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There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924029194665 Changes in Mental Traits with Age Determined by Annual Re-Tests By FOWLER DELL BROOKS Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy^ in the Faculty of Philosophy, Columbia University Published by teachers College, Columbia WLnibttaitp New York City i 9 2 I Changes in Mental Traits with Age Determined by Annual Re-Tests By FOWLER DELL BROOKS Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, in the Faculty of Philosophy, Columbia University Published by TEcachet* College. Columbia ©ntberfiitp New York City i 9 2 I V ;*■ oo uk i 1. 1- U w I V I u {• I 'r V: Copyright, 192 1, by Fowler Dell Brooks 3?- f\SlOS23 ■*e 3 e < ACKNOWLEDGMENT To the late Professor Naomi Norsworthy and to Professor E. L. Thorndike, of Teachers College, I am indebted for suggestions which led to the selection of the problem of this research. Stim- ulating, helpful supervision of the work of this research is but one of the many things for which I am deeply indebted to Professor Thorndike. For their cooperation in giving the tests I am under obligation to the critic teachers of the intermediate and junior high school departments of the Training School of the Mankato, Minnesota, State 1 eachers College. Very great assistance has been rendered by my wife, Stella Nattier Brooks, in scoring papers, calculating coefficients of cor- relation and correcting them for attenuation, making long and tedious computations for tables, and checking all calculations. F. D. Brooks CONTENTS PAGE I. Purpose and Plan of Investigation . i II. The Subjects: The Tests ...... 3 III. Historical Survey of Experimental Data on Age and Changes in Mental Traits . . . . 7 1. Introduction ... ... 7 2. Non Re-Test Experiments . . . . . . 8 3. Re-Tests of the Same Individuals 17 4. Data Recalculated for Direct Comparison with Results of Min- nesota Re-Tests 23 IV. Status of the Subjects by Age and Sex . .... 28 V. Amount and Rate of Yearly Improvement . . 37 1. Method of Treating Data 37 2. Rate of Improvement in Simpler Mental Functions 44 3. Rate of Improvement in Memory Functions . 46 4. Rate of Improvement in Higher and Informational Functions 48 5. Rate of Improvement Shown in Tests Grouped upon D fferent Bases of Classification ... 52 6. Conclusions as to Rate of Improvement . 52 7. Sex Differences .... . 53 VI. Rates of Gain Shown by Other Investigations: Rates of Gain from Combination of Other Data with Minnesota Re-test Data . . .... 56 VII. Current Psychological Opinion and the Results of Re-Tests 70 VIII. Correlations between Mental Traits at Different Ages 74 IX. Correlations between Gains in Different Groups of Func- tions for a Two- Year Interval 78 X. Correlations between Intellectual Ability and Rate of Improvement . . 81 XI. Summary 83 XII. Bibliography . 85 INDEX OF FIGURES NUMBER PAGE i-a to 7-b Distribution of Subjects by Age, Sex and Grade .... 29 8 Sigma Gains in Simpler Mental Functions by Age and Sex, Min- nesota Re-Test Data . -45 9 Sigma Gains in Memory Functions by Age and Sex, Minnesota Re-Test Data . . . .... 45 10 Sigma Gains in Higher Functions by Age and Sex, Minnesota Re-Test Data .... .... 50 11 Sigma Gains in Informational Functions by Age and Sex, Minnesota Re-Test Data 5° 12 Sigma Gains in Simpler Mental Functions by Age and Sex, Composite Average of All Data ... .... 66 13 Sigma Gains in Memory Functions by Age and Sex, Composite Average of All Data ... 66 14 Sigma Gains in Higher Functions by Age and Sex, Composite Average of All Data .66 TABLES PAGE I. Showing the Average, Standard Deviation, P.E.t.-obt.av., and P.E.t.-obt. s.d. for Each Sex at Each Age in Each Test . ... 31 II. Showing the Number of Boys and Girls of Each Age Taking the Tests 36 III. Per Cent of Boys at Each Age, Equalling or Exceeding the Median Girl's Score of the Same Age in Each Test 36 IV. Showing the Number of Boys and Girls of Each Age making the Improvement shown in Tables V, VI, and VII . . . 37 V. Median Yearly Improvement in Gross Score for Each Age, Sex, and Test ... . . ... 38 VI. Data of Table V, divided in Each Case by the Appropriate Average Standard Deviation of Ages Eleven, Twelve, and Thirteen . . 40 VII. Average Gains, Four Groups of Similar Functions, in Terms of the Average S.D. of Ages Eleven, Twelve, and Thirteen: for Boys and Girls 43 VIII. P.E. (in Terms of the S.D.) of Yearly Gains for Each Age and Sex in Each Group of the Similar Functions 44 IX. Showing the Yearly (S.D.) Gains in the Two Immediate Memory Tests, Nos. 11 and 12 47 X. The Yearly Sigma Gains in Tests of Higher and Informational Functions, Each Test being Given a Weight of One 48 XI. Average Yearly Gains in Terms of Sigma, for Simpler Mental Functions, for Data from Other Investigations . . 57 XII. Average Yearly Gains in Terms of S.D. for Memory Functions, for Data from Other Investigations . . 58 XIII. Average Yearly Gains in Terms of S.D. for Higher Functions, for Data from Other Investigations 59 XIVi Average Yearly Gains in Memory and Higher Functions in Terms of the S.D. for Pyle's 1920 Data ... 