t school prior to completing grade twelve, returning later to complete high school. Those, however, who took grade twelve i n 1955-56 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 matricula- tion 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 their f i n a l year were considered. No students who were repeating f i r s t year Arts, or a part thereof, whether taken previously at U.B.C., Victoria College, or 6 as Senior Matriculation, were included. Only the students who registered for at least fifteen units were included. The course taken included English 100 - 1 0 1 , Mathematics 100 or 1 0 1 , a foreign language, a science, and an elective, whether an additional science or a non-science. C Sources of Data The delimiting factors were found on students' Registra- tion cards. A l i s t of accredited schools was kindly supplied by Mr. H.M. Evans, Department of Education, Victoria. 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 transcripts, averages were computed. Students' f i r s t year standing, as determined by Ap r i l results were obtained from the Registrar's Office. Counselling f i l e s were used as a supplement when neces- sary, and c i t y schools were contacted about questionable cases. D Assumptions The v a l i d i t y of this study depends on the c r i t e r i a used. In this connection i t was necessary to make a number of assump- tions . It was necessary to assume that the criterion of letter grades i s a reliable one} that i s , that the same letter grades from different 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 letter grades i s strongly suggested by the Department of Education and since most schools apparently conform to this pattern, the assumption has some justi f i c a t i o n . In addition to the use of letter grade averages, per- centage averages from Departmental examinations were used with the assumption that they would provide a more reliable criterion. 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 Edu- cation reportedly makes the results more reliable. Conway ( 1 3 ) and Conway and Brown (Ih) give a detailed account of the methods employed in scaling. It was also necessary to assume that the marking of exam- inations at university and therefore the f i n a l standing i s re 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 for 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 Departmen- t a l examinations were high, wrote a l l examinations i n order to be eligible to win a scholarship. In order to define "high", 65 per cent average or better was used. The cases i n which a student was required to write perhaps one examination and wrote the rest for scholarship purposes, or for practice, would be too few to contam- inate the data s u f f i c i e n t l y to invalidate i t . 8 Because i t was impossible to contact each student or each school, i t was assumed that, aside from the students who wrote Departmental examinations for scholarship purposes, the stu- dents who wrote one examination or more did so because their work during the year was below a MC M level and they were therefore not recommended. 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 is required to write an examination, or exam- inations, for disciplinary reasons. On occasion, too, a student i s required to write because of poor attendance. Schools vary i n their regulations regarding required attendance. Since i t was im- possible to determine and eliminate a l l of these cases, the assump- tions 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 individual students by telephone and letter • E Limitations of Study The results, that i s , the predictive value of this thesis, can apply only to f i r s t year Arts and Science students whose high school background and programmes at university are comparable to those of the students used as the sample i n this study as defined earlier. It i s recognized that f i r s t year performance i s not per- fectly representative of academic success or fa i l u r e . It i s l i k e l y 9 that some students of limited academic a b i l i t y might satisfactorily complete f i r s t year but due to the effort 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 validity of the results 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 earlier, for the purposes of this study this r e l i a b i l i t y is assumed. It i s , however, questionable. In individual counselling, knowledge of high school back- ground alone i s not sufficient to predict success. It should be considered together with an evaluation of aptitude test results, of the kind used by the University of Brit i s h Columbia Counselling Department, and with,other data supplied by the student about him- self. CHAPTER II REVIEW OF LITERATURE A Introduction The investigation of academic prediction i s one of the most popular of educational studies. The number of journal ar- ti c l e s and books on the subject i s very large, especially since the 1 9 3 0 1s during which time there was an increased interest i n these matters. The subject has been studied with various methods and from various points of view. Investigations include predic- tion with such variables as high school performance, standard achievement tests, intelligence as measured by a single test or a battery of tests, social and economic data, personal data, i n - terest and motivation, and combinations of variables. Studies show that i t i s impossible to predict perfectly the achievement of a l l entrants, and that there are cases of suc- cess or failure that cannot be discovered u n t i l the student has tried to do university work. As Trlbilcock (M-6,p.5*+6) says; "While i t i s wasteful and otherwise undesirable to have the unfit in college, i t i s also wasteful and otherwise undesirable to keep the f i t out of college. For many students there i s no adequate test of fitness except the actual attempt to carry college work." However, there i s no doubt that i t i s an advantage to both the uni- versity and the students to evaluate as accurately as possible the students 1 chances of success or failure i n university work. Much work has been done on the evaluation of the efficiency of high school performance as a predictor of university success. One 11 of the arguments i n favour of using such a predictor is that i t is an economical one. The administration of intelligence and ap- titude tests i s comparatively costly. High school records are relatively easily obtainable; they require a minimum of time, ef- fort and expense to put into practical use. Above a l l , i t i s generally agreed by authors i n the f i e l d that high school perfor- mance is the best single criterion of university success. Whether used alone, or combined with other variables, such as academic ap- titude test results to give a more sensitive method of prediction, high school performance should always be considered i n prognosis. The reason for the efficiency of high school marks i n prediction i s aptly explained by Travers (*+5» p.155) . "The value of high school grades for predictive pur- poses i s undoubtedly a result of the fact that they represent a combination of a b i l i t y and motivational factors operating in much the same way as they w i l l operate i n college. The advantages of these circum- stances seem to outweigh the factors that tend to reduce the valid 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 sig- nificant. They are also the easiest for 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 a b i l i t y . " 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 tests, concluded that, although multiple correlations prove more efficient, the most efficient single predictor of success at uni- versity 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 test. Using various combinations of the variables, they found that the combinations containing high school rank were more effective than any other combination, and that the best single variable for prediction was high school rank. Emme ( 2 2 ) , i n his review of studies carried out i n the late 1930*s concluded from his data that the best method of fore- casting college success is to use a formula including a combina- tion of variables but that the best single criterion i s rank i n high school graduating class. Similarly, Harris ( 2 8 ) , i n his review, concluded that although a combination of intelligence rating and high school achievement gives a higher correlation with college marks than either alone, high school grades alone show a higher correlation than intelligence rating alone. Froelich (25)» 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 intelligence rating increases the predictive efficiency of any single index, but that high school rank i s the best single criterion for predicting university success. Combinations produced multiple correlation coefficients approaching . 7 0 . High school rank alone yielded coefficients be- tween . 5 0 and . 6 0 . Byrns (10), divided students into four groups according to their position i n high school and compared them with their av- erage grades i n f i r s t year college. She then reversed this pro- cess, dividing freshmen into four groups according to college achievement and compared them with their 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 for students who rank low in high school to rank low i n college. 