ae +s Relee ee em THE UNIVERSITY. OF ILLINOIS LIBRARY STI.26 CS9|\d ee , sD The person charging this material is re- sponsible for its return on or before the Latest Date stamped below. Theft, mutilation, and underlining of books are reasons for disciplinary action and may result in dismissal from the University. University of Illinois Library L161— O-1096 DETAILED FACTORS IN LATIN PROGNOSIS BY?) ORLIE M. CLEM, Pu.D. ASSOCIATE PROFESSOR OF EDUCATION YPSILANTI STATE NORMAL COLLEGE TEACHERS COLLEGE, COLUMBIA UNIVERSITY CONTRIBUTIONS TO Epucation, No. 144 Published by Teachers College, Columbia Cnibersity New York City 1924 pyrig Co ht, 1924, by Ortiz M. Crem ay z dt ve. DIET RL SO eo ACKNOWLEDGMENTS A stupy of this character can be carried on only through the sympathetic codperation of many persons. I am indebted chiefly to Professor Thomas H. Briggs under whose keen insight and kindly guidance the study has been made. His careful and pains- taking criticisms were always a source of helpfulness and encour- agement. My thanks are due to Professors Rudolph Pintner and Gonzalez Lodge for many valuable aids and suggestions. Special - gratitude is felt towards Dr. Herbert Anderson Toops, of the Bureau of Educational Research of Teachers College. His advice and direction in statistical technique have been invaluable. My thanks are due to Mrs. Zaida Minor, also of the Bureau of Educa- tional Research, for her untiring statistical assistance. Space will not permit an individual acknowledgment of gratitude to all teachers and pupils who participated in the study. The heads of the classical departments at each school, Miss Elizabeth Nammack at Wadleigh, Mr. Michael Solomon at De Witt Clinton High School, New York City, and"Dr. Ernest Riess at Boys’ High School, Brooklyn, have my sincere appreciation for their full codperation and many kindnesses. It was they who made the study possible. O. M. C. 5920257 iil Le Vs VII. CONTENTS PAGE . BRIEF SURVEY OF PREvViIousS STUDIES. . ... . 1 PEE EL ROBLES re ae eee eral When ee, So hh OS Data . 4 1. Plan of the Eenerinent UE ek ie er a 2. Subjects . . Saat ee tn ee A 3. Factors Goniderd ‘ot Each Pupils BN eae ae AEE CMlerione tare a ee eee aa 1S STATISTICAL TREATMENT OF DaTA. ... 2a 1. Tabulation and Transmutation of Raw fect, aa Es 2. Raw Coefficients of Correlation SAREE Tt Wo ee Be) 3. Significance of Raw Correlations .. 21 4. Effect of Detailed Factors as Shown by Multiple Ratio Correlation Coefficients, and Selection of ETORNOSISSLACLOTS* rin ee Meme st orate, 2G PPL RACTICAT IMPLICATIONS | oe en ee a RS) CAD OUMMARIZED CONCLUSIONS 44-0 . 8. ek tS ee 4D ACEP ENT Nae en eet aan eee oe. ae) A OL DETAILED FACTORS IN LATIN PROGNOSIS CHAPTER I BRIEF SURVEY OF PREVIOUS STUDIES To reduce misdirected effort is the first aim of any study in educational prognosis. Tbe method, if it is to be other than spec- ulative, requires an analysis of the factors which have made for success In a given situation with a view to determining the probable effect of the same factors in a second situation. Assuming that specific abilities are required in different types of learning, the problem of the investigator is to devise means for segregating and measuring these specific abilities, as a basis of prognosis. Previous to this study, four investigations have been made in the field of prognosis. In 1914, Dr. Truman Lee Kelley! investigated the relative predictive value of elementary school marks, teachers’ estimates, and some special tests upon the success of pupils in mathematics, history, and English, in the first year of the high school. Apply- ing the regression equation for the first time to educational meas- urement, Kelley found the individual and combined prognostic values of: 1. A pupil’s average in Grades 4-7. 2. The teacher’s estimate of a pupil on four traits: intellec- tual ability, conscientiousness, emotional interest, and oral expression. 3. The scores of pupils on some special tests in school subjects. Kelley’s results showed that these instruments of prognosis should be ranked in order of importance as listed above. Dr. Agnes Low Rogers,” in 1918, developed a group of six tests for predicting ability in mathematics. She ascertained that 1 Kelley, Truman Lee: Educational Guidance. Teachers College, Columbia University, Contributions to Education, No. 71. New York, 1914. 2 Rogers, Agnes Low: Experimental Tests of Mathematical Ability and Their Prognostic Value. Teachers College Contributions to Education, No. 89. New York, 1918. 1 2 Detailed Factors in Latin Prognosis mathematical ability was not a general trait, but was made up of a series of loosely connected capacities; that consequently no single test was an index to mathematical ability. Algebraic, geometric, and verbal abilities seemed to be of equal significance in math- ematical ability. Dr. Elbert Kirtley Fretwell,! in 1918, used as a basis of prognosis a group of standardized tests. He found that “academic success in the first year of the junior high school could be predicted more successfully by a group of standardized educational tests than by either elementary school marks, or teachers’ estimates, or age.” In 1921-22, Dr. William Sims Allen? conducted an investigation entitled A Study in Latin Prognosis. Dr. Allen, at the beginning of the first semester, 1921-22, gave twenty-one psychological tests to three hundred sixty-four boys taking first year Latin in the Boys’ High School, Brooklyn. At the end of the semester he gave to the same pupils eleven pairs of Latin tests devised by Professor Thomas H. Briggs. These tests were constructed so that they could be objectively scored and covered the eleven types of work done in the first semester of Latin. Dr. Allen, through multiple correlation procedure, chose from the twenty-one psychological tests a prognosis battery of six tests which gave the highest corre- lation with the eleven Latin tests used as criterion. These six tests: Briggs Analogies Tests Alpha and Beta, Thorndike Word Knowledge Tests A and B, Rogers Interpolation Tests 1 and 2, when combined gave a multiple correlation coefficient of .588. They also predicted ability as well in mathematics and English as in Latin. 1 Fretwell, Elbert Kirtley: A Study in Educational Prognosis. Teachers College Contributions to Education, No. 99. New York, 1919. 2 Allen, William Sims: A Study in Latin Prognosis. Teachers College Contribu- tions to Education, No. 135. New York, 1923. YU, CHAPTER II THE PROBLEM x THE purpose of this study is to find the effect of certain detailed factors upon a pupil’s success in first year Latin, to choose the most effective factors, and through multiple correlation to obtain their combined effect as a basis for prognosis. Dr. Allen used one factor as a basis for prognosis,—psychological tests. The aim of the present study is to find the influence of many possible factors, including those measured by the Allen Battery of six tests. The original analysis of the problem was, made on the basis of, “What are the possible factors which in- fluence a pupil’s success in first year Latin?” Obviously the original list was incomplete because no one can bottle up all the human influences affecting a pupil’s Latin product. | However, the original list was greatly abbreviated. Some factors were elim- inated because they appeared too subtle and elusive for our present scales of measurement; others because data could not be secured, or if at all only with too great difficulty; others because they would not lend themselves to statistical treatment. Of the factors re- tained, it was not presumed at the outset that each had equal reliability when taken at its face value. For example, the age of a pupil is an objective measure which should be accurate. But “the average number of minutes daily”? which a pupil says he spends in the preparation of Latin is a different kind of measure. Some pupils may have little ability in estimation. Some will by nature estimate too high and others too low where they themselves are concerned. Honesty with self may be an important factor. Practically every degree of reliability is represented by the various factors as shown by the correlations in the three schools studied. One of the important aims of this study is to find to what degree the various factors are reliable for different groups. | The purposes of this investigation then are: _ 1. To find in the groups studied the empirical effect of ee detailed factors on success in first year Latin, regardless of what their reliability may subjectively appear to be. 2. To build up a battery of factors as a basis for prognosis, " having consideration for the availability and objectivity of data. | 3 = CHAPTER III DATA 1. PLAN OF THE EXPERIMENT Tus study supplements the one made by Dr. William Sims Allen, 1921-22, in the Boys’ High School, Brooklyn, entitled A Study in Latin Prognosis. It was arranged for by the department of secondary education of Teachers College in codperation with the classical departments of three schools of New York City: Boys’ High School, Brooklyn; Wadleigh High School; De Witt Clinton High School. 2. SUBJECTS | \ Phe subjects for this experiment consist of three groups: Group 1. Two hundred fifteen boys in the Boys’ High School, Brooklyn, who had elected to study Latin. They were the ones still remaining in school of the three hundred sixty-four used by Dr. Allen in his experiment. Dr. Allen notes that the original three hundred sixty-four were grouped in eleven classes, the groups having been made according to the pupils’ scores in the Otis group test of mental ability; they were taught by four teachers. No boy had previously studied Latin. The average age was thirteen and one half years. Group 2. Ejghty-eight first year girls of the Wadleigh High School, New York City. Of the eighty-eight who took the prog- nosis tests at the beginning of the semester, eighty remained in school and took the Latin tests at the end of the semester. This study deals with the eighty pupils. The girls were grouped in Latin classes at Wadleigh according to the Terman group test of mental ability. From the Latin classes in the school, one class was chosen at the lower, one at the middle, and one at the upper range of ability. The average age was slightly less than fourteen years. Group 3. One hundred ten first year boys of the De Witt Clin- ton High School, New York City. Of the one hundred ten who took the prognosis tests at the beginning of the semester, one hun- dred three remained in school and took the Latin tests at the end ¢ Data 5 of the semester. This study deals with one hundred three pupils. They were sectioned according to the Otis group test of mental ability, and the three classes used in this study were selected on the same basis as at Wadleigh. The average age was slightly more than fourteen years. — ) 8. Factors CONSIDERED FoR EAcH Pupin Approximately sixty separate items were considered for the three groups. They have been classified under sixteen heads called throughout this study, “Factors.’’ Factors V, VI, and VIII were omitted from Group 1 for reasons explained later. Factor I. Scores Made in Each Test of the Allen Prognosis Battery. The tests are: 1. Briggs Analogies Test Alpha.? . Briggs Analogies Test Beta.’ . Thorndike Test of Word Knowledge A. . Thorndike Test of Word Knowledge B.° . Rogers Interpolation Test 1.4 . Rogers Interpolation Test 2.4 > Or em OO rw A brief description of these tests follows: Briggs Analogies Tests Alpha and Beta consist of 72 items. They measure knowledge of form and ability to see relationship between words. Thorndike Tests of Word Knowledge A and B consist of 100 items each. They measure the ability to recognize the meaning of words. Rogers Interpolation Tests 1 and 2 consist of 107 items each. They measure the ability to interpolate numbers, that is, to supply omissions in a series of varied arithmetical progressions. For the first group of pupils (215 boys, Boys’ High School, Brook- 1 For a more complete description of these tests see: Allen, A Study in Latin Prognosis, p. 4. 3 2 Copies of the Briggs Analogies Test may be secured from Professor Thomas H. Briggs, Teachers College, Columbia University. 3 Copies of Thorndike Word Knowledge Tests may be secured from the Bureau of Publications, Teachers College, Columbia University. 4 Copies of Rogers Interpolation Test may be secured from the Bureau of Pub- lications, Teachers College, Columbia University. 6 Detailed Factors in Latin Prognosis lyn) the scores secured by Dr. Allen in these tests were used. The tests were scored by fifteen teachers of Boys’ High School and checked by Dr. Allen. The second group of pupils (80 girls, Wadleigh High School) were given the above tests by the writer at the opening of school, September, 1922. The papers were scored by three Latin teachers and checked by the writer. The third group of pupils (103 boys, De Witt Clinton) were given the tests by the writer at the opening of school, September, 1922. In this group the three classes were taught by the same teacher. The papers were scored by this teacher and checked by the writer. Factor II. Intelligence Quotient. For the first and third groups the Otis group test of mental ability was used, and for the second, the Terman. Strictly speak- ing, the term I. Q. should apply only to the Binet-Simon scale. But the administration of the Binet-Simon scale to such a large group in an experiment of this character is impossible. Hence, in school administration the term I. Q. has come into rather common acceptance in dealing with groups of pupils measured by either of the above tests. Each test is accompanied by a table for the transmutation of raw scores into approximate I. Q.’s. It is not claimed that they are as accurate as the I. Q. of the Stanford Revision of the Binet-Simon Test. Factor III. Age. The age was secured at the beginning of the semester. The time it was taken, however, would in no way affect the correlations inasmuch as we may add, subtract, divide, or multiply a series of scores by the same constant without affecting the correlation. Factor IV. High School Attendance. The number of days attendance during the semester was used. Factor V. Elementary Attendance. The number of days attendance during the last year of the elementary school was used. This factor is lacking for Group 1. Factor VI. Elementary School Marks for the Last Year, in All Subjects. The promotion marks of both the teacher and the principal were used for the following fifteen items: Data 7 1. Reading 9. Geography 2. Grammar 10. Music 3. Composition 11. Drawing 4, Spelling 12. Cooking (Science for Group 3) 5. Penmanship 13. Sewing (Shop for Group 3) 6. Arithmetic 14, Physical training 7. Arithmetic 15. General estimate 8. History and civics No elementary school marks were obtainable for Group 1. Pro- motion cards are destroyed after a year at the Boys’ High School, and no duplicates are kept at many of the elementary schools. Factor VII. High School Marks in All Subjects. The semester mark for each pupil was secured in the following subjects: Group 1 Group 2 Group 3 Latin Latin Latin English English English Mathematics Biology Biology Drawing . Civics Mathematics Music Drawing Civics Physica] training Music Drawing Physical training Music Physical training Elocution Facror VIII. Ranking of Pupils by Teachers on the Following Twelve Traits: b—_ . Perseverance . Industry . Earnestness . Nerve stability . Orderliness . Self-confidence . Accuracy . Right attitude toward criticism . Frequency in securing help from teacher . Promptness and regularity in doing work . Ability to work independently . Desirable social and moral attitudes Oo COs SD Or & OC WO tet et © = © No rankings were secured of the pupils in Group 1. Because of the possible changes in administration and instructional force, and also the lapse of time, it was thought that a ranking made after a year would be impracticable. To the teachers of Groups 2 and 3 the following blank was given: Detailed Factors in Latin Prognosis RANKING OF PUPILS BY TEACHERS Each teacher will please rank his or her pupils on the following points. ing them use this method: In rank- 1. Give those in the highest 10 per cent of the class a rank of 1. 2. Give the next 20 per cent a rank of 2. 3. Give the next 40 per cent a rank of 3. 4. Give the next 20 per cent a rank of 4. 5. Give the next 10 per cent a rank of 5. SACALILLY TVYOJ GNV TVIOOS ATavuUlsaq ATING ~INAdAGN] WHOM, OL ALITIGY WUOM ONIOG NI f ALIVVINDAY AGNV SSANLANOUgG : AGNI ONANDS PAR RL PR eRe) Cigale eee seals d1d}{ ONIMNOTSG NI AONANDAUT msouny voomsay ovomr| [TTT EEE sora PEE someones PT LTTELETELEL ELL semen OT CCC wanorors [TTP TPEPEPE EEE ELLE Seem SA AUBEUEURAUEUORUSENEUEGRELGBUEEAELAER oS SBE Bee SBR GE BSE. | | | HRSA SHHASHRHAHNHSCrNOAS 2 ned pe et et et CN NAMES OF PUPILS ScHOOL TEACHER SECTION Data 9 (it will be noted from the above blank that each teacher was asked to rank his or her pupils on the twelve traits by dividing them into five groups. Those in the upper 10 per cent were to be given a rank of 1, those in the next 20 per cent a rank of 2, those in the next 40 per cent a rank of 3, those in the next 20 per cent a rank of 4, and those in the lowest 10 per cent a rank of 5. It was thought that this method was just as accurate and not nearly so laborious as ranking each pupil in a position relative to every other. | The following set of directions was also given to each teacher. No particular merit is claimed for these directions. The ranking would possibly have been just as reliable without them. To at- tempt to define perseverance by the use of other words is difficult; and so it is with many of the other traits. DIRECTIONS FOR RANKING PUPILS Each teacher in ranking pupils will please consider the following interpretations: PERSEVERANCE: Ability and tendency of pupil to keep at, to continue, whatever work under- taken, regardless of difficulty or unpleasantness. INDUSTRY: Attention to work at hand. Pupil is alert and active in taking up new tasks and in carrying them through. EARNESTNESS: Pupil is serious and intent in his work; he is purposeful, determined, and eager. NERVE STABILITY: Nerve condition of pupil is stable and balanced. There are no disorders which harass or handicap him in his work. ORDERLINESS: Pupil is neat and orderly in his work. SELF-CONFIDENCE: The pupil believes in self, has faith in his own ability to do things. ACCURACY: Painstaking, careful in work; has details correct. Riegut ATTITUDE TOWARD CRITICISM: Takes criticism without resentment and attempts to remedy faults. PROMPTNESS AND ReauLarity In Dorne Work: Does work at the time required, and regularly. FREQUENCY IN SEcuRING HELP rromM TEACHER: Rank on number of times pupil secures help, or the amount. Do not consider the effectiveness of the help in this ranking. Asinity TO Work INDEPENDENTLY: Pupil shows initiative and originality, power to proceed alone without help from teacher or another. 10 Detailed Factors in Latin Prognosis DESIRABLE SoctAL AND Mora ATTITUDES: Habits and manners of pupil are such that he gets on well with his fellows and has a wholesome influence among them. Factor IX. Study and Conditions for Study. 1. Amount of outside help on Latin and by whom given. 2. Attendance at movies. 3. Amount and character of daily sleep. Factors IX to XVI were secured from pupils near the close of the semester by means of the questionnaire which follows: QUESTIONNAIRE USED FOR SECURING FACTORS IX TO XVI Name of Pupil eis c.¢- es ba Last, First, Middle Initial Address of Pupil soc35 0 fu fea Oe < oe ee I. Stupy AND CONDITIONS FOR STUDY If father write “father”; if brother, write ‘‘brother,”’ etc.) 8. If you do receive help, what is the average number of minutes daily?......... (Number of minutes) 4, Estimate the number of times you go to the movies each week.............. 5. What is the average number of hours that you sleep daily?.................. (Give to nearest hour) 6. Do you sleep about the same number of hours each night?.................- (Answer yes or no) II. InpIvipvuAL INTERESTS AND AMBITIONS 1. Do you plan to attend high school next year?.................0ccccecevces 2. Do you plan‘to graduate from high school... .J.1.5s) +25 > o+s one ee (Answer yes or no) 8. After high school, what do you expect to do? You will show this by placing a check before one of the following. If you are not quite sure, check the answer which seems more nearly correct. 