59 XV. Average Yearly Gains in Simpler, Memory, and Higher Functions, in Terms of the S.D., Woolley Re-Test Data 60 XVI. Average Gross Gains in Memory — Netschajeff 63 XVII. Average Gross Gains in Memory — Lobsien 64 PAGE XVIII. Composite Average of Data from Tables VII, XI to XV, formed by Giving the Following Weights: Minnesota Re-Test Data, 10; Woolley Re-Test Data, 10; Gilbert, i; Pyle 1913, 3; Pyle 1920, 3; Bickersteth, 3; Oxford Girls, 3 ; Dewey, Child and Ruml, 4. . . 64 XIX. Number of Cases in Table XVIII at Each Age . 65 XX. Composite Average of Data from Tables VII, and XI to XV, formed by Assuming Growth from 9 to 15 the Same inAll Investiga- tions, and by Giving the Same Weights as in Forming Table XIX . 68 XXI. Correlation between Mental Traits Measured at a Two- Year In- terval, Uncorrected . . . . . ... 75 XXII. Correlation between Mental Traits Measured at a Two-Year Interval, Corrected for Attenuation . . 75 XXIII. Correlation between Two-Year Gains in Different Groups of Func- tions, Uncorrected . 78 XXIV. Correlation between Two-Year Gains in Different Groups of Functions, Corrected for Attenuation 79 XXV. Correlation between Intellectual Ability and Amounts of Gain in Different Groups of Functions, Measured at a Two-Year Interval: Uncorrected and Corrected for Attenuation . . . 81 PURPOSE AND PLAN OF THIS INVESTIGATION In discussing the influence of maturity upon individual differ- ences, Thorndike (1914, pp. 275ff.) points out the complexity of the problem in the respect that changes in an individual's mental traits with age may possibly be due to at least three factors: (1) the maturing of the trait, (2) the influence of training upon it, and (3) " the influence of both maturity and training upon the ability to understand and the wish to follow instructions and the ambition to do well in tests." He further insists that a knowledge of differ- ences in mental traits with age does not tell us much about the influence of maturity upon these changes unless we can parcel out their causes among these three factors, and, that such parcelling out is practically impossible. Turning to the more general problem of changes with age he says, " So far upon the supposition that by changes in mental traits with age, we mean changes in the same individuals measured at different ages. The average change would then be the average of the changes in all the individuals studied. But in the studies that have been reported, the difference between the figures for, say, ten and eleven years, is not the average of the changes of all the individuals studied and need not in any real way describe them. " For (1) the difference between the average of a group at ten and of the same group at eleven years does not describe the real individual changes; and (2) when we measure ten- and eleven- year-olds as we find them in school or elsewhere, we cannot be sure that the eleven-year-olds represent what the ten-year-olds will become . . . To measure the development of mental traits with age we must repeat measurements upon the same individuals and for all purposes of inference preserve intact each of the individ- ual changes." This investigation seeks to find out what changes in mental traits take place with age, and it seeks to find them out in the only way they can be found out accurately — by discovering what changes actually do take place in the same individuals from one 2 Changes in Mental Traits with Age year to another. This involves re-testing the same individuals and giving appropriate statistical treatment to the resulting data. Two other purposes are (i) to investigate the correlation between mental functions at different ages of the same individuals, and (2) to study the relation of intellectual ability to rate of improve- ment over a longer period of time than has heretofore been reported upon — two years in this case. II THE SUBJECTS AND THE TESTS The subjects were one hundred and seventy-one children en- rolled in grades four to nine of the Training School of the Mankato, Minnesota, State Teachers College. They ranged in age from nine to fifteen, and represented a random sampling of various social and economic groups. Practically all of them had been tested by educational or psychological tests before taking the tests given in this investigation. Great care was taken that the conditions of testing, the way the tests were given, and the method of scoring should be uniform and according to the directions usually given in connection with each of the tests. There was practically none of the carelessness or lack of honest effort which is sometimes notice- able when a long series of tests are given by persons not connected with the schools in which the tests are given. The following tests were selected and were given in May, 1918, in May, 1919, and in May, 1920.. 