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 level i n college, one can there- fore be more certain that low high school average guarantees c o l - lege failure than good high school average guarantees college suc- cess . Dearborn (18,p. 192), as early as 1909* concluded that "If a pupil has stood i n the f i r s t quarter of a large class through high school, the chances are four out of five 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 five that the student••.who has been i n the lowest quarter of his class w i l l rise 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 university are slim indeed." Forty years later, in 19*+9 Dearborn said "...rank i n school per- formance i s s t i l l one of the best c r i t e r i a for predicting success in college." Ik Adams ( 1) , Schmitz (39), Weintraub and Salley (^9), Samenfeld (37), and Frederickson and Schrader (2*f), i n their sep- arate studies a l l agreed that high school achievement i s the most efficient single instrument for predicting university performance. Canadian studies on this subject are few, but they agree with the American findings. The Alberta Progress Report (2,p.6*)> concluded, "The findings so far indicate that the best single pre- dictor of success at the University of Alberta i s the grade twelve average." They found a higher correlation between high school average and university average (r=.56) than between high school average and scholastic a b i l i t y tests (r = A 7 ) . 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 definitely higher averages than others. The study has not yet progressed sufficiently far 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 results and average marks at Victoria 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. 3 6 Very l i k e l y some of the university entrance candidates who failed could, i f given the opportunity, pass f i r s t year at Victoria College." » This i s a much higher passing rate than found i n the present study. 15 Authors i n this area show that there i s a significant positive correlation between high school average and college standing. Garrett (27>p .93)j concluded that, "Among a l l the fac- tors contributing to production of scholastic success i n college, the student's average grade i n high school continues to show the highest correlation with later college scholarship average." In examining thirty-two coefficients of correlation he found that they ranged from .29 to . 8 3 . Similarly, Wagner (*+7)> i n his sur- vey of forty-seven investigations, including two of his own, found correlation coefficients ranging from . 2 8 to . 8 6 . Seyler (*+0) calculated a correlation 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 Stovall ( 5 ) » came to the conclusion that although there is a positive correlation between high school and college marks, the correlation is so low that high school i n - dex i s not a very reliable criterion for selecting college stu- dents. Since they also concluded that marks differed in meaning from one high school to another, particularly with respect to size of school, i t may be that Puerto Rico is particularly 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 is no relation between standard of University Entrance examinations and standard of f i r s t year University results. 16 The art i c l e reported that causes of failure are discoverable only in university. Since this is just a newspaper a r t i c l e , and the quotation may be taken out of context, i t is d i f f i c u l t to appraise it s r e l i a b i l i t y . C Rec ommendations With regard to 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 university of recommended and non-recommended students as de- fined i n this province. Brown and Nemzek ( 8 ) , however, in a system f a i r l y similar to the one used i n this 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 valid for group d i f - ferentiation, i t i s not satisfactory for individual purposes. The authors feel that the numbers of those recommended who are not suc- cessful and of those not recommended who are successful are so large that i f this system is to be used as a method of selection, i t should be examined for improvement. In the local study mentioned earlier, Wallace (M^p.Sl) stated that the accreditation system i n this province is a satis- factory one for selecting students capable of doing college work. He found that; ( 1 ) "If a student i s recommended by an accredited school i n five or a l l six of the compulsory university entrance subjects, his chances of passing f i r s t year at Victoria College are 98*+ i n one thousand." !7 (2) "If a student i s recommended i n four of the com- pulsory university entrance subjects, and has to write the other two, his chances of passing f i r s t year are 865 i n one thousand." (3) "If a student i s recommended i n three of the com- pulsory university entrance subjects and has to 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 partially a subjective evaluation. In this 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 Arizona. The rating sheets included thirteen 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 to do independent work, a b i l i t y to budget time, adaptability, social maturity, cultural background and health. At the bottom of the sheet was included a request for an estimate of the pupils' probable success in college. An ari t h - metic average of a l l rating was calculated and then correlated with f i r s t semester marks at college. The authors found a correlation x The very high passing rate of recommended students reported by Wallace i s at least i n part due to a different recommendation policy. 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 for recommendation has been lowered to C. 18 coefficient 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 correlation so l i t t l e that i t did not justify the added effort or expense. D High School Repeaters L i t t l e work has been done on high school repeaters and their success at college. It i s believed by some educators that a student gains by repeating high school courses because the review involved results i n a better foundation for subsequent university work. Sarbaugh (38,p.l78) discovered that analysis of data re- garding repeaters negated this possibility. "It appears, then, that not only do enforced repetitions of high school courses re- flect an absence of college aptitude as measured by the ACE and a lower level of high school achievement as indicated by Regents average, but they also tend to presage inferior achievement on the college level." Coffield and Blommers (12) investigated this 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 repetition. In qualifying their conclusion they stated that a slow learner who repeats eventually does no better than an equally slow learner who does not repeat. Although this conclusion was 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 O year of secondary school. • o 19 E High School Subjects It i s a common practice among universities to demand the fulfillment of certain subject requirements by their entrants. The majority of studies dealing with the relationship between sub- jects taken i n high school and performance at university add up to the conclusion as stated by Harris ( 2 8 ) , that no subject or com- bination of subjects has any noticeable bearing on college perfor- mance. Douglass ( 1 9 ) , Rogers ( 3 5 ) , and Sorenson (*+2), i n their separate studies concluded that a pattern of subjects taken i n high school bears no relationship to university success. According to Darley ( 1 7 ) , patterns of high school subjects are less valid as predictors: of college achievement than high school achievement and a measure of a b i l i t y . Garrett ( 2 7 ) concluded that the belief that any particu- lar pattern of secondary school subjects, especially foreign lan- guage, influences college success has been repudiated by most studies. However, there are a few exceptions. For example, Ross ( 3 6 ) found a correlation between college grades and the number of social or natural science units taken i n high school. Ferguson ( 2 3 ) found a positive relationship for Latin and a negative one for His- tory. Bovee and Froehlich ( 6 ) found a relationship between the number of language units i n high school and grades i n college. F R e l i a b i l i t y of Criteria How much dependence can be placed on marks or letter grades as criteria? Crawford and Burnhams ( 15 ,p.65) voiced their 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.l+26) agreed that college marks must be made more reliable i f prediction i s to be improved. Bou and Stovall (5) offered the criticism that an A or B i n one school i s not necessarily equivalent to an A or B i n another school. Brigham1s statement (7»P»57) is relevant here: "I think that everyone who has worked i n this f i e l d i s becoming tired of assuming that the criterion - the college - i s i n f a l l i b l e and that the sources of evi- 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 faulty that a perfect instrument of prediction could not correlate higher than .kO or .50 with the college result." G Conclusions In summary, i t i s found that the most efficient method of predicting university success i s by the use of a prediction for- mula including a number of variables, one of which should be the high school average. High school average alone i s the best single predictor. Correlations between high school average and university performance are positive, ranging from .28 to .89. Accrediting high schools to permit them to recommend stu- dents capable of doing university work, is found to be a satisfac- tory system of selection. Repetition of high school courses suggests inferior uni- versity achievement. 