1. To attend college . To attend teacher-training or normal school . To go to trade school . To go to some special] school . To work at home . To go to work away from home aS Or & 09 Data if 4. As your life work, what are you planning for? Place a check before one of the following. If you are not quite sure, check the one which seems more nearly correct. 1. Business 3. Profession 2. Trade 4. Home III. Oursipr Worx 1. Do you take music lessons outside of school? © © 0; 0 Bio 0 oe 6 66) .6 6 8 0 be 8 6 6 6 8S et se 8 6 eee eer DEPOT OUTS Weel Vr 17. Fee oleate td hed ast Ge One bio Paes s ove dae (Give number) 3. Do you study any language or any school subject outside of school?.......... (Answer yes or no) eR WORLD Ole gato nic cue sos Average number of hours weekly?............... (Give number) SO you work outside of school'for’your parents? eo. cleis ie ene a diene 6 cs oretele (Answer yes or no) 6. If so, what is the average number of hours that you work for them weekly?...... (Answer to nearest hour) (Answer yes or no) A. If you do work for others besides your parents, what average number of (Give to nearest hour) B. Name or kind of work which you do for those who are not your parents... . C. How much money do you receive per week on the average for this work? eee eee ee ee ee ee ee es eee sense ee ese ee ee ee ere ee ese seers os eee ees ee ee eevee (Dollars) (Cents) IV. Srupy, AND Ranxincs or Pupits (1) (2) (3) (4) (5) Names of Study Importance Preference Preference Subjects at Home of Subject for Subject for Teacher |S | | — ———————_—— |) FESS | —————— | LN es ee | | ee | — | _S— | SSSSSFSSFSSsE SEE 12 Detailed Factors in Latin Prognosis V. Exrra-Curricuuar ACTIVITIES Go down the following list. Check once those activities in which you have par- ticipated. Check twice those activities in which you have held an office, during the semester. 1. General Organization 12. Dramatic Club 23. Court 2. Athletic Association 13. Debating Club 24. Assembly 3. Hockey 14, Literary Society 25. Class Officer 4. Basket-ball 15. Poetry Club 26. Official Section Officer 5. Foot-ball 16. Bank 27. Roosevelt Memorial 6. Swimming 17. Newspaper Association 7. Track 18. Magazine 28. Red Cross 8. Tennis 19. Handbook 29. Library 9. Orchestra 20. Curricula Club 30. Honor Roll 10. Glee Club 21. Lunch 31. Boy Scouts 11. Band 22. Fire Drill 32. Camp Fire Girls 33. Hi Y. The writer, in giving the questionnaire to the pupils, explained for their protection that no teacher would be in the room during the time it was given, that the answers would be treated as con- fidential, and that the pupils should write what they actually believed. It is the opinion of the writer that they did this to a very great degree. Factor X. Individual Interests and Ambitions. The following data were secured: 1. Plan for the following year. 2. Does the pupil plan to graduate? 3. Plan after graduation. 4. Plan for life work. Factor XI. Outside Work. The following data were secured: 1. Amount of time given to music lessons. 2. Amount of time given to the study of any language or any school subject outside of school. It was explained here that the question meant any language or any school subject which the pupil was not then studying in school. 3. Amount of time given to work for parents outside of school. 4. Amount and kind of work done for persons besides parents with amount of money received. Factor XII. Amount of Home Study. Factors XII to XV were secured by means of the rectangular chart on the questionnaire. The pupils of the three schools Data 13 studied the same subjects in each respective school. The names of these subjects were written on the blackboard, and each pupil copied the list into column (1) of the chart. In column (2) he wrote opposite each subject the average amount of time spent daily on study at home. The pupils in each of the schools did no study at school, inasmuch as the schools operate on the double session basis. Factor XIII. Importance of Subject. Each pupil was asked to rank in column (3) the subjects listed in column (1) in “what he considered their order of importance to him.” ‘The most important was to be given a rank of 1, the next important 2, and so on. Factor XIV. Preference of Pupil for Subject. Using the same method as above, each pupil was asked to rank in column (4) the subjects as he liked them, regardless of their importance or any other consideration. Factor XV. Preference of Pupil for Teacher. Using the same method as above, each pupil was asked to rank in column (5) the teachers of the various subjects as he liked them. Factor XVI. Participation of Pupil in Extra-Curricular Activi- ties. From a study of the extra-curricular activities of the three schools, an inclusive list was made of all those of any importance to which freshmen were eligible. The pupil was asked to check once those activities in which he had participated, twice those in which he had held an office, during the semester. 4, Tur CRITERION [iy he criterion used in this experiment was a group of Latin tests given at the end of the semester... For Group 1, the results of Dr. Allen’s experiment were used. He gave eleven Latin tests devised by Professor Thomas H. Briggs. One test was given to each of the following fields:é 2 2 3 — 1. Nouns 2. Vocabulary 3. Construction 4, Derivation 1 For a more complete description of these tests, see: Allen, A Study in Latin Prognosis, p. 9. 14 Detailed Factors in Latin Prognosis 5. Syllabification 6. Gender 7. Pronouns 8. Conjugation 9. Pronunciation 0. Translation from English to Latin 1. Translation from Latin to English pt ee <. Each test was constructed so that it could be scored in objective units, so easy that the poorest pupil could make some score, and so difficult that the best pupil could not make a perfect score. The methods of scoring, timing, and administration were similar to those of any good standardized test. For Groups 2 and 8 a series of ten tests, devised by the writer and paralleling those of Professor Briggs, was given. The pro- noun test was omitted inasmuch as the subject had not been covered in the two texts used. Only one set of tests was given to Groups 2 and 3 owing to the high reliability of the two forms. These tests covered the materials in the texts of the two schools. (_In order that all pupils might more adequately be measured, the tests included only materials studied by the poorest section. It may readily be claimed that this penalizes the brightest section; yet the plan seems more desirable than to test the poorest section on materials they have never studied. - For Groups 1 the Latin tests were Stored by the Latin teachers of Boys’ High School, Brooklyn, and checked by Dr. Allen. For Groups 2 and 8 the papers were scored by the Latin teachers of Wadleigh and De Witt Clinton High Schools and checked by the writer. CHAPTER IV STATISTICAL TREATMENT 1. TABULATION AND TRANSMUTATION OF Raw ScorRES The Criterion. For each of the three groups a combined weighted criterion score was computed for each pupil in the following manner: In Dr. Allen’s experiment, thirteen Latin teachers weighted the eleven tests... The median of their weightings is shown in Table I. TABLE I Wericuts Given THE LaTIN CRITERION TEsts BY THIRTEEN Latin TEACHERS Test Weight NOUNS ea Cane state ade ial ee on tae Bea ea cB fc ope sha es 9 OV ONSITE re ee pete etree eed aes I ees a ah 10 OTISLEUCLIOLU Me ae Se Rats te ove ate ere Ramla wired vas 11 DCrIVAL itt etre tee se fate eine toe ae Ce OG ee wierd a ace 6 IMLS DIN CALIGNin eet orc kee ett pie sea tr Pe ts oleae baa cos 5 CPST irr teeny Shee eee eet) eee ee ae oe dag sy Sieg wisi wd 5 PE POUULS Pompey rt eel eee ots, CEE hc chlo eos “av Giale 9 Ce aTEA Te ASOT is Gre 8 a RON let Wie ef ON WR ee a Er 16 eer OAC LAE LON eee ere ene ne ane he ante b's vin eines 4 ransigtion trom bnghisit tOnLAtyy ys. ccs. fos ete se alee 2 ease 12 Prasislation (ont LAtinitO LNClISl.. | oc: doe oeee sence ase 13 In weighting any series of tests for purposes of statistical com- putation, it is necessary to take account of the standard deviations of each test. Hence, the weighted score in any test is equal to the actual score divided by the standard deviation, times the weight assigned. ‘The combined weighted criterion score of any pupil in all the tests is the sum of the weighted scores. ae S =the combined weighted criterion score desired for each pupil. B, B, Bs . . . By=the weights assigned each test in the above table. X1, Xo, X3 . . . Ai=the raw scores made by a pupil in each test. 1 Allen, A Study in Latin Prognosis, p. 19. 15 16 Detailed Factors in Latin Prognosis Then, the formula becomes: XxX. XxX. S=B,—=+B, + ousie NPs +By — O71 02 O11 The formula at first sight appears laborious, but in actual practice becomes rather simple. By, Bo SO). SB and: ‘ow og, eres to are constant. each test. Hence, we may write the formula: B B B s=— X,4+—X.+ Oe eS += Xu 01 02 O11 il So when hes By Sete Bu have once been obtained for O71 02 O11 each test, they may be used for every pupil within the group. The process then becomes merely one of finding for each pupil the sum of the test scores after each is multiplied by a single constant, the quotient of the B divided by the sigma. The same sigmas were used for Group 3 as for Group 2 for the following reasons: 1. The groups were of the same school grade, had been selected on the same relative intelligence basis, and were of approximately the same age. 2. Assuming that the sigmas of the different tests were slightly different in Group 3, the change in variability for all the tests would be a fairly constant ratio. Hence, the correlation of the various factors with the criterion will not be materially affected. The combined weighted criterion scores for each pupil were next transmuted, for purposes of correlation on the chart devised by Dr. Herbert Toops. All the correlations in this study were done by the Toops’ method. The formula follows: S[(@X+2Y9 —2(X—Y)"]— (2X) x ZY) VN(2X)?—(ZX)2 VN(SY)?