1. Number Checking. Woodworth- Wells Number Checking Tests. Four tests were given each year, crossing out 5's, 7's, 4's and 8's. Ninety seconds were allowed for each test. The score is the sum of the correct cancellations in each test. Omissions and wrong cancellations were very rare, and have been neglected in scoring. 2a. Handwriting Quality. Quality of handwriting in ordinary written work. Class-room teachers selected at random two different sets of papers handed in by children in the ordinary school sub- jects. These sets were written a week to ten days apart. They were scored according to the Ayres scale, Gettysburg edition, the mid- point scores on the scale being given, and were all scored by a thoroughly competent person. The score given is the sum of the scores on the two papers. 2b. Handwriting Quality. Quality of handwriting on two tests in handwriting, given a week to ten days apart. Scored as in 2a. The score is the sum of the scores on the two tests. 2C. Handwriting Speed. The two tests of 2b were also scored for 4 Changes in Mental Traits with Age * speed. The score is the sum of speeds in two tests, expressed in letters per minute. 2bc. Handwriting Quality and Speed. As a single quantity to represent the handwriting achievement the quality and speed of 2b and 2c were combined by using the arbitrarily chosen formula: Score = Quality + >^ speed. 3. Spelling. Sixty words from columns Q, S, and U of the Ayres Spelling Scale were used. The words were dictated in simple sen- tences, the pupils copying the sentences. The score is the number of words correctly spelled. 4. Visual Vocabulary. Thorndike Reading Scales A2 and B, Visual Vocabulary. Both tests were given as follows: h.2% and Bx in 1918 and 1920, and A2y and By in 1919. Comparable parts of the tests were counted so that total possible scores each year were the same. The score is the number of words correct on the two tests, the highest possible score being 190. 5a. Courtis Arithmetic, Form B, Attempts. The four fundamental operations were tested. The score is the sum of the number of prob- lems attempted in the four tests. 5&. Courtis Arithmetic, Form B, Rights. The four fundamental operations were tested. The score is number of problems right in the four tests. 3ab. Courtis Arithmetic, Form B, Combined Attempts and Rights. Combined by the formula: Score = Average of attempts and rights. 6. Woody Arithmetic Scales, Series A. The four fundamental operations. The score is the sum of the problems right in the four tests. 7. Stone Reasoning Test. Stone's directions for scoring were followed, additional weight being given for the more difficult prob- lems, and credit being given for all correct reasoning steps regardless of the numerical computations. 8. Composition. The subjects wrote for fifteen minutes on the common subject, "What I Would Like to Do Next Saturday." The papers were scored by five competent judges, on the basis of the Nassau County Supplement to the Thorndike-Hillegas scale. The score is the average of these five scores. q. Opposites. Woodworth-Wells, first list beginning "long, soft." Responses that were correct for any commonly accepted meanings of The Subjects and the Tests 5 the words were scored one. Time, 120 seconds. The highest possible score is 20. The score is the number right. 10. Directions. Pintner-Toops Directions Test. Given and scored according to directions given in Journal of Educational Psychology, March, 191 7. A perfect score is 27, being that of superior adults. 11. Immediate Auditory Concrete Memory. Whipple's three-, four-, five-, six-, seven-, and eight-term lists used. The score is sum of words recalled and written down, regardless of order. Perfect score is 33. 12. Immediate Auditory Abstract Memory. Whipple's abstract lists. Score is sum. of words recalled regardless of order. Perfect score is 33. 13. Memory for English Equivalents of Italian Words. On each of three consecutive days pupils were given a printed list of twelve Italian words and English equivalents. Three minutes were allowed for study. These slips were then collected, and printed test slips (containing the Italian words in different order from that of the study lists) were distributed. Two minutes were allowed to write the English meanings. The nine lists used for the three yearly testings were arranged to include words that seemed of approximately equal difficulty, though no attempt was made to standardize them scientifically. The writer doubts very much, however, from a study of the results that the three lists of any year were on the whole equal to the three lists given in any other year. The score is the sum of number of correct English words given in three lists. Perfect score is 36. 14. Substitution, Woodworth-Wells. Five Geometric Forms. Time allowed, 90 seconds. Omissions were very rare. Score is number right minus number of wrong substitutions. 