21 It i s generally found that there i s no relationship be- tween pattern of subjects i n high school and college success. However, there are a number of exceptions, showing a certain amount of relationship. Scholastic c r i t e r i a are found to be somewhat unreliable, hampering effective predictions. CHAPTER III METHODS OF INVESTIGATION A Data Gathering Techniques The sample of 737 students were chosen on the basis of the delimiting factors stipulated earlier. A card was then made out for each student. On each card was recorded the following i n formation: (a) name and registration number (b) high school attended and whether accredited (c) majors taken in high school (d) subjects taken i n grade twelve and the mark for each (e) average letter 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 for scholarship e l i g i b i l i t y (g) whether supplemental written or subjects repeated (h) f i r s t year university standing i n Ap r i l A sample card i s shown i n Appendix A 1 . High-School Records A letter grade average was calculated from each student grade twelve mark. First attempt marks were used. In almost a l l cases these were June marks, whether i n letter grade form or per- centage form. If a student, however, took the course during the 23 summer or through correspondence, the f i r s t attempt mark recorded under August results was used. While most marks are i n letter grade form, many records include varying numbers of percentage marks which are results of Departmental examinations. The latter were converted to letter grades, using the Department of Education Scale: 8 6 - 1 0 0 = A 7 3 - 8 5 = B 6 6 - 7 2 = C+ 5 8 - 6 5 = C 5 0 - 5 7 = C- Failed = E To obtain over-all average, the following equivalents were used: A = 5 B = h C+ = 3 C = 2 C- = 1 E = 0 The closest letter grade average was used. Up to and including . 5 was counted as the lower letter 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. Practically a l l subjects are valued at five units of credit each. For English *+0, however, two marks are given, one for language and one for literature, constituting five units. A mean 2k of the two marks was calculated and this weighted mark was then pooled with the other marks to calculate the over-all average, whether i n terms of letter grade or percentage. In other cases, where two or three subjects i n one f i e l d , such as Industrial Arts, made up a total of five units of credit the same weighting tech- nique was used. However, because the cases i n which a student took just one subject carrying less than five units were too few to con- taminate the data, the mark for that subject was pooled with the rest without being weighted. In counting the number of Departmental examinations a stu- dent was required to write, English kO again presented a problem. However, because University Entrance standing i s not complete u n t i l both parts are passed, the writer decided to count i t as one Depar- tamental examination whether one part or both were written. Similarly, when determining whether a student was re- 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 results and i n terms of: (a) First Class Honours (80-100 per cent) (b) Second Class Honours (65-79 per cent) (c) Pass (50-6*+ per cent) (d) Supplemental (failure in one to six units of credit, whether or not marks sufficiently high i n those courses to write supplementals) 25 (e) Failure (failure in more than six units of credit, thus granted no credit) (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 their standing upon writing supplementals i n August. However, for the purposes of this 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 classified into groups according to grade twelve achievement and the groups were then compared i n terms of freshman standing. To determine whether any significant difference existed among the groups, Chi-Square technique was employed. As an extension, to explore further where the difference lay, Kimball's (29) formula for the partition of Chi-Square was used. An example of this method of partition i s shown in Appendix B. Contingency coefficients were calculated to determine the degree of relation- ship between the variables and the criterion. Specifically, Chi-Square, Kimball's partition of Chi- Square and contingency coefficients were calculated i n the following comparisons: 1. Averages and Standing at F i r s t Attempt (a) Groups based on letter grade averages, A, B, C+, C, C- and E were compared i n terms of f i r s t year standing. 26 (b) The students who wrote three or more Departmental examinations (i) because they attended non-accredited school, ( i i ) because they were not recommended although at- tending accredited schools, ( i i i ) because they wished to write for 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 80 to 9 ^ per cent Group 2 65 to 79 per cent Group 3 50 to 6 -̂ per cent Group k Below 50 per cent In this problem, i n addition to the use of the Chi-Square tech- nique, t-tests were used to test differences between means of adja- cent groups. (c) A l l students were classified as either (i) those who had a clear pass at f i r s t attempt through recommendation or by writing Depart- mental examinations, or ( i i ) those who were required to write one supple- mental or more and/or to repeat one subject or more. Their standing in 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 factors. If a school 27 is accredited, the principal and staff have the authority to re- commend students on the University Programme whose letter grade standing i n a given subject i s C or higher. Thus they are promo- ted 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 relation to f i r s t year standing. 3. Majors In order to obtain University Entrance standing i n B r i t i s h Columbia, students must obtain credit i n required courses: four years of English, three years of Social Studies, two years of general Science, two years of a foreign language and three years of Health and Personal Development. In addition, they must obtain credit i n at least seven optional courses, at least three of which must be taken at an advanced level, such as a f i f t h year of English, (English 91) or two additional years of a foreign language (91 and 92). Other possible advanced electives are Social Studies, Mathe- matics, Science, Commerce, Industrial Arts, Home Economics. These advanced electives are commonly called Majors. 28 (a) Students were grouped according to what majors they completed in high school: (i) those completing majors which included Mathe- matics and Science but excluded English and Social Studies, ( i i ) those completing majors which included English and Social Studies but excluded Mathematics and Science, ( i i i ) those completing English, Social 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 classified 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 detail the results of the s t a t i s t i - cal analysis. A Averages and Standing at Fi r s t Attempt 1. Letter Grade Average Considering high school letter grade averages f i r s t , Table I shows the distribution of these averages with correspond- ing f i r s t year university standing. TABLE I FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL LETTER GRADE AVERAGE Grade 12 Letter Grade Average First Class Second Class Pass Supp.Fail De- ferred With-Did not drew -V/rite Totals A 20 9 2 1 2 - 3k B 15 100 32 ^9 7 3 h 1 211 C+ 1 37 63 9*f 56 3 13 6 273 C 2 15 57 76 . 2 17 3 172 C- 5 29 6 3 **3 E 3 1 Totals 36 IhQ 110 207 171 9 ±3 13 737 x The four who failed at f i r s t attempt subsequently wrote supple- mentals or repeated subjects and obtained University Entrance Standing. Examination of this table alone would lead to the con- clusion that university standing i s not independent of high school letter grade average. In order to eliminate small frequencies, Table II 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 in high school. TABLE II FREQUENCIES (PERCENTAGES IN PARENTHESES) GF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL LETTER GRADE AVERAGE (SMALL FREQUENCIES -COMBINED) First Year University Standing Grade 12 Letter Grade Average First Class ( J O Second Class ( * ) Pass 0 0 . No Credit 0 0 Totals (%) A 20 ( 5 8 . 8 2 ) 9 (26.1+7) 2 ( 5 . 8 8 ) 3 ( 8 . 8 2 ) 3k ( ^ . 6 1 ) B 15 ( 7 . 11 ) 100 ( ^ 7 . 3 9 ) 32 ( 1 5 . 1 7 ) k-9 ( 2 3 . 2 2 ) 15 ( 7 . 1 1 ) 211 ( 2 8 . 6 3 ) C+ ( ^37) 37 ( 1 3 . 5 5 ) 63 (23.08) 9k ( 3 ^ 3 ) 78 ( 2 8 . 5 7 ) 273 (37.01+) C ( 1?16) 15 ( 8 . 7 2 ) 57 ( 3 3 . 1 * 0 98 ( 5 6 . 9 8 ) 172 (23.3*+) C-,E 5 (10.61+) 1+2 ( 8 9 . 3 6 ) k? ( 6 . 3 8 ) Totals 36 ( h.QQ) (20.08) 110 Q1+.92) 207 ( 2 8 . 0 9 ) 236 ( 3 2 . 0 2 ) 737 From this table i t can be seen that only about 1+0 per cent of the sample of students completed f i r s t year with f u l l cre- dit i n A p r i l , 28 per cent obtained partial credit, and 32 per cent obtained no credit. Of the students with A average, about 85 per 31 cent obtained f u l l credit, and this was done at honours level. Of the B students almost 70 per cent obtained f u l l credit; of the C+ students only about 37 per cent obtained f u l l credit. Less than nine per cent of the C students obtained f u l l credit, and none of the C- and E students did so. Less than ten per cent of the l a t - ter group obtained partial credit. These are but a few of the many comparisons that can be made from the table alone. A l l show a positive correlation, de- scriptively speaking, between high school letter 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 univer- sity standing i s independent of high school letter grade average, a Chi-Square of 528.1*+ with 16 degrees of freedom was calculated. This value i s very highly significant (P^ . 