—(ZY)? The chart of Dr. Toops for plotting the scatter diagram consists of eighteen steps running from 0-17, inclusive. The method of transmutation is as follows: The lowest score made by any pupil in a group is subtracted from the highest score plus one. This gives the inclusive range. The inclusive range is then divided by 18 (the number of steps in Statistical Treatment jive the chart) and the quotient represented by the next higher integer taken as the class interval. The transmutation scale is then built up. Step 1 extends from the lowest score to a number which is equal to the lowest score plus one less than the class interval. Steps 2, 3, etc., are built up in the same manner. Tabulation and Transmutation of Factors. The same method of transmutation was used for the various items of the sixteen factors as for the criterion. The original scores of practically all items were expressed in definite numerical units so that they could be treated statistically without alteration. The following excep- tions need explanation. The elementary school marks were recorded in terms of the first letters of the alphabet. A transliteration was made on the follow- ing basis: A=6)b-—6>, b=45C=1. More involved formulae for the process are available,! but for practical purposes the above method is probably as reliable as any other. It is used by the Institute of Educational Research of Teachers College in its vocational guidance inquiry. A convenient scale for transmuting all the elementary marks, including the averages of two or more, extending from 10 to 60, was used. In the case of the various rankings: 1. Ranking of pupils by teacher on 12 traits. 2. Ranking by pupil of (a) importance of subject; (6) preference for subject; (c) preference for teacher, it will be recalled that 1 represented the highest score, 2 the next highest, and so on. In the statistical treatment, these values were reversed in order that the correlations might be expressed positively rather than negatively. Thus, 1=7, 2=6, 3=5, 4=4, 5=3, 6=2, 7=1. ~ In the case of “ plan after graduation,” as shown previously, the pupil checked on the questionnaire one of six possible items: Score Assigned PEG AL EeNC CONOUR. Ss a ttn ete oe Pa ens, Sol dee ahik oes On on 6 To attend teacher training or normal school. ............. 5 PERE MEO PACE SCHOOL OREN eN CS PAS wee diac oietd ae eon aaa ole GPO SOL0e SDECIAD SCDOOL: 2. Seak\iecsick eckeswa «sale Delay at 4 SO WORK Bie isemere ate erie as sig wy sb cle y lati c= foke se ieee rs ‘oO go tower Way ir0Mm homies. hs chs. ves a caiue vase e 1 1 Kelley, Educational Guidance. 18 Detailed Factors in Latin Prognosis These items were ranked by a group of students of education on the basis of “academic interest”? and assigned the numerical values following each item. In the case of “‘plan for life” the four items: Score Assigned Business. ois ps as Re Saale s Cate ae ee Loe ee eee 3 Trade x o:tic vas sho Beas he We ie ee is Cece bie eee ee eee Q Professions e320), eo ci aise ee eee 4 Home foe et oe ey ee Oe ee eae 1 were ranked in the same manner as above on the basis of “aca- demic interest,’ and assigned the numerical values following each. Inasmuch as the items of the sixteen factors were practically the same for the three groups, in building up the transmutation scales for both the criterion and the factors, a sufficiently large allowance was made in the inclusive range of the first group treated to include any probable scores in the other groups. A single exception to this is the I.Q. of Group 1, shown at the end of Table II. For Group 1, the transmuted scores of Dr. Allen were used for the criterion and the prognosis tests. Table II shows the gross scores corresponding to steps of the Toops’ chart in the combined weighted Latin criterion, and in all items of the various factors. The class interval is also given. 2. Raw CoeEFFICIENTS OF CORRELATION Table III which follows shows the raw correlation of all vari- ables with the Latin criterion. The probable error is shown in each case. Obviously, no correction for attenuation was made, for in the case of many factors only one measurement was or could be possi- ble. Then, too, as Truman Lee Kelley! has indicated, correction for attenuation presumes an ideal relationship while the funda- mental aim in any prognosis study is to obtain data as they exist and can be secured under normal conditions. Dr. Allen, in the case of some of the psychological tests, corrected for attenuation but made no use of the corrections in his study, realizing their relative unimportance from the point of view of the practical administrator. 1 Kelley, Educational Guidance. Step Class Interval Combined Weighted Latin Criterion 858-890 825-857 792-824 759-791 726-758 693-725 660-692 627-659 594-626 561-593 528-560 495-527 462-494 429-461 396-428 363-395 350-362 297-329 33 Factor I Briggs | Thorndike Alpha | Prognosis and Tests Beta A and B 68-71 102-107 64-67 96-101 60-63 90-95 56-59 84-89 5200 78-83 48-51 72-17 44-47 66-71 40-43 60-65 36-39 54-59 32-35 48-53 28-31 42-47 24-97 36-41 20-23 80-35 16-19 24-29 12-15 18-23 8-11 12-17 4-7 6-11 0-3 0-5 4 6 ScALE FOR TRANSMUTING THE CRITERION AND ALL Facrors TO THE Toors CHART Facror II| Facror III | Facror IV Inter- Hich School polation 1.Q. Age Gh di ay (ana? endance 119-125 144-147 190-192 88-89 112-118 140-143 187-189 86-87 105-111 136-139 184-186 84-85 98-104 1382-135 181-183 82-83 91-97 128-131 178-180 80-81 84-90 124-127 175-177 78-79 77-838 120-123 172-174 76-77 70-76 116-119 169-171 74-75 63-69 112-115 166-168 72-73 56-62 108-111 163-165 70-71 49-55 104-107 160-162 68-69 42-48 100-103 157-159 66-67 35-41 96-99 154-156 64-65 98-34 92-95 151-153 62-63 Q1-27 88-91 148-150 60-61 14-20 84-87 145-147 58-59 7-13 80-83 © 142-144 56-57 0-6 76-79 139-141 54-55 of 4 3 Q TABLE II Facror V Factor VI | Facror VII Factor VII Factor IX Factor X Facror XI Factor XII Teachers’ Rankings . : : Plan : Time Combined Elementary Elementary ED Single Sum of | Minutes | Movie Daily After Flan Music Outside Worl Spent Study of Attendance ve et Rees Trait pean eres stipe Sleep | Grad- ro Lessons | Language Pp for on All Subjects, ea aEKs Fale aur uation arents Study Except Latin 189-190 ere 95-99 my. 85-89 17 17 17 17 17 eg 34-35 102-107 187-188 58-60 90-94 Goes es g0-S4 | 16 16 16 16 16 16 32-33 96-101 185-186 55-57 85-89 15 55-57 | 75-79 | 15 15 15 15 15 15 30-81 90-95 aia 183-184 52-54 80-84 14 52-54 | 70-74 | 14 14 14 14 14 14 28-29 84-89 280-299 181-182 49-51 75-79 13 49-51 | 65-69 | 13 13 13 13 13 13 26-27 78-83 260-279 179-180 46-48 "10-74 12 46-48 | 60-64] 12 12 12 12 12 12 24-95 79-77 240-259 177-178 43-45 65-69 11 43-45 | 55-59] 11 11 11 rl 11 11 22-23 66-71 220-239 175-176 40-42 60-64 10 40-42 | 50-54] 10 10 10 10 10 10 20-21 60-65 200-219 173-174 37-39 55-59 9 37-39 45-49 9 9 9 9 9 9 18-19 54-59 180-199 171-172 34-36 50-54 § 34-36 40-44 8. 8 8 8 8 8 16-17 48-53 160-179 ° 169-170 31-33 45-49 7 31-33 | 35-39 ‘i i" 7 7 7 7 14-15 42-47 140-159 167-168 28-30 40-44 6 28-30 30-34 6 6 6 6 6 6 12-13 36-41 120-139 165-166 25-27 35-8 5 25-27 | 25-29 5 5 5 5 5 5 10-11 30-35 100-119 163-164 29-94, 30-34 4 22-24, 20-24, A 4 4 4 A 4 8-9 Q4A—29 80-99 161-162 19-21 25-29 3 19-21 | 15-19 3 8 3 3 3 8 6-7 18-23 60-79 159-160 16-18 20-24 Q 16-18 | 10-14 2 Q 2 2 2 2 4-5 12-17 40-59 157-158 13-15 15-19 1 13-15 5-9 1 i 1 1 1 1 2-3 Gu 20-389 155-156 10-12 10-14 0 10-12 0-4 0 0 0 0 0 0 0-1 0-5 0-19 Q 8 D 1 3 5 i 1 1 il 1 1 Q 6 20 Preference Importance of Pupil of Subject for Subject Liv aye 16 16 15 15 14 14 13 13 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4, 3 3 2 Q 1 1 0 0 1 1 Preference of Pupil for Teacher 17 16 15 Cr wmwoePonwkms Factor XIII| Facror XIV | Facror XV | Factor XVI Extra- Curricular Activities SO WWE aArAaNtNe I. Q. for Group I 189-195 182-188 175-181 168-174 161-167 154-160 147-153 140-146 133-139 126-132 119-125 112-118 105-111 98-104 91-97 84-90 77-83 70-76 Statistical Treatment SHowine Raw Cogrricients or CoRRELATION oF ALL VARIABLES TABLE III Wits Latin Criterion Factor I Prognosis Tests 1. Briggs Analogies Alpha....... 2. Briggs Analogies Beta........ 3. Thorndike Word Knowledge A 4. Thorndike Word Knowledge B HLNSETPOlAbiONu lint. oe. 2c Oremmterpolation’2...4,0-6 00. sore Facror II 7. Intelligence Quotient........ Facror III 8. Age Factor IV 9. High School Attendance...... Factor V 10. Elementary School Attendance. Factor VI Elementary School Marks in All ubjects 1. Combined Average of Elemen- tary Reading, Grammar, Com- position, and Spelling........ 12. Arithmetic (Average of Two INE a ee hoa (ERS ee 13. Combined Average of History and Civics and Geography.... 14. Combined Average of Penman- ship, Music, and Drawing.... 15. Combined Cooking and Sewing PAWOTS GCS Ath tis kts nies A. Science alone for Group 3 B. Shop alone for Group 3. . TG. Physical Training... 02). oo. % 17. General Estimate............ 18. Combined Average of 15 Marks PADOVG aisahe shel bin Cietlarctivs skate Facror VII High School Marks in All Subjects 19. Semester Mark, Latin........ 20. Semester Mark, English...... 21. Semester Mark, Biology...... 22. Semester Mark, Mathematics. 23. Semester Mark, Civies....... 24. Semester Mark, Drawing..... 25. Semester Mark, Music....... 26. Semester Mark, Physical Train- MIN s PEs aot et, hrs 8k cleelelee Boys’ HicH Corre- lation 27. Semester Mark, Elocution.... Factor VIII Teachers’ Ranking of Pupils on Twelve Traits 28. Teacher’s Ranking Persever- PIO OG ened wits Mosh tris pharm 29. Teacher’s Ranking Industry... 30. Teacher’s Ranking Earnestness 31. Teacher’s Ranking Nerve Sta- ULL Veet a cn cate, ee eee 32. Teacher’s Ranking Orderliness. 33. perber Ranking Self-Confi- TIO Ge Cie a cw ole nis ate Sekt ete oie P. able Corre- Error lation -————— | —————————————_.- J. | | ——— ee ee 0366 .4348 0330 . 5034 0404 .3001 0408 1772 0429 . 0847 0450 . 3440 0401 .4778 0426 | —.3847 0460 2684 .0832 3307 3227 2840 2188 . 3076 .0955 4368 4088 0281 8371 0347 5182 6964 .0343 .4030 0443 1375 0422 1054 0458 1967 5138 5589 5228 3165 5688 . 