15. Letter-Digit Substitution. Three different tests. At the top of page were printed the ten digits. Under each was printed a letter. Below this key were printed in four rows one hundred ten digits in mixed order. Subjects were allowed 120 sees, on each test, to make the substitutions in consecutive order from the first. The same three tests were given each year. Scores were computed on basis of number right minus number of wrong substitutions. Omissions were very rare and were not considered in scoring. Score is sum of scores on three tests. Perfect score is 330. 6 Changes in Mental Traits with Age 16. Reasoning. Part of omnibus test devised by Thorndike and McCall. The score is given in terms of penalties. For the parts used a perfect score would be zero, while the poorest possible score would be 36. 17. Trabue Language Completion Scales. Scale C was given in 1918, scale B in 1919, and scale D in 1920. Scored according to Trabue's directions, each sentence scoring 2, I, or o. Perfect score is 20. 18. Thorndike Reading, Alpha 2, Paragraph Reading. Papers scored, using Kelley's tables for computing individual scores (Teachers College Record, May, 1917). 1 p. Army Alpha. Given to those tested in 1920. Scored according to directions given in manual. 20. Thorndike Group Intelligence Test, III, Series L. Given to group tested in 1920. Given and scored according to directions furnished by the author. The following tests were not given in all three years: 10, iq, and 20. Test 10 was given in 1919 and 1920, the other two being given in 1920 only. Twenty-six of the subjects took the following tests only: Nos. 1, 2a, 2b, 2c, 4, 8, 11, 12, 13, 14, 15, 17, 18 — twice, at year intervals. Seventy-eight of the subjects took all of the tests two years. Sixty-seven of the subjects took all of the tests three years. Ill HISTORICAL SURVEY OF EXPERIMENTAL DATA ON AGE AND CHANGES IN MENTAL TRAITS I . INTRODUCTION It is not within the scope of this investigation to consider the literature on the relationship between mental and physical devel- opment. Those who desire experimental data on this problem will find extensive bibliographies in Whipple (1910, 1914), Burk (1898), Meumann (1907, 191 1), and in the Psychological Review Index. Experimental work first concerned itself with testing one or more functions in one or more individuals — usually adults — to illustrate some psychological law or principle. Then the question of the development of different functions led to the examination of children. The earlier studies were often limited to experiments upon a few children of two or three grades or ages ; quite often they were qualitative in character and more or less complex. Later there were devised simpler tests, the results of which could be treated quantitatively. Such quantitative results were often reported according to the grade the child had reached in school, the age, if mentioned at all, being the average age of the grade. There are numerous experimental studies which seek to trace the devel- opment of mental functions in this way. Greater refinement and precision in the technique of measurement have finally led to carefully devised, standardized, objective tests and exact quan- titative treatment of results, and to the reporting of results, not only by grades but also by age and sex. There is a vast mass of experimental literature on the problem of age and changes in mental traits. Space permits reference only to the most significant parts of it. It seems wise, therefore, to omit reference to practically all investigations which report results in either of the following ways: (1) by grade only, or by average age (except where average age, such as 9 years, 7 months, 15 days, is the average age of persons within a single year span, e. g., from 9.0 years to 9.9 years) ; (2) by age, but not seperately for 8 Changes in Mental Traits with Age boys and girls. Reporting by grade is of very practical value in administration and has value in psychological study, but for an exact knowledge of individual differences, especially of differ- ences in growth or development, it is too crude a method ; we must have age data as well. I have omitted much of the data not giving results separately for boys and girls in order to bring together results of investigations which have been presented in the same way as my own. I have presented results separately for boys and girls in all tests and at all ages. This has been done, not because of any belief in pronounced sex differences in mental traits or in the development of mental traits, but because it seems desirable that data from all investigations should be presented in such a form as will make them available for any future studies of sex differences. The efficiency of single mental functions, or of narrow groups of functions, in relation to age, while the subject of a great many studies during the past thirty years, has, still, been investigated in nearly all cases by testing a group of children of different ages once or a few times, with usually only a short interval of a few hours or days between the tests, and with no re-tests of the same individuals six months or a year later to determine individual changes. Age status has been determined from these groups, and the differences between different age norms have been