0 0 1 ) . The n u l l hypo- thesis was therefore rejected i n favour of the alternative hypo- thesis that there i s a difference among the groups i n a positive direction; that i s , that there i s a positive association between high school letter grade average and freshman standing. To ascer- tain the degree of relationship, a contingency coefficient was calculated, C = . 6 5 , which indicates a high correlation.* To eliminate the cells with small expected frequencies, S K and i n order to obtain a 3 by 3 table for the partition of Chi- Square, categories were combined further to produce Table III. x Maximum value of C i n a 5 by 5 table i s \89h ( 2 6 ,p.3 9 0 ) . SH In Table II there were two cells with expected frequencies of / less than 5 , and one c e l l with expected frequency of 5 . 0 7 . Although the majority of statisticians would not approve, according to Coch- ran ( 1 1 ) , the number of small cells is not out of proportion. 32 TABLE III FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL LETTER GRADE AVERAGE (REDUCED TO 3 BY 3 CONTINGENCY TABLE) Grade 12 Letter Grade Average F u l l Credit Supp. No Credit Totals A, B 176 51 18 2h$ C+ 101 9^ 78 273 C, C—j E 17 62 l*fO 219 Totals 29h 207 236 737 Combining categories caused some loss of power, reducing Chi-Square to 2 ^ 5 . 6 6 . The reduced value, with four degrees of free- dom, i s s t i l l very highly significant (P / . 0 0 1 ) . Partitioning the above Chi-Square into i t s components, values were calculated to 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 credit or just partial credit). Chi-Square ( 2 ) = 2 6 . 7 2 (difference between A, B group and C+ group i n terms of obtaining some credit or no credit at a l l ) . Chi-Square ( 3 ) = 33»98 (difference between A, B, C+ groups com- bined and C, C-, E groups combined i n terms of obtaining f u l l credit or just partial credit). Chi-Square (U-) = lk-5.71 (difference between A, B, C+ groups combined and C, C-, E groups combined in terms of obtaining t some credit or no credit at a l l ) . 33 Each single degree of freedom Chi-Square i s significant at .001 level of confidence indicating that each component contributed to making the total Chi-Square significant. Chi-Square (h) provided most of the contribution. Prom these statistics the following conclusions can be made. a. There is a significant 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 partial credit. b. There i s a significant 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 partial) or no credit at a l l . c. There is a significant difference, i n favour of the A, B, C+ groups combined, between the performance of this combined group and the C, C-, E groups combined in terms of obtaining f u l l credit or just partial credit. d. There i s a significant difference, i n favour of the A, B, C+ groups combined, between the performance of this combined group and that of the C, C-, E groups combined i n terms of obtaining some credit ( f u l l or partial) or no credit at a l l . More than half (about 59 per cent) of the total variation was contributed by this category. 3k 2 . Percentage Average Considering only the students who wrote three or more Departmental examinations, Table IV shows the distribution of the grouped percentage averages with corresponding f i r s t year univer- sity standing. TABLE IV FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL PERCENTAGE AVERAGE RE- SULTING FROM DEPARTMENTAL EXAMINATIONS Firs t Year University Standing Grade 12 Percentage First Second Pass Supp. F a i l De- With- Did not Totals Average Class Class ferred drew Write 8 0 - 9 1 $ 29 27 2 2 1 6 1 6 5 - 7 9 ^ 2 28 16 15 2 3 1 1 68 50-61$ 1 5 25 ^9 11 3 9** Below 50% 2 12 h 1 1 9 s Totals 31 56 23 63 3 17 5 2h2 H These students subsequently wrote supplementals or repeated sub- jects and obtained University Entrance standing. As before, observation of the table alone would lead one to conclude that there is a positive relationship between high school percentage average and freshman standing. In Table V the groups with no credit are combined, and the relative 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) Fir s t Year University Standing Grade 12 Percentage • Average First Class ( J O . Second Class ( 5 0 Pass ( 5 0 Supp. ( J O No Credit ( J O Totals ( J O 80-9k$ 29 (k7.5k) 27 (Mf.26) ( 3?28) (3.28) (1.6k ) 61 (25.21) 65-79$ ( 2?9k) 28 ( k l . l 8 ) 16 (23.53) 15 (22.06) 7 (10.29) 68 (28.10) 50-6U$ 1 ( 1.06) 5 ( 5.32) 25 (26.60) 63 (67.02) 9k (38.8k) Below 50$ (10*53) 17 (8if.if7) ( 7.85 Totals 31 56 23 88 2k2 (12.81) (23.1k) ( 9.50) (18.18) (36.36) About 95 per cent of the top group (80-9^$ average) ob- tained f u l l credit. Approximately 68 p er cent of the next group (65-79$ average) obtained f u l l credit; only about six per cent of the next group (50-6^$ average) did so, and none of the bottom group passed. St 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, is highly significant (P/.001) . A high degree of relationship i s shown by a contingency coefficient of .70. To eliminate cells with small expected frequencies,* and in order to obtain a 3 by 3 table for the partition of Chi-Square, H In Table V there were four cells with expected frequencies of less than 5. In view of this comparatively high proportion of small cells Chi-Square was computed with reservation. The follow-ing Chi-Square, with four degrees of freedom provides a more satis-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) Fir s t Year University Standing Grade 12 Percentage Average F u l l Credit Supp. No Credit Totals 8 0 - 9 ^ 58 2 1 6 1 65-79% ^6 15 7 68 Below 6% 6 27 80 113 Totals 110 88 2*+2 Loss of power was again evident. Chi-Square with four de- grees of freedom was calculated to be 1 6 0 . 2 9 . Nevertheless, this reduced value is s t i l l highly significant (P / . 0 0 1 ) . Partitioning this Chi-Square into i t s component single de- gree of freedom Chi-Squares, the following values were calculated: Chi-Square ( 1 ) = 1 1 . 1 8 (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 partial credit). 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 in terms of obtaining some credit 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 65 per cent i n terms of obtaining f u l l credit or just partial credit). 37 Chi-Square (h) = 1 0 9 . 3 7 (difference between students with averages of 65-9 1*- per cent and those with averages below 65 per cent in terms of obtaining some credit or no credit at a l l ) . One of these values, Chi-Square ( 2 ) , i s insignificant and contri- buted v i r t u a l l y nothing to the total variation. The other three are significant at . 0 0 1 level of confidence. Prom the foregoing statistics the following conclusions can be made. a. There i s a significant difference i n freshman stand- ing 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 credit or oust partial credit. This category contributed about seven per cent to the total variation. b. There i s no significant difference i n freshman stand- ing 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 credit ( f u l l or partial) or no credit at a l l . c. There i s a significant difference i n freshman stand- ing 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 credit or just partial credit. This category contributed about 25 per cent to the total variation. d. The most significant difference i n freshman stand- ing 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 credit ( f u l l or partial) or no credit at a l l . This category contri- buted about 68 per cent of the tot a l variation. 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 de- viations of the students grouped according to freshman standing. A steady decrease i n mean value is 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 12 De- partmental Exams Firs t Class Second Class Pass Supp. No Credit Mean 81+.68 78.1+1 6 9 . 7 8 6 3 . 0 7 5^.57 Standard Deviation > . 1 0 5 . 6 9 6 . 6 7 1 0 . 0 8 7 . 7 2 Number 31 56 23 ¥+ 88 Adjacent means were tested with t-tests , and the follow ing values were calculated: a. Between f i r s t and second class honours standing: t = 5.hO d.f. = 85 39 b. Between second class honours and pass standing: t = 5 . 8 2 d.f. = 77 c. Between pass and supplemental standing: t = 3 . 2 6 s d.f. = 5 5 . 7 d. Between supplemental and f a i l standing: t = 5 .^2 d.f. = 130 A l l t values but the third one are significant at . 0 0 1 level of confidence, and the third one i s significant at . 0 1 level of confi- dence. These results substantiate the preceding conclusion that freshman standing i s not independent of high school percentage average. 3 . Standing at First 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 supple- mentals and/or repeated grade twelve subjects, Table VIII shows their distribution 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 Fir s t Year University Standing Grade 12 Perfor- First Second De- With- Did not mance Class Class Pass Supp. F a i l ferred drew Write Totals Passed at Fir s t Attempt 36 1^8 109 198 133 8 28 9 669 Wrote Supps. and/or Re- peated Subjects 1 9 38 1 15 k 68 Totals 36 1^8 110 207 171 9 k3 13 737 In Table IX the groups with no credit have been combined and the relative proportions in 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) First Year University Standing Grade 12 Performance First Second Pass Supp. No Totals Class Class Credit (%) (%) (%) (%) (%) (%) at F i r s t 36 l*f8 109 198 178 669 Attempt ( 5 . 