5614 W ADLEIGH Prob- able Error Corre- lation 19 Des Wirt CLINTON 20 Detailed Factors in Latin Prognosis TABLE IlI—(Continued) Boys’ Hiau W ADLEIGH De Wirt CLINTON Corre- ers Corre- eaOrs Corre- eae lation | Frror | lation | Brror | lation | Error 34. Teacher’s Ranking Accuracy. . .6334 | .0451 .6728 | .0364 35. Teacher’s Ranking Right Atti- tude Toward Criticism....... 5472 | .0528 .5411 | .0470 36. Teacher’s Ranking Frequency OF Hel pits tic cues nee eee cere .382388 | .0675 .3191 | .0597 37. Teacher’s Ranking Promptness .5968 | .0485 .4850 | .0509 38. Teacher’s Ranking Ability to Do Independent Work....... .6187 | .0465 .6788 | .0359 39. Teacher’s Ranking Social and Moral vA Chitudes sol acs cic ete .4710 | .0587 .5426 | .0469 Factor IX Study and Conditions for Study 40. Minutes of Outside Help Daily On: Watiits neuekoce «oe .0132 | .0460 | —.0355 | .0753 | —.0970 | .0659 41. Average Number of Movies per IW eels aaddion ae tae iets aeneete —.0872 | .0457 | —.1721 | .07382 | —.1664 | .0647 42. Average Number of Hours of Sleep daily SeeraG sata cles soe —.0070 | .0460 | —.0585 | .0751 .1249 | .0655 Factor X Individual Interests and Ambitions 43. Academic Interest as Shown by Plan After Graduation....... —.0367 | .0459 .1989 | .0739 .1850 | .0642 44, Academic Interest as Shown by Piansformlile rns eee cece —.1727 | .0446 | —.1252 | .0742 .0275 | .0664 Factor XI Outside Work 45. Time Spent Weekly Taking Music bessons? i.e sa cence .0323 | .0460 .1770 | .0730 .0880 | .0660 46. Time Spent Weekly on Any Outside Language or School SuDjeCtam che oie een ee .0979 | .0456 .1190 | .0743 .1042 | .0658 47. Time Spent Weekly in Work FOr UPAreNLS wee eeateee nese eter —.0439 | .0459 | —.0058 | .0754 | —.1029 | .0658 Facror XII Amount of Home Study 48. Average Time Spent in Study Daily baglish soda ee er .0778 | .0457 | —.2496 | .0707 | —.1456 | .0651 49. Average Time Spent in Study Daily sloatina em arenes —.1540 | .0449 | —.1433 | .07389 | —.1859 | .0642 50. Average Time Spent in Study Dailyeiology:cte eee oe —.2424 | .0710 | —.0702 | .0662 51. Average Time Spent in Study Daily, Mathematics......... .1616 | .0448 .0469 | .0664 52. Average Time Spent in Study Dailys-Civicse sean cere —.0598 | .0458 | —.2552 | .0705 .1056 | .0658 53. Average Time Spent, English Plus Civics, Plus Biology. . —.2975 | .0687 | —.0515 | .0663 54. Average Time Spent, English Plus Civics, Plus Biology, Plus Mathematics. os. soe 3001 6160 5037 0003 MT DOIK OUI on ta ig Aa oe a's Ae ese rayge: 6014 5318 0284 PCE TMRLION! 1. dha thts Gis cess okate .0847 . 2155 . 5040 . 0006 PAbetHOlalolr o..,, eset oh os ee . 3440 . 8942 SR oe a — 3847 — .0798 .6107* .1073* From Table VI we observe that age makes by far the most effective contribution, raising Beta from .5034 to .6107. Briggs Alpha adds practically nothing when Beta is in the combination. The same relation exists between the two forms of the Thorndike tests, as shown throughout this experiment. The two forms of each pair have a high self-correlation. Allen, with one from each of the three pairs of the prognosis tests in combination, secured with the criterion a correlation of .578, practically as high as with all six tests. General estimate, which is a rating of the elementary teacher and principal, ranks second, with I.Q. and elementary average a 32 Detailed Factors in Latin Prognosis close third. Elementary attendance is relatively unimportant as would be expected from the low criterion correlation. Arith- metic makes the greatest contribution among the academic sub- jects. The non-academic subjects in the combination seem more effective than the academic. The reason will be suggested later. Age was next placed in the combination, and the remaining 15 items tested for inclusion as the third factor. Table VII shows the results. TABLE VII SHowinGe Trestinc or 15 PrepictiveE Facrors ror ADDITION TO COMBINATION (Briacs Beta anp AGE) WaADLEIGH GROUP Amount added to Ty (Age) (Tio) Briggs Beta and Age, .6107 ATTA Cremer e Le ao rrie can aa Meee —.1108 . 6129 . 0022 PLHOFOCIKG Au wutnne tas be weertie cutee — .0515 .6110 .0003 Mhoriike: Byes be as ee — .0212 . 6249 .0142 Titerpolation: } iac.c cee wate os ee — .0637 .6121 .0014 Interpolation 2ieq. boa so toe — .2209 .6170 .0063 TU Ses ELE Ny, iP OG ery eee — .5708 .6110 .0003 Elementary Attendance............. — .0004 .6128 .0021 ANC RSG? Ce Sy ip eee Bw — 2537 6115 0008 Aribhiinetic £4, jhe s eee Pies.) Se — 2341 . 6168 .0061 ACE Cs G oie. meee oe ee — .1490 .6155 .0048 Axi (BAM DEY Osc ae ee oe — .0042 | .6336 0229 Ata Heit aie hed Se hh ey a Bee .0827 .6410* .0303* Piysieal Al pairing 3. 2 aang ons ae — .0723 . 6134 .0027 General Nstimate, } 2 ase 8. oe — .2796 .6275 .0168 Elementary Average................ — .1622 . 6306 .0199 Inasmuch as age enters into the I.Q., it appears that when age is in the combination, I.Q. ceases to function. On first, but not second thought, it would seem startling that the sewing and cook- ing average stands first in the above table. “If you wish to pre- dict a pupil’s success in first year Latin, secure her elementary sewing and cooking marks”’ would appear humorous to most Latin professors. Why does sewing and cooking come out ahead of, for example, arithmetic, or average (R, G, C,S)? It is evidently be- cause of its low intercorrelation with Briggs Beta. These last- named subjects, as shown by the criterion correlations, page 31, have more in common with Latin than sewing and cooking do, but they also have more in common with Briggs Beta. Hence, when Statistical Treatment 33 Briggs Beta is already in the combination, sewing and cooking make the greater contribution. Elementary average stands sec- ond, with Thorndike B a negligible amount less. Thorndike B was next placed in the combination. It was given precedence over sewing and cooking because of the less objective nature of these marks; also, incidentally, because the other two groups did not have sewing and cooking. It is probably more objective than elementary school average, and requires less labor. Table VIII shows the results. TABLE VIII SHOWING TESTING OF 14 PREDICTIVE Factors ror ADDITION TO COMBINATION (Briaes Bera, AcE, THORNDIKE B) WaADLEIGH GROUP Amount added to 7, (Thorndike B) Les) Briggs Beta, Age, Thorndike B, .6249 Briggs Alpha............... 5829 6249 .0000 PETIGEDTUIKG GN | ose tee tocoe hn « .9128 . 6322 .0073 Prlerpolraligne) sus vee eee .0950 . 6263 .0014 AMTERDOIRLION: 2. .2 5p ak os = 2451 .6318 . 0069 SCIP C Re etna td etiae Lo eate 3 7219 . 6276 .0027 Elementary Attendance...... . 0304 . 6270 .0021 MORO GE S\uee 3606 6269 0020 Mthichicees, <6 Fieeo cs .1527 . 6299 .0050 Cite AGS) ee ae . 3361 .§332 . 0083 Tee TO Aiea eee 0560 6479 0230 Av. (S and Citak eee eee . 2509 .6618* .0369* Physical Uraming; 72228... 2571 . 6259 .0010 General Estimate........... .4330 6477 0228 Elementary Average........ . 3278 6484 0235 With the exception of sewing and cooking, elementary average with a correlation of .6484 stands highest. The other items re- main in about the same relative position as in the preceding tables. From an examination of the multiple ratio correlations of the foregoing tables, it is evident that the four most objective and most consistently outstanding factors are: Briggs Beta, Age, Thorndike B, and Elementary Average. They should go into the combination in this order; yet the results would be probably not far different, no matter in which order they were combined. An examination of the criterion correlations of these four factors for the Boys High and De Witt groups indicates, by and large, a close 34 Detailed Factors in Latin Prognosis correspondence. Allowing for certain evident reasons for dis- crepancy (such as the lowering of the Boys High correlations by the selection of those still in school at the end of the third semester) we should expect from the four factors comparable multiple ratio coefiicients. ‘The procedure follows in Section C. For purely experimental reasons, however, it was decided in the case of the Wadleigh group to add to Briggs Beta, Age, and Thorn- dike B (giving sewing and cooking precedence over Elementary Average) three more of the original 17 items, solely on the basis of the amount they would add to the highest multiple ratio correla- tion coefficients. The three items proved to be: Average (sewing and cooking), Physical training, Average (penmanship, music, and drawing). Tables IX, X, and XI show the results. TABLE IX SHowine Testine or 13 Prepictive Factors ror AppDITION TO COMBINATION Brices Brera, AGE, THORNDIKE B, AVERAGE (SEWING AND COOKING) WADLEIGH GROUP Amount added to Briggs Beta, Age, 7, (Sewing and (r,) |Thorndike B, Sew- Cooking) ing and Cooking, .6618 Brigze Aina <, Soc wee ee . 2030 . 6626 . 0008 PPRorndike®A. Sy. bitciae nes . 3020 . 6629 0011 Piterpoisuonl . os, kee ee — .0148 . 6626 .0008 Interpolation’ 622.4 .< tthoe . 1268 . 6663 . 0045 DP ORS Foon tt eee nee 1754 . 6629 0011 Elementary Attendance..... .3461 . 6622 . 0004 AVALR GAR, 'S)o eile nt 4938 . 6646 . 0028 ATIENMICHG? sb Se er eae ee . 1582 . 6642 . 0024 Ary (Hy CRG ate Ge ka) au eat . 5394 . 6620 . 0002 AVG PAVED pry eee Slee 4699 .6657 .0039 Physical ‘Traming:: is. 2. ./..% 4523 .6754* .0136* General Estimate........... . 5232 . 6648 . 0030 Elementary Average........ .6918 . 6622 . 0004 When the remaining items are tested for their contributions to the combination: Briggs Beta, Age, Thorndike B, (Sewing and Cooking), Physical Training, (Penmanship, Music, and Drawing), none of them make contributions worthy of consideration. General Estimate, .6903, which stands highest, adds only .0029. It might be possible by placing a few more factors in the combination to raise .6903 to .70 or more, but the effort as shown by the above Statistical Treatment TABLE X 35 SHowine Testine or 12 Prepicrive Facrors ror ADDITION TO COMBINATION Briaes Bera, Ack, THornpike B, Sewine AND CookinG, PuysicaL TRAINING WaADLEIGH GROUP r,, (Physical feo, Training) Le RIA OS TASS ok eh oe «ates . 2095 . 6764 PE ROTUCIKGPA yy os ee aes as . 2164 .6773 BALLET POLALION Li ato ysis sien 4 . 1643 .6756 Teter pormvtlon 22" ate ts Gl . 0322 . 6782 | UE Re SR a aie ir . 1303 . 6756 Elementary Attendance...... . 38019 .6755 canis 8158 Cok GR) Ia ole Sane ae . 5099 6754 APIRIINOUG LE st. fue ec ce «> . 