taken as the changes due to age. As Thorndike points out, such changes do not represent the changes in the same individuals, and such differences may or may not be the real individual changes with age. 2. NON-RE-TEST EXPERIMENTS Any study of changes in mental traits with age must refer to the pioneer work of Binet, who after many years of careful, experi- mentation finally published in 1905 the Binet-Simon tests of intelli- gence, which were revised, by the authors in 1908 and in 191 1, by Goddard, by Kuhlmann, and later, by Terman and others at Stan- ford University. All of this work is too well known to require any further reference or any evaluation. Binet and Henri (1894) after testing school children on memory of words say, "We have not succeeded in establishing clearly, in the primary elementary schools, which include pupils from seven to Historical Survey of Experimental Data 9 twelve years of age, the influence of age on the number of words reported. We do not doubt that this difference exists but it is possible that it produces an effect little marked between seven and twelve years; it is possible also that the conditions, always changing a little some of the group experiments, have introduced into the results of different classes, some differences which have masked those of age. . .One observes between the first class (cours superieur) and the fourth class (cours elementaire) (the highest and lowest grades of the elementary school) a mean difference of less than one word." Later experiments by other investigators have shown that there is a difference in memory span, between ages seven and twelve, of one to two words. Another of the earlier important studies of purely mental func- tions was that of Ebbinghaus (1897), who examined several hundred school children, using mental arithmetic, memory, and his "combination method." His data are given by grade or class, and by sex, though the average age of the classes is also given. Ziehen (1898) investigated the association of ideas in children eight to fourteen years of age. He is one of the first to use re-tests of the same individuals over a period of a half year or more; some of his subjects were re-tested over a period of two and a quarter years. He concluded that the speed of association (free or uncontrolled) increases with age, whereas Winteler, Wreschner, and Rusk (1909) find that "for different children the speed of association bears no direct relation to age," and that "no conclusion, however, can be drawn from present results as to the relation of speed of association to age in the case of the same child." Ziehen's re-tests are more re- liable measures of what age means for an individual, but he took no account of practice effect, nor did he re-test enough individuals to give any conclusive results. Smedlay (1902) investigated the development of immediate memory by testing 937 Chicago boys and girls, ages seven to nine- teen, in visual and auditory memory for digits. Finding small sex differences, he reports data for sexes combined. Auditory memory develops more rapidly up to fourteen than thereafter, though there are times of slow growth, notably from eight to nine and from eleven to thirteen ; visual memory develops more rapidly also up to fourteen, with gains and losses after that time, reaching, however, as in the case of auditory memory, its highest point at nineteen. Smedley 10 Changes in Mental Traits with Age says of his results, "There is no 'memory period', no period in early school life when the memory is stronger than it is at any later portion of the child's life, a period especially adapted to memorizing." I give here his results in terms of per cent correct at different ages. No. And. Vis. No. And. Vis. Age Tested % % Age Tested % % 7 19 36.4 35-2 H 114 66.2 80.5 8 58 44.6 42.8 15 94 65.6 78.2 9 100 45-0 47-4 16 77 66.9 81.3 10 89 49-4 56.4 17 56 65-5 84.1 n 9i 55-4 64.7 18 25 67.2 77-5 12 93 55-7 72-3 19 12 70.0 85-3 13 109 - 57-9 76.8 We do not know just how typical of school population were the children examined by Smedley; selection no doubt was playing a part during the later ages ; nor do we know how well those examined do represent all children of the same ages. Thorndike (1917) has shown that school population is made up of a selected group and that the higher the age, the greater is the amount of selection. In the absence of any careful study of the composition of the group tested we can only guess at the extent to which they represent children of these ages. Winch (1906), interested in Dr. Rivers' investigations of visual illusions among primitive peoples, conducted an experiment upon 42 English boys, ages eight to fifteen, to see if the civilized child passes through the same stage of development found in the savage. Three different tests of the vertical-horizontal illusion were made with each boy for each of the three forms of the test. Recalcu- lating his data upon the age basis, and computing the illusion in the average per cent of error for each age, we get the following: Age