3 8 ) ( 2 2 . 1 2 ) (16.29) ( 2 9 . 6 0 ) ( 2 6 . 6 l ) ( 9 0 . 7 7 ) Wrote Supps. and/or Repeated 1 9 58 68 Subjects ( l . * f 7 ) (13>2*0 ( 8 5 . 2 9 ) ( 9 . 2 3 ) Totals 36 1^8 110 207 236 737 1+1 It i s interesting to note that of the tot a l sample of 737 students, only about nine per cent entered university after having had to make more than one attempt at passing a subject or subjects. Of this group of 68 students, only one student passed f i r s t year university. It 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 university. 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 is highly significant (P^.001), indicating that the two groups dif f e r i n freshman standing. The degree of relationship, C = .35* i s not as high as would be expec- ted due to the fact that only one of the categories contributed to the total variation, as i s seen below. In the partition of the tot 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 partial) or no credit at a l l . Its value, 97.67, i s about 97 per cent of the total variation and i s significant at .001 level of con- fidence. It was not possible to partition the tot a l further i n the usual manner in view of the cells with frequencies of zero and one.36 x Maximum values for C i n a rectangular table are not known (32,p.182), but are less than 1.00, as in square tables, approaching 1.00 only as the number of cells 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 university entrance standing i n the upper categories i s indicative of a difference in performance. 1+2 However, using Kimball's method in reverse, a Chi-Square of 53»88, significant at .001 level of confidence, was calculated i n com- paring the two groups i n terms of whether they obtained partial credit or no credit at a l l . It may be concluded that students who enter university with successful f i r s t attempts at completing university entrance standing obtain a higher freshman standing than those who are re- quired to write supplementals and/or to repeat subjects. B. Accreditation Table X shows the distribution, with corresponding univer- sity standing, of students who attended non-accredited schools, stu- dents who attended accredited schools and who were recommended i n a l l subjects and therefore did not write Departmental examinations, those who were recommended but wrote Departmental examinations for scholarship e l i g i b i l i t y , 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 F i r s t Year University Standing Status First Second De- With- Did not Class Class Pass Supp.Fail ferred drew Write Totals From Non- Accredited Schools Recommended, did not write Recommended, wrote for Scholarship Not Recom- mended 3 6 3 10 6 5 82 70 100 37 28 k9 16 16 2 9 18 8 1 125 2 3 3 8 2 30 1 8 32 309 115 27k Totals 36 l*f6 107 207 170 8 k 3 13 7 3 0 * x Total number has been reduced by seven students who wrote depart- mental for a variety of reasons other than the usual one and there- fore could not be fi t t e d into any of the categories i n the table. In Table XI the students obtaining no credit have been combined and the relative proportions i n terms of percentages are given. The proportion of students attending non-accredited schools was too small to perform any s t a t i s t i c a l analysis. However, i t can be seen that the proportions of these students i n the categories pertaining to university standing do not differ greatly from the to- t a l proportions. The proportion of f i r s t class standings i s some- what higher for the group from non-accredited schools, and the pro- portion of pass standings is somewhat lower, but the proportion of failures i s almost identical. The proportion of students from non- accredited schools obtaining f u l l credit 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 First Class First Year University Standing Pass Second Class ST No Credit Totals C D From Non- Accredited 3 6 3 10 10 32 Schools ( 9.37) (18.75) ( 9.37) (31.25) (31.25) ( *f.38) Recommended Did Not 5 82 70 100 52 309 Write ( 1.62) (26.5*0 (22.65) (32.36) (16.83) (̂ 2.33) Recommended Wrote for 28 *+9 16 16 6 115 Scholarship (2*+.35) (^2.6l) (13.91) (13.91) ( 5.22) (15.75) Not Recommended 9 18 81 166 27^ ( 3.28) ( 6.57) (29.56) (60.58) (37.53) Totals 36 lh6 107 207 23^ ( .̂93) (20.00) ( H K66) (28.36) (32.05) 730 As would be expected, the students who were recommended but wrote Departmental examinations for scholarship e l i g i b i l i t y were the best students at university. Of this group approximately 67 per cent were honours students; a total of over 80 per cent obtained k5 f u l l credit; only about lk per cent had supplemental and only about five per cent obtained-no credit. tions, but should be noted. Even the best students from high school f a i l sometimes and may have supplemental at university. Similarly, i t must be noted that about three per cent of the stu- dents who were not recommended achieved second class honours and about six per cent passed. These are small proportions, unques- tionably, but they do exist. 1. Recommended and Non-recommended Subjects In order to test the difference in 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) The latter 19 per cent might well be considered excep Grade 12 Standing F i r s t Year University Standing First Class Second Class Pass No Credit Totals Recommended 33 131 86 116 58 k2k ( 7.78) (30.90) (20.28) (27.36) (13.68) (60.7̂ 5) Not Recommended 9 18 81 166 27k ( 3.29) ( 6.57) (29.56) (60.58) (39.255) Totals 33 IkO 10lf 197 22k 698 _____ < k.73) (20.06) (1^.90) (28.22) (32.09) k6 This table alone shows that recommended students perform at a higher level at university. Almost 59 per cent of this group obtained f u l l credit, as contrasted with ten per cent of the non- recommended group. Less than lk per cent of the recommended group as opposed to over 60 per cent of the non-recommended group obtained no credit. Table XII with four degrees of freedom yielded a Chi-Square of 219.10, which is highly significant (P^.001), and a contingency coefficient of .*+9. The latter shows a positive and reasonably high correlation, i n spite of the lack of contribution of one of the categories as explained below. In the partition of Chi-Square, the following single de- gree of freedom Chi-Squares were calculated: Chi-Square (1) = ,k6* (difference between recommended and non- recommended 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 stand- ing) . Chi-Square (3) = **7«5l (difference between the two groups i n terms of obtaining f u l l credit or just partial credit). Chi-Square (k) = 168.03 (difference between the two groups i n terms of obtaining some credit or no credit at a l l ) . Chi-Square (1) is insignificant and contributed v i r t u a l l y nothing to the total variation. Chi-Square (2) i s significant but only at x Small c e l l frequencies are involved i n this Chi-Square .05 level of confidence, contributing only somewhat to the t o t a l . Chi-Square (3) i s significant (P^.001), contributing about 20 per cent to the total, and Chi-Square (*+) i s highly significant (P/.001), contributing about 76 per cent to the total variation. Thus i t may be concluded that recommended students achieve higher standing at university than do non-recommended stu- dents. That i s : a. There i s no significant 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 partial credit. d. Most of the difference i s i n terms of obtaining some credit ( f u l l or partial) 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 to write from one to six Departmental examinations. Table XIII gives the distribution of the number of Departmental examinations written with the relative university 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 Fir s t Year University Standing Departmentals Written First Class Second Class Pass Supp. F a i l De-ferred With-Did not drew Write Totals 1 9 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 6 1 2 1 Totals 9 18 81 125 3 30 8 27k In Table XIV categories are combined to eliminate small cells 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 university. Ap- proximately 52 per cent of the students writing one or two examin- ations failed to obtain any credit, while over 78 per cent of the students writing three or more examinations did so. RO- TABLE XIV FREQUENCIES (PERCENTAGES IN PARENTHESES,) OF UNIVERSITY FRESHMAN STANDING BASED ON NUMBER" OF DEPARTMENTAL EXAMINATIONS WRITTEN (SMALL FREQUENCIES COMBINED) Number of First Year University Standing Departmentals Written F u l l Credit (%) Supp. (%) No Credit {%) Totals (%) 1 21 hi 6h 126 (16.67) (32.5^) (50.79) (M-5.98) 2 if 23 31 58 ( 6.90) (39.65) (53A5) (21.17) 3 or more 2 17 71 90 ( 2.22) (18.89) (78.89) (32.85) Totals 27 ( 9.85) 81 (29.56) 166 (60.58) 2?h Table XIV with four degrees of freedom yielded a Chi- Square of 2*f.06 which is significant at.001 level of confidence. The contingency coefficient of .28 i s positive although not very high. However, i t s lack of magnitude may be explained by two pre- vailing conditions: 1. the range of the total group i s extremely restricted;* 2. two of the categories f a i l to contribute to the tot a l variation. In the partition of the total variation, the following single degree of freedom Chi-Squares were calculated: x A high correlation cannot be found i n a restricted range. Wert, Neidt and Ahmann (51,p.76). 