2621 . 6796 Ged 2 Oa C) eet ee 4485 6763 on EA tS ES Oe ge ek Be 4758 .6874* General Estimate........... . 5564 .6857 Elementary Average........ . 6749 . 6827 TABLE XI Amount added to Briggs Beta, Age, Thorndike B, Sew- ing and Cooking, Physical Training, . 6754 .0010 .0019 . 0002 . 0028 . 0002 . 0001 . 0000 , 0042 . 0009 .0020* . 0003 . 0073 SHOWING TESTING oF 11 PreEpictive Facrors ror ADDITION TO COMBINATION Brices Brera, AGE, THORNDIKE B, (SEWING AND Cooxina), PHysicaL TRAIN- ING, (PENMANSHIP, Music, Drawine) WaDLEIGH GRouUP r_,(Penmanship, ee) Music, Drawing) i RIPIBOSPA LDN Sica. ees aes .0401 .6877 PE HOINOIKE A. | cisco s ce Ze tine <> . 0680 . 6891 interpolation | os foes 0473 .6877 Interpolation’... a8 .0703 . 6899 Pe eS oe ot ee a — .0019 . 6882 Elementary Attendance...... . 2086 . 6875 WA ast ties Cre Cae) Sa ae wink es . 3886 . 6896 PPAR IIDENAG is ee nas sane 8 , 2512 . 6890 TA 1 U8 bad GAGE Deane Oe ae , 8548 . 6875 General Estimate........... .4566 .6903* Elementary Average........ . 6082 .6877 Amount added to Briggs Beta, Age, Thorndike B, Sew- ing and Cooking Physical Training, (Penmanship, Music, Drawing) . 6874 . 0003 .0017 . 0003 . 0025 . 0008 .0001 . 0022 .0016 . 0001 .0029* . 0003 36 Detailed Factors in Latin Prognosis experimental procedure would not be justified. The accretions are too small and, as previously stated, the data are not sufficiently objective for a prognosis scale. A correlation of .69 is the correla- tion with the Latin criterion, secured in the case of the Wadleigh group, when factors are selected regardless of objectivity, solely on the basis of how much they will add. C TrEstTInG oF Four Basic Factor CoMBINATION FoR Eacu Group The four basic factors selected in the Wadleigh group: Briggs Beta, Age, Thorndike B, and Elementary Average, were placed in the combination and tested for each of the other groups. Table XII shows the intercorrelations of the four factors for the three groups. TABLE XII SHOWING INTERCORRELATIONS OF Four Basic Factors ror THE THREE GROUPS Boys Hieu WADLEIGH De Wirt Ciinton Thorn- Thorn- | Elem. Thorn-| Elem. Beta Age | dikeB| Beta Age |dikeB| Av. Beta Age |dikeB| Av. Briggs Beta. —.2772) .3931 —.0798) .6014) .4451 — .2482] .2873] .1922 ABO cre acejehs — .2772 — .1225|}— .0798 — .0212|— .1622|}— .2482 — .2922)— .1865 Thorndike B.| .3931)}—.1225 .6014|— .0212 .8278| .2873|}—.2922 2514 Elem. Aver- BIO eas .4451|— .1622| .3278 — .1922)—.1865} .2514 Table XIII shows the multiple ratio coefficients when one, two, three, and four of the factors are in the combination. The accretions to the previous coefficients are also shown. We note from Table XIII that the four basic factor combination gives for the De Witt Clinton group a coefficient of .7227; for the Wadleigh, .6484; and for Boys High, .5639. The coefficients in the case of the De Witt Clinton group, as various factors are added, run considerably higher than in the case of the Wadleigh. In the De Witt group, Age, with a criterion correlation of —.57, makes a tremendous contribution. The Boys High correlations run con- siderably lower for reasons that have been explained. We have selected from Allen’s group those pupils still in school at the end of the third semester. By this selection, as seen on page 21, the Statistical Treatment 37 TABLE XIII SHow1nG MuurtieLe CoErricrENts ror THREE Groups witH Four Basic FAcrors IN THE COMBINATION De Wirt Boys Hicu WADLEIGH aren aus Amount Amount Amount ’ Added , | Added ' Added IC to IC to IC to Tic! Tic! ric Briggs Beta alone........ .5314 5034 A721 Briggs Beta, Age......... 5475 | .0161 | .6107 | .1073 | .6614 | .1893 Briggs Beta, Age, Thorn- UIKeR IA AY eee see . 5639 .0164 | .6249 .0142 | .7080 . 0466 Briggs Beta, Age, Thorn- dike B, and Elementary PAMTEYADO . Gtncta saree ys . 6484 -0235 | .7227 0147 criterion correlation of Briggs Beta has fallen from .56 to .53; Thorndike B, from .38 to .34. Also, due Jargely to this selection, the correlation of Age with the criterion in this group runs con- siderably lower. No elementary marks were obtained for this group. Had scores in the four basic factors for all of Allen’s pupils been secured, the results for this group would no doubt approximate those of the other two. D ADDITION OF OTHER Factors TO THE Four Basic Factor CoMBINATION It should be clear from the preceding pages that the applica- tion of the Toops’ multiple ratio correlation formula makes it pos- sible to construct norms at different levels. If we give one test or use one factor, we obtain a certain multiple ratio correlation. The addition of another test or factor gives a higher correlation, and so on. ‘The significance of different correlations will be indi- cated in the next chapter. To be practical administratively, the amount a test or factor adds must justify the extra effort required. It was decided to add the other factors in the experiment to the “four basic factor combination.”’ From a practical point of view it was not necessary to go through the statistical computation for every individual item. For example, the correlations of the twelve 38 Detailed Factors in Latin Prognosis traits with the criterion run close together. Having the contri- bution of one to the multiple correlation ratio, we can estimate fairly closely the contribution of another. Thus, the foregoing data in this experiment made it possible to abbreviate somewhat the complete list of items in the following ways: 1. The elementary school average showed consistently with the criterion and in the combination approximately as high a correla- tion as any elementary school mark. Being an average, it is more reliable than any of them. Hence, elementary average was the only item used for the elementary marks. 2. English and mathematics showed the highest consistent cor- relation with the criterion of any of the high school marks. So the average of the English and mathematics marks was used as a single item from the list of high school marks. The Wadleigh group did not have mathematics; so English alone was used. 3. The correlations of the twelve traits run close together for each group. ‘Two items were placed in the combination: (a) Ac- curacy. (b) Sum or composite score on all traits except “fre- quency of help.” 4. From the factor, “time spent on study,’ two items were selected: (a) Time spent on Latin. (b) Combined time spent on other subjects. , By the above plan the original list was reduced to 24 items exclusive of the “‘four basic factors.”’ Tables XIV and XV, fol- lowing, show respectively for the Wadleigh and De Witt Clinton groups the following data: 1. Intercorrelations of the 24 items with each of the four basic factors. ; 2. Multiple ratio coefficients. 3. Amount each factor adds to the four basic factor combination. Tables XIV and XV show that in each of the two groups only three items make any significant contributions, when tested with the four basic factor combination. These three factors are: (English and mathematics), accuracy, sum of traits. They add in the case of each group as follows: De Witt Wadleigh Clinton (English and Mathematics)................ 04 .07 AGCUTECY 0") 0 cps ae See ce eles ee 14 .08 Sum of Traits Gries ee peter eee Beene .16 .10 ONOORWNH CONDOR Whe Re rt OO 12 1 te Co 15 eT, 18 19 20 21 22 23 24 _ a Statistical Treatment TABLE XIV 39 SHOWING TESTING oF 24 IreMs witraH “‘ Four Bastc Facror CoMBINATION”’ . Briggs Alpha... ee: be, eee MeL HOYNCIKC Al addeces oe Mabmternolation: 1.505 .o< eee meiner polavlony 2s. icc coe: . Elementary Atte . Av. (English & Mathema- ndance.. HICS) Ge oe tehiae ores WPL OCULBOT s/o )no ae 6 sacle Pe OUMMIOL LTalts.t tous Saat . Minutes of Help MAIVEO VICES reve ele 10 bre 6.8 (6 eep . Plan after Graduation.... PEP Ia TY TOL. Lilte’. 7, See eek . Music Lessons. . . Outside Languag eee wen ws CB rita «210s bowWorkitor Parents... 3.0. Slime Spent, watin ss... 2 . Time Spent, Other Subjects . Importance of Subject.... . Preference for Subject.... . Preference for Teacher... . Extra-Curricular 3, bP Oo) 8! ow a WADLEIGH GROUP INTERCORRELATION Briggs Thorn- Beta Age dike B 8990 | —.1108 5829 6160 | —.0515 .9128 2155 0637 .0950 8942 | —.2209 .2451 6071 | —.5708 .7219 0950 | —.1691 | —.0295 0689 | —.0004 .0304 6367 | —.1329 .6670 1281 | —.2810 | —.0071 .1876 | —.2974 0424 — .0671 | —.1218 | —.1397 .0548 .0809 | —.0811 .0774 — .0418 1164 .0646 | —.2628 .0626 .0205 | —.0238 | —.0034 .0416 | —.1942 | —.0504 .0080 | —.0973 | —.0449 — .0750 . 2049 .0823 0687 .1145 . 2266 — .3106 2101 | —,2865 —.0876 | —.0225 | —.0369 — .2993 | —.1965 | —.5116 3954 | —.0558 | —.6521 1473 | —.0019 2154 TABLE XV SHOWING TESTING OF 24 IrEMs witH “‘ Four Basic Factor CoMBINATION”’ . Briggs Alpha... ee NOENGIKGrA] packets cect EinterpolabioneL sea\ cr, 5.2cr- SInterpolation: 2.3.2.0. .: Sb atkey ew eis. at ef 6 (e; © 10) 6\'8\ 161s (6, 0".6 . Av. (English & Mathe- matics) ids +’: . Minutes of Help iw OL Ov.a at a! 07's p AOCULBOY 2. vers ssa ns oe es Plt OE. Era tes ahscyseas Ree epee, o) ove) eye aS Cesare peewee 5 eek one ae ep ; . Plan after Graduation.... S Plan tor [Late 2c ooo oe te oe . Music Lessons. . ol feA SUP Ae, 0' iw ve: . Outside Language....... . Work for Parents........ Te Lime spent, LAatli~e.2... . Time Spent, Other Subjects . Importance of Subject... . Preference for Subject.... . Preference for Teacher... . Extra-Curricular eee eo eo tie De Wirt Cruinton Group INTERCORRELATION Briggs Thorn- Beta Age dike B 8640 | —.3077 BLS 2453 | —.3449 .8205 4041 — .3452 1159 4412 | —.3215 .1973 .4401 | —.6603 .6476 .1815 .0311 | —.1082 —.0063 | —.0496 | —.1250 4518 | —.4346 3137 2833 | —.5172 1923 2873 | —.4589 1738 — .1631 .0964 0302 — .1163 .0740 | —.1276 .0335 | —.2194 1451 2350 — .1250 rLLoL 0899 — .2141 — .0088 1155 | —.1381 | —.0037 —.0006 | —.1006 | —.0170 0276 1442 — .1633 — .1319 1061 | —.1882 — .0865 .0934 — .1946 — .0434 | —.1038 1091 2453 | —.3968 2277 2219 — .2401 3741 0384 .0089 0739 40 Detailed Factors in Latin Prognosis Preference for teacher adds .07 in the case of Wadleigh, but only .01 in the case of De Witt Clinton. Preference for subject adds .02 and .03, respectively, for the two groups. Movies, and aca- demic interest as shown by plan for life work, each adds .02 in the case of Wadleigh, but neither factor makes any contribution to De Witt Clinton. The contributions of all other factors are insig- nificant. Inasmuch as (English and mathematics), accuracy, and sum of traits do not belong to the purely predictive class of factors, Tables XIV and XV verify the fact that, for predictive purposes, the four basic factor combination is in all probability the best com- bination. Sum of traits, which includes accuracy, makes a greater contri- bution than accuracy alone. Both accuracy and sum of traits make a greater respective contribution than (English and mathe- matics). Hence, it was decided to retain sum of traits in com- bination with the four basic factors and to add (English and mathematics). With five factors in the combination: Briggs Beta, Age, Thorndike B, Elementary Average, Sum of Traits, the multiple ratio coefficients are .8049 and .8239, respectively, for Wadleigh and De Witt Clinton. Adding English to Wadleigh and (English and mathematics) to De Witt Clinton, the coeffi- cients become .8241 and .8400, respectively. These two multiple ratio coefficients, with six factors in the combination: Briggs Beta, Age, Thorndike B, Elementary Average, Sum of Traits, (English and mathematics), are the highest accumulated correlation co- efficients obtained in this experiment. They were obtained by sifting the data of the sixty items of the experiment for elements in common or indicative of success in first year Latin, as measured by the Latin criterion tests used in the experiment. As stated previously, four of these items belong to the purely predictive type: Briggs Beta, Age, Thorndike B, Elementary Average. The fifth factor, Sum of Traits, is “‘affective’’; the sixth, (English and mathematics), is predictive in the event that first year Latin be not commenced until the second semester. Otherwise, it is affec- tive or relational. It will be recalled that, in the case of the Boys High group, ele- mentary average and sum of traits are lacking. Thus, we have for this group only four of the six factors selected above, and only three of the four basic factor combination. An examination of Statistical Treatment 41 the low criterion correlations of many items of this group shows a close correspondence with the criterion correlations of the other two groups. Reference to Tables XIV and XV shows that such low criterion correlations can make no significant contribution, and that the testing of them is a waste of time. It was decided, therefore, to test the following eight items with three basic factors in the combination. ‘The results are shown in Table XVI. TABLE XVI SHOWING TEsTING OF 8 ITEMS witH THREE Basic Factors IN THE COMBINATION Boys Hicu Group INTERCORRELATION Amount Added . ey) to Briggs Ape Thorn- foal Beta dike B 5639 High School Attendance.....| —.0515 | —.0274 | —.0577 | .5639 . 0000 English and Mathematics... . .5037 | —.2503 4347 | .6558* | .0919* Preference for Teacher...... — .0448 .0615 | —.0237 | .5786 .0147 Binsrnciice A Se) ose ees .9752 | —.1320 8072 | .5669 0030 Interpolation’) © o.can. « oers .3194 | —.1932 3070 | .5667 0028 PreeETOaONiee-. tek ote .1994 | —.1887 .1710 | .5640 .0001 Briggs Alpha............... 8203 | —.2255 3987 | .5640 | .0001 LO io eae te MER sui Si ee gn ni 4848 | —.2143 5809 5652 0013 (English and mathematics) gives a correlation coefficient of .6558 when added to the combination. It contributes .09, prac- tically the same as in the case of the other two groups. Preference for teacher adds .01. The other additions are even more trivial. For this group, in which only four of the six factors used in the other two groups are available, the highest correlation coefficient obtained is .6558. CHAPTER V PRACTICAL IMPLICATIONS In this experiment, multiple ratio correlation coefficients have been secured for the following combinations: 1. The four basic factor combination: Briggs Beta, Age, Thorndike B, Elementary Average. 2. The six factor combination: Briggs Beta, Age, Thorndike B, Elementary Average, Sum of Traits, Average (English and Mathematics). 3. The Allen Prognosis Battery: Briggs Analogies Tests, Alpha and Beta; Thorndike Word Knowledge Tests A and B; Rogers Interpolation Tests 1 and 2. 4. The Allen Prognosis Battery plus Age and Elementary Average.! 5. The seven factor combination for the Wadleigh group: Briggs Beta; Age; Thorndike B; Sewing and Cooking; Physical Training; Penmanship, Music, and Drawing; General Estimate. TABLE XVII SHowING MuttieLe Ratio CoErricieENts oF ALL COMBINATIONS FOR THREE GROUPS Boys High | Wadleigh | De Witt Clinton . Four Basic Factor Combination. . . . 56394 . 6484 7227 1 2, Six Factor Combination......... . 6558» 8241 . 8400 8. Allen Prognosis Battery.......... . 5634 . 6672 4, Allen Prognosis Battery plus Age and Elementary Average....... . 6582 TATA 5. Seven Factor Combination for the Wadleigh Group. ............- . 6903 8 Hlementary average lacking. b Elementary average and sum of traits lacking. Table XVII shows the correlation coefficients obtained for these combinations with the three groups. Only three factors of the four factor combination are present for the Boys High group: 1 Age alone raises Allen Battery to .6419 and .7324 for Wadleigh and De Witt Clinton, respectively. 42 Practical Implications 43 Briggs Beta, Age, Thorndike B. Only four factors of the six factor combination are present for the same group: Briggs Beta; Age; Thorndike B; Average of English and Mathematics. In the practical interpretation of the above coefficients, two questions suggest themselves: First, in terms of the data of this experiment, what do the correlation coefficients for these five combinations represent? 1. The first combination consists of four predictive factors, that is, factors for which objective data may be secured before the pupil begins the study of Latin. 2. The second combination consists of four predictive factors, a fifth which is “‘affective,” and a sixth which is predictive in the event that first year Latin be not commenced until the second semester. This combination shows the achieve ment of pupils of a given age and capacity who in the judgment of the individual teacher possess certain traits of character and of industry. 3. The third combination is predictive and consists of six ob- jective factors. 4. The fourth combination consists of eight objective factors, all of which are predictive. 5. The fifth combination consists of three objective factors and four of a less objective nature. The second question which suggests itself is, ““What do these correlations mean? How are they to be interpreted?” No one can tell with absolute accuracy just what a coefficient of correlation means. Professor Edward L. Thorndike in Tables XVIII and XIX, which are used here with his permission, has given the best approximation. Table X VIII shows when the cor- relation of any factor or combination is .60, that 39.2 per cent of the first tenth will be placed in the first tenth, 20.4 per cent of the second tenth will be placed in the second tenth, 13.7 per cent of the third tenth in the third tenth, andso on: Table XIX shows the distribution of successive tenths of the group when the correla- tion is .80. In this case, 56.2 per cent of the first tenth will be placed in the first tenth, 23.1 per cent of the second tenth in the second tenth, and so on. Of all the correlations in Table XVII, Figures 1 to 4, with the discussion which follows, illustrate the significance of four specific Ad Detailed Factors in Latin Prognosis correlations. They range from .5634 to .84. Figure 1 shows for the Wadleigh group the distribution of pupils on the Allen Prognosis Battery and the Latin criterion, correlation .5634. Figure 2 shows for the Wadleigh group the distribution of pupils on the six factor combination and the Latin criterion, correlation .8241. Figure 3 shows the distribution of pupils for De Witt Clinton on the Allen Battery and the Latin criterion, correlation .6672. Figure 4 shows the distribution of pupils for the De Witt Clinton group on the six factor combination and the Latin criterion, correlation .84. The composite score of pupils in each of the above combinations was found by the method explained on page 16. The constant quo- tients were obtained by dividing the true weight of a factor by its sigma. By a careful examination of Figures 1 to 4 in relation to pupil achievement, as measured by the teacher’s mark at the end of the semester, the following facts are revealed. A WaDLEIGH GROUP On Figs. 1-4 the circles indicate the pupils who failed Latin. Of the 80 pupils, 11 or 13.75 per cent failed Latin for the semes- ter, the passing mark being 60 per cent. Although the criterion was not used as final examination, 100 per cent of the failures were below the average on the criterion; 81.8 per cent were below the average on the Allen Battery. If we choose some arbitrary score, such as 8 on Figure 1, we find that 54.5 per cent of the failures and four pupils who passed are below 8. The average mark of these four is 81.25 per cent; 63.6 per cent of failures and nine who passed fall below 9 on the Allen Battery. The average mark of those who passed was 78 per cent. On the six factor combination (Figure 2), 18.2 per cent of the failures and no one who passed fall below 3; 27.3 per cent of the failures and no one who passed fall below 4; 72.7 per cent of the” failures fall below 5, that is, in the lowest decile, with no one who passed included. B Dre Wirt CLinton GRouP In the case of the Allen Battery, 20 per cent of the failures and seven pupils passed by the faculty are below 8. The average Practical Implications AD ¢ EEE gE tet totter te eee a ae / UU SES 2a Da a DL TR ee TT SE RS | Wa EECA tet PE _ 0 We \\ a | cy calcd al ES Fa DD tre FH Q ee oer ee ye rien nr anlar | fo SUES ed ea | ON TTS a Bad a oa Ts | Ve + NCS EATS ed (a 2c GT EH ST A | 3 a} } Hy sp a ee oe We ik on | ea a eS | ie da 24S NT aR SB 2 P| ee 0 a Fe a ONS | a8 P| ° 1 ed 3 + 5 10 it [a tS 4 tS) IS 17 ME AN-IL-8 LATIN CRIT & RibO'N: Figure 1. SHowi1na DistrRiBuTIon or WADLEIGH GROUP ON ALLEN PROGNOSIS BATTERY AND THE LATIN CRITERION ey SS 2 TE Ba ee Ee | LA Ee oe / Raa ESR gepzeeeenoad usnee ial i MEAN 2 SS ae ee ea a | ial SIX FACTOR COMBINATION. | Sn Be Seas ek Sat) Sep NN Rh pe be eB eee es et eG en Bo) SiO th eS. 1A CIS. 16 OF MEAN-I1.