Error in Per Cent 8 9 10 11 12 13 14 15 14.09 16.92 9.29 11.31 6.13 5.63 5.41 3.10 The small number of cases, two to eight at each age, enables us to say merely that the amount of illusion seems to decrease with age. Historical Survey of Experimental Data ii Norsworthy (1906) gives results of different tests given to children of different ages. Some of the tests were given by herself and others by Professor Thorndike. The following tests were given to the number of children (between ages eight and sixteen) indicated after each test: A and a-t tests, 900 cases; memory for related words, 288 cases; memory for unrelated words, 270 cases; part-whole test, 504 cases; genus-species test, 511 cases; opposites I, 605 cases; opposites II, 608 cases. Dividing the gross gains from one year to the next by the average of the P.E. for ages eleven, twelve, and thirteen in each test, and combining the tests which were given to the same children, we have the following P.E. gains from one year to the next: Age A and a-t Memory Related and Unrelated Part-Whole Genus- Species Opposites I Opposites II B G B G B and G B and G 8-9 •423 •273 • 568 .613 .650 •615 9-10 ■554 •329 .278 1.072 1. 000 .500 IO-II ■773 •592 .079 .342 1-550 .748 11-12 •654 .482 .468 -.257 .000 •452 12-13 ■452 .420 .212 .146 .200 ■352 13-H •552 •527 .164 .323 .000 .302 14-15 •4°4 .312 .000 .000 .100 .185 15-16 •403 .242 .107 .261 .000 •152 The results above age thirteen must be considered in the light of the following statement by Norsworthy: "In some of the measure- ments I could not obtain enough records from school children over thirteen to make the standards of median and probable error reliable. In these cases, as I have records from adults, I followed the general trend of the curve and filled in the standards for ages fourteen, fifteen and sixteen. This is especially true of the intelli- gence tests." It should be noted that on the whole there is a gain in all functions with age. It should be noted here that the cancellation of letters, digits, etc.,. is one of the most widelv used tests. This is now known to be a test 12 Changes in Mental Traits with Age of the lower or simpler functions. Norsworthy classes it as a matur- ity test. Its correlations with intelligence have been found to be small but positive, Brown (1910), Burt (1911), Simpson (1912), and Wyatt (1913) finding coefficients from .00 to .45; Whipple (1914) found negative correlation with intelligence. Pyle (1915) says of this test, "Ability to do the cancellation test has no relation to the ability shown in the other tests" — completion, logical memory, oppo- sites, genus-species, part-whole, word-building. Ellison (1903) studied the definitions given to twenty-seven abstract words by 209 boys and 253 girls, ages eight to fifteen. Definitions were classified as those (a) by sample, (b) by abstract phrases, and (c) by equivalents (synonyms and fair definitions). The first kind of definition was very common with eight- and nine- year-olds, but was much less common with increasing age. Defini- tion by abstract phrases increased in frequency up to twelve years "with a slight (though perhaps accidental) fall for the thirteen-, fourteen-, and fifteen-year-olds." Definition by equivalents in- creased noticeably with age in the case of both boys and girls. The girls were found superior to the boys at almost all points in ability to define. The progressive organization of experience in more com- plex ways, evidenced by increased ability to define abstract words, is shown to be an accompaniment of increased age. Tucker (191 1), also interested in Rivers' studies, conducted an experiment upon 124 elementary school children in Cambridge, England, and 41 English adults to find the effect of age upon color vision for red, blue, and yellow. The thresholds for boys and girls, ages five, six, seven, eight, and ten, show a decrease as we go from younger to older. The average thresholds are as follows : Age Boys . . . Girls Chotzen (1912) after testing 236 mental defectives in the Hilf- schule at Breslau concludes (as do Bloch and Lippa after their re-tests of mental defectives) that the development of the feeble- minded follows that of the normal, only in retarded rate, and that the greater the age, the greater the retardation. His distribution curves, showing the retardation by ages of the defectives, tested by the Binet-Simon tests, have pronounced modes as follows: for 5 6 7 8 10 72.0 69.0 53-2 46.9 37.0 83.0 60.4 544 45-3 38-o Historical Survey of Experimental Data 13 the seven- and eight-year-olds at one year retardation, for the nine-year-olds at two years retardation, and for the ten-to-thirteen- year-olds at three years. Smith (1913) with 25 boys and 5 girls of six and twelve years, in perception of facts in pictures, found that perception becomes more complex with increase of age, that there is greater power of analysis, a more active mental attitude, more improvement in discovery of detail, and greater individual differences among the older children. Valentine (191 