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 partial credit). 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 partial credit). 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 cre- dit at a l l ) . Chi-Square (1) is significant at .05 level of confidence and con- tributed about 18 per cent to the total variation. Chi-Squares (2) and (3) are not significant, while Chi-Square (h) i s significant at .001 level 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 is 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 is in favour of the students who wrote just one. (b) There is no difference between the same two groups in terms of obtaining some credit ( f u l l or partial) 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 in terms of obtaining f u l l or partial credit. (d) The greatest variation 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 credit ( f u l l or partial) or no credit at a l l . The difference is in favour of those who wrote fewer Departmental examinations. C. Majors Table XV shows the distribution of the students talcing various combinations of major subjects with their relative f i r s t year standing. 52 TABLE XV FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL MAJORS High School F i r s t Year University Standing Majors Fi r s t Second De- With Did not Class Glass Pass Supp.Fail ferred drew Write Totals Ma., Sc., Eng., Soc. St. 18 h 2 21 kQ 25 3 5 1 163 Ma., Sc. h 20 22 38 *+6 1 V? 3 151 Eng., Soc. St. 2 h 2 3 3 1 15 A l l other Combin- ations 12 82 65 118 97 5 20 9 H08 Totals 36 IkQ 110 207 171 9 3̂ 13 737 It was the writer's intention, among other comparisons, to compare the freshman standing of the students who took Mathe- matics and Science as majors butwho omitted English and Social Studies from their programmes with the students who took English and Social Studies as majors but who omitted Mathematics and Sci- ence. Owing to the small number of the latter the idea was aban- doned. This group is 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 relative proportions are given in terms of percentages. TABLE XVI FREQUENCIES (PERCENTAGES IN PARENTHESES) OF UNIVERSITY FRESHMAN STANDING BASED ON MAJORS (SMALL FREQUENCIES COMBINED) High School F i r s t Year University Standing Majors First Second Pass Supp. No Totals Class Class Credit ( J O ( J O ( J O 0 0 ( J O ( J O Ma., Sc., Eng., Soc. St. 18 (11.0k) k2 (25.77) 21 (12.88) k8 (29 M) 3k (20.86) 163 (22.12) Ma., Sc. k ( 2.65) 20 (13.2k) 22 (lk.57) (25.16) 67 (Mf.37) 151 (20.^9) A l l other Combin- ations lk ( 3.3D 86 (20.33) 67 (15.W 121 (28.60) (31.91) k23 (57.39) Totals 36 1̂ 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 Social Studies as majors. Table XVI, with eight degrees of freedom yielded a Chi- Square of 37.3k, which i s significant at .001 level of confidence and a contingency coefficient of .22, showing a positive corre- lation, 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, yielding a reduced Chi-Square of 21.l+6 which, neverthe- less, is s t i l l significant at .001 level of confidence. TABLE XVII FREQUENCIES OF UNIVERSITY FRESHMAN STANDING BASED ON HIGH SCHOOL MAJORS (REDUCED TO A 3 BY 3 CONTINGENCY TABLE) High School First Year University Standing Majors F u l l No Credit Supp. Credit Totals Ma., Sc., Eng., Soc.St. 81 - 8̂ 3>+ 163 Ma., Sc. if6 38 67 151 A l l other Combinations 167 121 135 *+23 Totals 29*+ 207 236 737 In the partition of the latter Chi-Square the following single degree of freedom Chi-Squares were calculated: Chi-Square (1) = l.hO (difference between students with Eng- l i s h , Social 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 partial credit). Chi-Square (2) = 19.91 (difference between students with Eng- l i s h , Social Studies, Mathematics and Science majors and those with just Mathematics and Science majors i n terms of obtaining some credit or no credit at a l l ) . Chi-Square (3) = . l 1 * (difference between students with English, Social Studies, Mathematics and Science majors combined with the students having just Mathematics and Science ma- jors, and the students with any other combination of ma- jors, i n terms of obtaining f u l l credit or just partial credit. Chi-Square (*+) = .01 (difference between students with Eng- l i s h , Social Studies, Mathematics and Science majors com- bined with the students having just Mathematics and Science majors and the students with any other combination of ma- jors, i n terms of obtaining some credit or no credit at a l l ) . These results indicate that only one of the categories caused the total variation to be significant. Chi-Square (2) i s significant at .001 level 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, Social Studies, Mathematics and Science majors and the group with just Mathematics and Science ma- jors i n terms of obtaining some credit ( f u l l or partial) or no cre- dit at a l l . There is no difference between these two groups i n terms of obtaining f u l l credit or just partial credit. There i s also no difference, on any basis, between the combined group of students taking English, Social 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 university than the students who have taken the science majors without the humanities, i n that fewer of the former f a i l . Table XVIII shows the distribution 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 First Year University Standing Majors First Second De- With Did not Class Class Pass Supp.Fail ferred drew Write Totals Foreign Lang .Major 21 65 32 18 h 1 3 191 No foreign Lang .Major 15 83 78 160 153 5 2̂ 10 5̂ 6 Totals 36 1M-8 110 207 171 9 3̂ 13 737 Again a l l those with no and relative proportions i n terms be seen only about 26 per cent of guage major. credit are combined i n Table XLX, of percentages are given. As can the students took a foreign lan- 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 First Year University Standing Majors First Second Pass Supp. No Totals Class Class Credit 0 0 ( J O ( J O ( J O ( J O ( J O Foreign 65 1+7 26 Lang.Maj. 21 32 191 (10.99) (3^.03) (16.75) (2k.61) (13.61) (25.92) No Foreign Lang. Maj. 15 83 78 160 210 5k6 ( 2.75) (15.20) (llf.29) (29.30) (38.1+6) (7^.08) Totals 36 IhQ 110 207 236 737 From the proportions in,this table i t appears that the students who included a foreign language major i n their programmes achieve higher standing at university. 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 credit. Less than 1*+ per cent of the former as contrasted with over 38 per cent of the latter obtained no credit. To test whether the difference i s significant, Chi-Square with four degrees of freedom was calculated to be 73.67. This value i s highly significant (P/.001). The degree of relationship is moderately high, the contingency coefficient being .30, with one of the categories making no contribution to the total variation, as seen below. In the partition of the above Chi-Square, the follow- ing 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 in terms of obtaining f u l l credit or just partial credit). Chi-Square (k) = kO.lk (difference between the two groups i n terms of obtaining some credit or no credit-at a l l ) . The f i r s t of these four values i s insignificant; the other three are significant at .001 level of confidence. Chi-Square (k) con- tributes more than half (5k per cent) to the total variation. From these s t a t i s t i c s , i t may be concluded that: a. There is no significant 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 significant difference between the two groups i n terms of obtaining honours or just a pass standing. c. There is a significant difference between the two groups i n terms of obtaining f u l l credit or just partial credit. d. The most significant difference between the two groups i s i n terms of obtaining some credit ( f u l l or partial) or no credit at a l l . In each of the last three cases above, the difference was in fa 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 this f i e l d , results obtained in this study show that there is a definite positive re- lationship between high school achievement and university perfor- mance. Better students in high school are better students at university. 