& LATIN CRITERION. Figure 2. SHowrne DISTRIBUTION OF WADLEIGH GROUP ON THE “Srx Factor CoMBINATION”’? AND THE LATIN CRITERION 46 Detailed Factors in Latin Prognosis eee eo 16 PREM cn ke = RM RMRIGRSILEC Doicicnen TRIG mses ES may, S Ee, ars rai te a aie is mets a Po far ee yA Se On| _7 Wi Mean. ee ah o Ml oa i z § oi Pe et eal aS ROR Me Re PEE Sie a is BS) cA oe Aa Rise ae a ee fata i a xf ee Be ek Nee Remen re oe fa DAB es c= pe I le Set ea aa 2 AO SIL Ie SO NE TS oe MEAN-1.8& LATIN CRITERION. Figure 3. SHowi1ne DIstrRiBsuTion or DE Witt Ciinton Groupe on ALLEN Prognosis BATTERY AND THE LATIN CRITERION Son ea SF Ost = ats Ns So eas MEAN-II-8 LATIN CRITERION. ee Figure 4. Snowrne Distrrsution or Dr Wirt Ciinton Group ON THE “SIX Factor CoMBINATION” AND THE LATIN CRITERION Practical Implications AT mark of these seven pupils is 75 per cent. Forty per cent of the failures and fourteen who passed are below 9. The average of these nine is 74.6 per cent. In the case of the six factor combination, 40 per cent of the failures and one pupil who passed are below 3. The mark of this one pupil is 65 per cent. Ninety per cent of the failures and six pupils who passed are below 4. The average of these four pupils is 66.66 per cent with no one above 75 per cent. One hundred per cent of the failures and ten who passed are below 5, that is, in the lowest quartile. These ten have an average mark of 69 per cent with no one above 75 per cent. The lowest decile in- cludes 60 per cent of the failures with only two who passed. The average mark of these two is 70 per cent. The preceding analysis shows that the six factor combination is very much more effective than the Allen Prognosis Battery in selecting pupils on the basis of achievement. While this is true, it must be recognized that the six factor combination contains two factors not actually obtainable until the pupil is in high school: Sum of Traits, English and Mathematics. The Allen Prognosis Battery, with Age and Elementary Average also in the combination, giving correlations of .6582 for Wadleigh and .7474 for De Witt Clinton, would probably show a selective efficiency midway between the Allen Battery and the six factor combina- tion. The relative selective ability of the various correlation coefficients, given in Table XVII, may be approximately obtained from Tables XVIII and XIX and the foregoing illustrations. TABLE XVIII DISTRIBUTION OF AVERAGE OF SUCCESSIVE TENTHS OF THE GROUP WHEN r=.60 (APPROXIMATE) tat tenth... hsv. 2 “8 eS 29 4.6 6.6 9.7 | 18.7 | 20.4 | 39.2 2nd tenth....... Hv, 2.6 4.3 6.0 8.2 | 10.38),-18.0 | 15.6 | 18.7 | 20.4 Srd tenth. ...:... 1 os: 4.3 6.4 res LO de | ee else deen ah oot mel ede Com ee One Cree ime eden dy 4th tenth....... 2.9 6.0 8.2 9.8 | 11.4 | 12.4 | 13.2 | 13.5 | 13.0 OE Sth tenth....... 4.6 SeZe MLO gl tale ZEON 2 Os bares etl iene 6.6 6th tenth....... CEOs On Se UIT L2eA eos Qala Ose 8.2 4.6 PUM CENED yes ac OA ele Oe ls OUP loe2e lta Aa Ve. 4 9.8 8.2 6.0 2.9 Sthetenth sa... « LS Vim L Oc Omi lei srl arom et legal LOee 8.2 6.4 4.3 1.8 Oth tenth. ...... 20.4 | 18.7 | 15.6 | 13.0 | 10.3 8.2 6.0 4.3 2.6 A 10th tenth....... 39.2 | 20.4 | 13.7 9:7 6.6 4.6 Zine 1.8 3, .2 This table was computed by Professor E. L. Thorndike and is used here with his permission. Detailed Factors in Latin Prognosis 48 TABLE XIX DISTRIBUTION OF ARRAYS IN SUCCESSIVE TENTHS OF THE GROUP WHEN r=.80 9th 8th 7th 6th 5th 4th 3rd 2nd Ist 10th Areas tHoOnte Pr yl ia ee ee eee a LN COIS PLO NL N aes OIADOWOOVOr NO 09190 OLIDN OD Hes ronan ian ian ie MFOOWMMOANINS ra HOD N19 O19 OD CON Soon len fan fan a SHIDO NO DOr H O21 DAO & Dh 0910 anne MODOOANRHOr ANMOMM~-OOM mrAANnd OOH OO INO rs MPN HOM OO OD MANNS AHR OMHHN Ist tenth 2nd tenth 3rd tenth 4th tenth 5th tenth 6th tenth 7th tenth 8th tenth 9th tenth 10th tenth. CHAPTER VI SUMMARIZED CONCLUSIONS I. The Briggs Analogies Tests, of all factors used in this experi- ment, are the best single objective measures for predicting achieve- ment in first year Latin. Either Alpha or Beta has a consistent average correlation of .50 with the Latin criterion tests given at the end of the semester. II. The Allen Battery of prognosis tests: Briggs Analogies Alpha and Beta; Thorndike Test of Word Knowledge A and B; Rogers Interpolation 1 and 2, predict Latin achievement for dif- ferent groups, with an average correlation of .60 or above. Allen obtained a correlation of .588 for 364 pupils in the Boys High School, Brooklyn. The writer, with the Allen Battery, secured a correlation of .563 for 80 girls at Wadleigh High School, and a correlation of .667 for 103 boys at De Witt Clinton High School. By the addition of age and the average of all marks for the last year of the elementary school, to the Allen Battery combination, the correlations were raised to .658 and .747 for Wadleigh and De Witt Clinton, respectively. Allen’s tests require 70 minutes of time, and the last two factors come from the school record. III. The four predictive factors: Briggs Beta, Age, Thorn- dike B, Elementary Average, give in combination a correlation of .648 for Wadleigh, and .723 for De Witt Clinton. To secure data for the first and third factors requires 26 minutes of testing. The other two are items of ordinary school record. When the Latin teacher’s judgment of pupils on eleven character and indus- try traits is added, as a fifth factor, to the above combination, the correlations become .805 and .824. To obtain this factor requires approximately an hour of the teacher’s time. High school Eng- lish added as a sixth factor to the Wadleigh group raises the corre- lation to .824. An average of high school English and mathe- matics added to the De Witt Clinton group raises the correlation to .840. The last factor is also an item of school record. IV. The following seven predictive factors: Briggs Beta; Age; Thorndike B; Sewing and Cooking; Physical Training; Penman- ship, Music, and Drawing; General Estimate; in combination, gave 49 50 Detailed Factors in Latin Prognosis for the Wadleigh group a correlation of .690. ‘The marks in this combination are for the last year of the elementary school. The factors for this combination were selected solely on the basis of how much they would add, regardless of their objectivity. V. The highest correlation coefficients for the Boys High group are below the highest for Wadleigh and De Witt Clinton. Two reasons for this are evident. First, two factors, Elementary Av- erage and Sum of Traits, are lacking for this group. Second, Allen’s original correlations were greatly reduced by the selection of 215 of his original 364 pupils still in school at the end of the third semester. The following four factors in combination: Briggs Beta, Age, Thorndike B, Average of English and Mathe- matics, give for this group a correlation of .656. APPENDIX ! Forms of the same Latin criterion tests were given to the Wadleigh and De Witt Clinton groups at the end of the second semester. There were 60 pupils still in school and available at Wadleigh, 67 at De Witt Clmton. Tables XX and XXI show the respective results for the two groups, using the data of the six factor com- bination that were secured the first semester. This combination consists of: Briggs Beta, Age, Thorndike B, Elementary Average, Sum of Traits, English and Mathematics (English alone in case of Wadleigh). Tables XX and XXI show that the correlations of the six factor TABLE XX SHOWING THE Six Factor CoMBINATION FOR THE SECOND SEMESTER WaADLEIGH GROUP INTERCORRELATION é Corre- | Amount CS —— | lation to Added terion Combi- tH Grol teres Thorn-| Elem. | Sum nation| ,, Age dike | Aver- of Eng- (r-/) Ic Beta B age | Traits] lish Ic Briggs Beta... . 2336 . .0854| .6870]} .3820|/—.0082] .4885] .2336 (A PORE hace ee —.0514] .0854 — .0003] — .1296} —.0303] —.1028] .2443 .0107 Thorndike B.. 3063] .6870} —.0003 .38550) —.0551] .6845) .3105 .0662 Elem. Average.| .3983] .3820}—.1296] .3550 .2669| .2262) .4327 ml 22 Sum of Traits. .3603} — .0082} —.0303] —.0551} .2669 Salalah an teye .0860 DIEING ivan ae .38460} .4885)—.1028} .6845} .2262) .1157 .5400 .0213 TABLE XXI SHOWING THE Srx Factor COMBINATION FOR THE SECOND SEMESTER De Wirt Ciinton Group INTERCORRELATION Corre- | Amount Cri- - ete Added terion ombi- to 4 Thorn- | Elem. Sum Eng- . (xc) | Briges| Age | dike | Aver- | of |lish and Sa. hee Beta B age | Traits | Math. Ic Briggs Beta... 4404 — .2446 2559 -1300D .1745 .4531] .4404 Te en a — .5380| —.2446 — . 2690] — .0806] —.3772| —.3899| .6252 . 1848 Thorndike B.. 2851 2559] — .2690 2921 0074 SPE ETAL worn Oi .0055 Elem, Average. 1425 . 1355} — .0806 2921 .1895| .4735) .6320 .0013 Sum of Traits. 5291 .1745| — .3772 .0074 . 1895 .4515| .7106 .0786 English and Wath: 2565 .6115] .4531] —.3899 DESY .4735}| .4515 . 7443 .0337 1 Tables showing complete data for this study are on file in the Teachers College Library. 51 52 Detailed Factors in Latin Prognosis combination for the second semester are .54 and .7443, respec- tively, for the Wadleigh and the De Witt Clinton groups. These are considerably lower than for the first semester. Selection has no doubt made the group more homogeneous, as proved to be true when Dr. Allen’s original group of 364 was reduced to 215. Inthe second place, the criterion tests in their present form seem designed primarily for the first rather than the second semester’s work. To be equally satisfactory for the second, they should be revamped to measure the specific material studied during the second semes- ter. This was not practicable in the present experiment. It would involve the development of a new set of tests, destroy comparability, and complicate the main problem. To devise a new set of tests, based on the same technique but designed pri- marily for material of the second semester, is suggestive for future experiment. It would make possible a more thorough testing of the combinations developed in this study. 00