3) tested 195 Dundee boys and girls, ages six to thirteen, and 146 adults in appreciation of eight concords and four discords played on the piano. Beginning at seven, as age increases there is a steady decline in the score representing the appreciation of the discords, the lowest score being that of the adults. With the concords the results are not so unambiguous, the appreciation score increasing until nine, and decreasing mark- edly at twelve and thirteen to a point slightly below that of adults. But the octave was one of the concords and probably accounts for part of the lower score at twelve and thirteen. Von Kathe and Busemann (1914) tested 487 children of the Volksschule in Essen, ages eight to fourteen, in power of observation and attention. They made eight tests, each time using three series of ten nouns each. They found average gross gains in words as follows : Age 8 to 9 to 10 Boys .8 .8 Girls .8 1.1 No variabilities are given. They find thus an increase with age for both sexes, and the smallest gains for both sexes at twelve to thirteen. Thompson and Smith (191 5) sought to determine the recog- nition vocabulary of children of different ages by using a random' sampling of 170 words out of a dictionary containing 35,100 words. They tested 238 boys and 229 girls, ages nine to fourteen. They find an increase in vocabulary with age; there is no increase with boys from thirteen to fourteen, but a rapid increase from eleven to thirteen: girls increase most rapidly from ten to eleven, and from twelve to thirteen. They found the P.E. due to sampling to be .019 to II II tO 12 12 to 13 13 to 14 .8 .6 •5 .8 •4 .1 1.0 .6 14 Changes in Mental Traits with Age or 700 words at ages eleven and twelve. I give here the per cent correct at different ages. Boys Girls 9 10 11 12 13 14 14.7 15-3 15-6 18.1 20.7 20.6 14.6 152 16.5 17.2 19.0 19.7 Their results correspond rather closely with those of Terman and Childs (1912) who tested orally 161 children, ages five to thirteen, and with those of Whipple (1915) who tested college students and members of the George Junior Republic, ages fourteen to eighteen. Kirkpatrick, on the other hand, found results which would indicate larger vocabularies than those found in the other three investi- gations. Terman and Childs found small increases from ten to eleven and from six to seven — one hundred words at each of these times. Anderson (See Whipple 191 5) carried on extensive experiments upon 405 boys and 421 girls, ages eight to sixteen, in memory for letter-squares, each subject making ten trials. From the data given by Whipple, I have calculated the average score for each age and sex. Age 8 q ■ 10 11 i2 13 14 is 16 No. of Boys tested . . 21 43 54 61 72 68 43 31 12 Score . . . 106.43 116.86 118.33 135-33 158.47 i53-°9 156.63 165.32 172.5 No. of Girls tested . 31 48 61 65 67 57 53 26 13 Score . . 106.61 109.17 127.79 143.77 I53-36 154-82 165.57 169.23 185.7 It will be seen from these figures that the thirteen- and fourteen- year-old boys did not make as high scores as the twelve-year-old boys, and that ability in this function increases with age, being greatest at the highest age for which data are given. In the case of the girls there is an increase from eight to sixteen, at each age. While I have not computed the variabilities, the gross gains tell us that the point of lowest gain for the girls is probably from twelve to thirteen. The median score, however, of the thirteen-year-old girls is less than that of the twelve-year-olds; also the fifteen-year median is less than that of the fourteen-year-olds. This means negative gains if we use the median as the measure of central ten- Historical Survey of Experimental Data 15 dency, but positive gains if we use the average. Without any discussion of the relative merits of the two measures, such discrepancies between the kinds of gain revealed by different statistical treatment of the data, should make us very cautious in our statements about the rates of gain. When we compare the boys' averages and medians we find by using the median that the same conditions exist as shown by the average with the following exceptions: the ten-year median is a fraction less than the nine-year median, and the sixteen-year is less than that of the fifteen-year-old boys. Ballard (1913-14) gives performance norms in the fundamental operations in arithmetic for 9176 boys and 9502 girls, ages eight to thirteen and a half, from sixty-nine London elementary schools. There were sixteen addition problems, each of four rows of three- place numbers; twenty-four subtraction problems of four-place numbers; twenty-eight multiplication problems, each of a three- place number by a one-place number; twenty- four short division problems, each of a four-place number by a one-place number. Each column correctly done in addition and subtraction, and each simple process in multiplication and division, each scored one point, so that an example correctly done in addition scored three ; in subtrac- tion, four; in multiplication, three; in division, three. Results are given for half-years. No variabilities are given. The time of each test was five minutes. Combining the scores in the four tests by add- ing the average scores at each age, we have the following performance norms, for boys and girls combined: 8 8yi 9 9yi 10 ioyi 11 11% iz i2yi 13 13H 63. 