2. Specific From the statistics employed, certain specific conclu- sions have been reached. (a) There i s a high positive relationship between grade twelve letter grade average and freshman standing. Students with a higher letter grade average have a better chance of achieving a higher standing at university. In particular, students with C+ average or better are less l i k e l y to f a i l than students with C av- erage or lower. (b) There i s an equally high positive relationship be- tween grade twelve percentage average, resulting from Departmental examinations, and freshman standing, particularly when the division point is 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 university, and in particular, a student whose high school average i s over 65 per cent has a much better chance of passing at university than one whose average is 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 risks. (d) Recommended students obtain higher f i r s t year stand- ing than non-recommended students. The difference is particularly noticeable when the division point is between obtaining some credit and f a i l i n g . That i s , there is 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 for s t a t i s t i c a l comparison with those from accredited schools, i n proportions alone they do not dif f e r i n standing from the students from accredited schools. (e) In spite of a very restricted range, there is some relationship between the number of Departmental examinations a stu- dent 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 is some relationship between major subjects taken i n high school and subsequent freshman standing, but only in a limited way. Fewer of the students f a i l who include i n their high school programmes both the humanities and the sciences as 62 majors (English, Social Studies, Mathematics, Science) than of those who take just the sciences (Mathematics and Science), omit- ting the humanities. There is no relationship evident in 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 compari- son i s made i n terms of f i r s t or second class honours standing, in which case there is no difference. The latter two conclusions are not in agreement with the majority of studies which find that university success i s indepen- dent of previous pattern of subjects. It is possible that students who take a l l four of the more academic majors and those who take a foreign language major in addition or in 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 for university work as a result 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 to do so by their teachers or counsellors. In any case, the situation i s indicative 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. A survey of the tables alone reveals deviations. 63 B Implications It is reasonable to expect i n any educational system that the better students i n high school have a good chance of being successful at university, 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 this study, therefore, confirm those of other investigations, 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 there- fore be emphasized. They are important not only i n prediction but also because they provide a strong argument i n favour of the system of recommendation used i n this province. Also pertinent to this province are the conclusions con- cerning high school majors, both the positive conclusion with re- gard to a foreign language major and the negative one with regard to the sciences. The student's choic:e and completion of certain 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 limitations of this study, i t may be said with a reasonable degree of conclusiveness that university success can be predicted from high school records. These records should therefore be examined carefully by counsellors when discuss- ing with students their future academic plans. Because individual prediction 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 factors which cannot be measured or controlled. 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 ma- triculation examinations is obviously a selective factor of great importance. Authorities i n testing have under- rated the predictive value of a student's high school record. But again i t is not easy to settle upon a mini- mum 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 university. The boy who seemed to be thoroughly stable and ready for college work, i n the eyes of his former principal, may have a rough and per- haps 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 financial problems. Perhaps the best that the university can do i s to make ample room i n i t s admissions plans for the merely 'good1, or at least, 'reasonably good1, youngster at the gate, and then within the gate provide as ample counselling f a c i l i - ties and financial assistance as i t possibly can." Not only do individual differences and personal prob- lems interfere with perfect prediction, but also does the unrelia- b i l i t y of both school marks and university marks. In this connec- tion Dale (16, p.198) comments: "Even i f a l l students have been correctly selected, not a l l w i l l pass. It is inherent i n the nature of examinations that some must f a i l . It is also inher- ent i n the nature of man that some professors w i l l set a standard which is higher than i t should be, just as others w i l l set a standard which is too low." In conclusion, the writer feels that i n spite of the hazards involved i n prediction, this study provides counsellors with s t a t i s t i c a l and factual evidence concerning high school rec- ords. It i s hoped that this evidence, combined with information gained from aptitude test results,» w i l l better prepare coun- x Luyendyk (30) and Shirran (^l) found that prediction of success can be made from results of certain tests administered by the University of B r i t i s h Columbia Counselling Department. 65 sellors to predict students' performance at university and to coun- sel effectively. The results of this study may also be of interest to University administrators for admissions purposes. C Recommendations for Further Study This study did not include students who omit, a science and/or foreign language i n f i r s t year. These are, i n the main, pre-Commerce students. It i s suggested that this group be studied i n some similar fashion. The importance of age, sex, and other factors such as mo- tivation, study habits, extra-curricular a c t i v i t i e s , and finances as factors in academic performance should be studied. In an attempt to evaluate more satisfactorily the i n f l u - ence of certain high school subjects on university success further work might be done with the factor of intelligence controlled. It might be worthwhile also to investigate the compara- tive 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 in university performance be- tween rural and urban school graduates would provide useful infor- mation, as would a study of difference between public and private school graduates. An investigation of the r e l i a b i l i t y of marking at univer- sity would be interesting. An investigation of the possibility 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 in 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 is embarrassingly evident that too many do go on to university." If the same waste of human resources exists i n this province, and there i s no reason to believe that B r i t i s h Columbia differs from Ontario i n this 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 university perfor- mance with the primary purpose of providing information for coun- sellors which they could use i n predicting the success or failure of university candidates. The high school variables used were letter 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 criterion of university performance used was f i r s t year standing in Ap 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 se- condary school i n B r i t i s h Columbia, were not repeating any f i r s t year university courses, and had had an uninterrupted secondary education. They had registered for at least fifteen units of course work, which included English 100-101, Mathematics 100 or 101, a foreign language, a science, and an elective. It was noted that the predictive value of this investi- gation can adequately apply only to students whose high school background and university programmes are comparable to those of the students used in this study. Further limitations are imposed by 68 the necessity of making certain assumptions regarding the r e l i a - b i l i t y of high school records and university marks. Literature which is relevant to the areas investigated i n this study was reviewed and conclusions were summarized. In order to determine whether the difference i n fresh- man standing was significant among students grouped according to the various high school variables, Chi-Square technique was em- ployed. To determine further where the difference lay, a method of partitioning Chi-Square was used. Contingency coefficients were calculated to show the degree of relationship between the var- iables and the criterion. From these statistics i t was found that there i s a high positive relationship between f i r s t year university standing and grade twelve average, whether i n letter 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 university than students who are required to write supplemental and/or to repeat subjects. It was also found that recommended students perform at a higher level at university 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 addition, some re l a - tionship was found between major subjects taken i n high school and f i r s t year university standing. Students who have included as ma- jors in their high school programmes Mathematics, Science, English and Social Studies, are less l i k e l y to f a i l at university than 69 students who take Mathematics and Science majors but who omit English and Social Studies majors. Also, students who have taken a high school foreign language major perform at a higher level at university than those who omit a foreign language major. It was concluded that, within specified limitations, the results indicated that high school records can be used effec- ti v e l y i n predicting university performance. It was suggested that some caution be exercised i n individual prediction since i n - dividual differences make perfect prediction impossible. For more sensitive prediction, It was further suggested that academic ab i l i t y test results be used to supplement high school records. BIBLIOGRAPHY 70 1. Adams, F.J., "Predicting high school and college records from elementary school test data," Journal of Educational Psychology, vol. 29, 1938, pp. 5 6 - 6 0 . ' 2. Alberta Progress Report. Matriculation Study Sub- committee February 1958? pp. 53. 3 . Ashmore, B., "High school teachers 1 marks as indicators of college success," Journal of the American Association of College Registrars, vol. 21, 19^6, pp. 219-230. k. Atkinson Study of Utiliz a t i o n of Student Resources. De- partment of Educational Research, Ontario College of Education, University of Toronto, 1957-58. 5. Bou, I.R., and Stovall, F.L., "A study of high school academic indices as a criterion for college admissions," Journal of Educational Research, vol. 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, vol. 53, 19^5, P P . 53^-537. 7. Brigham, C.C., "Admission units and freshman placement," Educational Record, vol. 15, 193k, pp. 57-67. 8. Brown, A.H., and Nemzek, C.L., "A comparative study of the college success of recommended and non-recommended students from one Detroit high school", Journal of Social Psychology, vol. 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, vol. 36, 1939, pp. k01-k20. 10. Byrns, R., "Predicting college success by high school grades," Nations Schools, vol. 10, No. 1, 1932, pp. 28-30. 11. Cochran, W.G., "Some methods for strengthening the common ./ chi-square tests," Biometrics, vol. 10, No. k. * 195k, pp. k i 7 - k 5 l . 71 12. Coffield, W.H., and Blommers, P., "Effects of non- promotion on educational achievement i n the elementary school", Journal of Educational Psychology, vol. M-7, 1956, pp. 2 3 5 - 2 5 0 . : 13 . Conway, G.B., "Understandable standards: the scaling of University Entrance Examinations," Canadian Education, vol. 11 , 1956, pp. 27-^1. l*f. Conway, C.B., and Brown, E.L., "The establishment of university entrance standards i n required and optional subjects," Canadian Education, vol. 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. 291 . 16. Dale, R.R., From School To University. London, Routledge and Kegan Paul Ltd., 195S PP» 258. 17. Darley, J.G., "A study of c l i n i c a l prediction of student success or failure i n professional training," Journal of Educational Psychology, vol. 29, 193«, PP. 335-35^. 18. Dearborn, W.F., "The student's background i n relation 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 risks," School and Society, vol. 3 5 , 1932, pp. lkO-lk-7. 2 0 . Drake, L.E., and Henmon, V.A.C., "The prediction of scholar- ship i n the College of Letters and Science at the University of Wisconsin," School and Society, vol. *+5, 1937, PP. 191-191*. 2 1 . Dressel, P.L., "Effect of the high school on college grades," Journal of Educational Psychology, vol. 3 0 , 1939, PP. 6 1 2 - 6 1 7 . \ 2 2 . Emme, E.E., "Predicting college success," Journal of Higher Education, vol. 13 , 19^2, pp. 263-267. 23. Ferguson, G.O. Jr., "Some factors in predicting college success," Sechool and Society,, vol. 37, 1933, pp. 566-568T 72 2h. Fredericksen, N.O., and Schrader, W.B., "A.C.E. Psychological examination and hign school - standing as pre- dictors of college success." Journal of Applied Psychology, vol. 36, 1952, pp. 261-265. 25. Froehlich, G.J., "The prediction of academic success at the University of Wisconsin, 1909-19I»-1," Bulletin of the University of Wisconsin. No. 235b, W l , pp. kh. 26. Garrett, H.E., Statistics i n Psychology and Education. Longmans, Green and Co., Toronto, 191+6, pp. *+93. 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^ vol. 18, 19^9-50, pp. 91-138. 28. Harris, D., "Factors affecting college grades; a review of the literature," Psychological Bulletin, vol. 37, 19**0, PP. 125-166. - 29. Kimball, A.W.,"Short-cut formulas for the exact partition of Chi-Square i n contingency tables," Biometrics, vol. 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 Br i t i s h Columbia, unpublished Master's thesis, University of Br i t i s h Columbia, Bri t i s h Colum- bia, 1952, pp. 87. 31. McLeish, J.A.B.,"Who should go to college?" Saturday Night. September, 1956, pp. 13-16. 32. McNemar, Q., Psychological Statistics . New York, John Wiley & Sons Ltd., 19^9, PP. 388. 33 Parkyn Report, Council of Educational Research, The Christ- church Press. New Zealand, June 13, 1958. 3^. Prescott, A.C., and Garretson, O.K., "Teachers' estimates and success i n college," School Review, vol. *+8, 19^0, pp. 278-28*+. 35. Rogers, H.W., "Success i n secondary school and college," School and Society, vol. *+0, 193^, PP. 33^-336. 73 36. Ross, F.C., "A method of forecasting college success," School and Society, vol. 3k, 1931, pp. 20-22. 37. Samenfeld, H.W., "Predicting college achievement," Journal of Higher Education, vol. 2k, 1953, pp. k32-k33. 38. Sarbaugh, M.E., "The effect of repetition of high school courses on college success," i n Studies i n Articulation of High School and College. University of Buffalo Studies, vol. 9, 193k, pp. 17k-l83. 39. Schmitz, S.B., "Predicting success in college: a study of various c r i t e r i a , " Journal of Educational Psychology, vol. 28, 1937, PP. k65-k75. kO. Seyler, E.C., "Value of rank i n high school graduating class for predicting freshman scholarship," Journal of the American Association of College Registrars, vol. 15. 19^9. DP. 5-22. k l . Shirran, A.F., Six Years Later, unpublished report on stu- dents registering in 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 collegiate success," Journal of Educational Research, vol. 19, 1929, pp. 237-25k. k3 . Stone, J.B., "Differential prediction of academic success at Brigham Young University," Journal of Applied Psychology, vol. 38, 195k, pp. 109-110. *fk. Symonds, P.M., Measurement in Secondary Education^ New York, MacMillan Co., 1927, pp. 588. k5. Travers, R.M.W., "Significant research on the prediction of academic success," in Donahue, W.T., et a l , The Measurement of Student Adjustment and Achieve- ment, Ann Arbor, Michigan, University of Michigan Press, 19k9, pp. Ik7-190. k6. Tribilcock, W.E., "Many of the 'Lowest Third' of our graduates are college material," Clearing House. vol. 12, 1938, pp. 5kk-5k6. k7. Wagner, M.E., "A survey of the literature on college perfor- mance prediction," in Studies i n Articulation of High School and College. University of Buffalo Studies, vol. 9 , 193k, pp. 19k-209. 7k Wallace, R.T., The Effectiveness of the Methods of Selection for Admission to Victoria College* unpublished Master's thesis, University of Br i t i s h Columbia Br i t i s h Columbia, 19^7, pp. 91. Weintraub, R.G., and Salley, R.E., "Graduating prospects of an entering freshman."^Journal of Educational Research, vol. 39, 19*+5, PP» 116-126. Welch, B.L., "The generalization of 'Student's' problem when several different population variances are involved," Biometrika. vol. 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 in Educational and Psychological Re- search, New York, Appleton-Century-Crofts, Inc. I9i?k, pp. k35. APPENDIX A Sample of Card Used for Gathering Data Name 1. 1957 Registration No, 2. Magee (A) 3 . Ma., Sc., Eng, h. Eng. ho C C Eng. 91 57% Ma. 91 61% Chem.91 C+ Phys.91 59$ Co. 10 C 5. C 6. 59% 7. N.R. (3) 9. F a i l 8. S.R. 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. First Year University Standing i n Apr i l . 76 APPENDIX B 2. Sample of Kimball's Method for the Partition of Chi-Square, 3 by 3 Contingency Table* Fir s t Year University Standing High School Letter Grade Average F u l l Credit Supp. No Credit Totals A, B 176 51 18 (a x) (a 2) (a 3) (A) C+ 101 78 273 (b x) (b 2) (b 3) (B) C, C-, E 17 62 ihO 219 ( c ^ (c 2) <c3> (C) Totals • 29h 207 236 737 (n 2) (n 3) (N) Chi-Square (1) = N[B(n2a-|_ - n-ja 2) - k{n2h1 - n ] L b 2 ) ] 2 ABn2n2 (A+B) (n x+n 2) = 737 [273(207x176 - 29^x51) - 2>+5( 207x101 - 29^x9^)32 (2*+5) (273) (29^) (207) (2̂ 5+273) (29^+207) = 39.26 Chi-Square (2) = N 2[b 3(a 1+a 2) - a 3(b- L+b 2)] 2 ABn3 (A+B) (n^ng) = 737)2 [78(176+5D - 18(101+9^)]2 (2*+5) (273) (236) (2U,5+273) (29̂ +207) = 26.72 » Reproduction of Table III, p. 32. Chi-Square (3) = N 2[c 2(a 1+l3 1) - c 1 ( a 2 + b 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 1 + c 2 ) ] 2 Cn^ (A+B) (n-j+n2) = 737 [1^0(176+51+101+9^) - (18+78) (17+62)] 2 (219) (236) (2^5+273) (29^+207) = 1^-5.71 2. Sample of Kimball's Method for the Partition of Chi-Square, 2 by 5 Contingency Table* Fir s t Year University Standing Grade 12 Standing Fi r s t Class Second Class Pass Supp. No Credit Totals Recom- 86 mended 33 131 116 58 k2k (a x) (a 2) (a 3) (ak) (a ?) (A) Not Recom- mended 0 9 18 81 166 27k (b x) (b 2) (b 3) (bi,) (be;) (B) Totals (»2? iko (n 2) 10k (n 3) 197 (i%) 22k (n 5) 698 CH) Chi-Square (1) = N 2[a 1b 2 - a 2 b i ] 2 AB n^^ri-j+r^) = (698J2 [33x9 - 131x0]2 (k2k) (27k) (33) (IkO) (33+lkO) = .k6 Chi-Square (2) = N 2 [b 3(aj+a 2) - a 3(b 1+b 2)] 2 ABn 3(n 1+n 2) (nj+n^ n^) = i 6 9 Q ) 2 Cl8(33+13D - 86(0+9)]2 (k2k) (27k) (10k) (173) (277) = 3.99 x Reproduction of Table XII, p. k5 79 Chi-Square (3) = N 2 Cbif.(a1+a2+a3) - Ai+Cb1+b2+b3)32 ABn^Cn-f^+n^) (n-j+n2+ n^+n^) = (698)2 [81(33+131+86) - ll6(0+9+l8)]2 (h2h) (2?h) (197) (33+1̂ +lOM-) (33+1̂ 0+10̂ +197) - = »+7.5l Chi-Square (h) = N 2 [b^(a1+a2+a3+aif) - a^b-j+b^b^+b^.) ] 2 ABn^n^+n^n^+nL,.) (nj+n2+ n^+n^+n^) = (698)2 [166(366) - 58(108)] 2 (h2h) (27^) (221+) (^l,.) (698) = 168.03

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