74.5 88. 105. 123.5 140. 133. 165.5 178- 188.5 197-5 205.5 At eleven only, is the score less than that of the previous half-year. If the scores had been combined by years, rather than by half-years the scores at each succeeding year would be greater than the score immediately preceding it. In the tests some children finished before time, and so were not fully tested; beginning at age twelve from 5% to 20% of the group did this; at thirteen and a half from 12% to 40% finished the tests before time was up. The differences between scores at the higher ages would have been greater had longer tests been given. Ballard also found that "the accuracy that comes with age varies directly as the speed of working." Gray (1915-16) gave Dr. Ballard's tests to 3645 boys and 3715 1 6 Changes in Menial Traits with Age girls, ages eight to thirteen, in the Leeds elementary schools. Results are given separately for boys and girls. No variabilities are given. Combining the results of the four tests we have the following: Ages 8 8}4 9 gyi io ioyi n nyi 12 iz l A 13 Boys tested 289 313 360 346 383 371 403 340 398 354 88 Score 49 74 90 no 126 142 158 167 171 185 192 Girls tested 286 338 345 350 387 355 398 400 404 342 106 Score ... 47 66 89 103 112 135 142 154 166 174 185 Here, as in Ballard's data, we find from 3% to 14% of the children at twelve and a half finishing before time, and 4% to 23% of the thirteen-year-olds. Errors on the whole were found to diminish as children grow older. The gain by years is shown to be fairly con- stant. As in Ballard's experiment more problems in each test would undoubtedly have shown greater gains in the higher years. Green (1915-16), using more carefully devised tests than those used by Ballard (a better selection of problems as to the number combinations involved, and enough problems in each test to avoid any child's finishing before time), tested 800 children, ages eight to thirteen. The averages, medians, and S.D.'s by half-years are given for boys and girls separately, for each of two schools. The gains from year to year in the four tests, in terms of the average S.D.'s of ages eleven, twelve, and thirteen, are as follows: Age 8 to p 9 to 10 10 to 11 11 to 12 12 to 13 Boys .... .892 .550 .412 —.0 Girls 648 .686 .388 .088 .465 Ballard (1915-16) tested 22,670 children (11,588 boys, and 11,082 girls) of the London elementary schools, using the Starch one-minute oral reading test. The results are given by half-years from ages six to ten, and from thirteen and a half to fourteen, for boys and girls separately. Ability as measured by this test is shown to increase with age, though the rate of increase is not regular. It is doubtful if much value attaches to a one-minute test of a reading function. Kimmons (191 6) tested 1920 boys and two different groups of girls, totalling 3552, ages seven to thirteen, for speed of handwriting in a five-minute test. His data show the following results in letters per minute: Historical Survey of Experimental Data 17 Age 7 8 Q 10 11 12 13 Boys .... 13.9 17.4 25.1 32.9 44.7 46.6 Girls (2488) 18.8 ,-, 21.4 29.3 36.1 44.5 49.3 Girls (1064) . . 21.6 24.2 34.0 47.6 59.7 64.5 70.5 The first two groups were being introduced to some new method in handwriting, and may not have had time to find their true speed levels. No variabilities are given. The boys' speed is shown by these figures to increase with positive acceleration until the age of eleven, with but slight increase from eleven to twelve. The girls make positive gains at all ages, with positive acceleration probably until the age of eleven, and with decreased positive gains the two following years. 3. RE-TESTS OF THE SAME INDIVIDUALS There has been reported a small number of investigations in which the same individuals have been re-tested at intervals of a year or half-year, and in which the results have been given by age. Ziehen's re-tests have already been referred to. Norsworthy (1906) re-tested 26 defective boys and 17 defec- tive girls (ages eight to sixteen) after an interval of one year, using a group of tests. Her conclusions are "(1) That among mental defectives a decided improvement in mental ability may be looked for after a lapse of a year, in some directions even exceeding that shown by ordinary school children. (2) That the greatest im- provement is not confined to those defectives most like ordi- nary individuals. (3) That the improvement is not equal in all directions, but that some mental functions improve more rapidly and to a greater extent than others, and that even the functions we designate as intellectual show marked improvement." She found that the defectives made the least improvement in the intelli- gence tests; memory tests came next, while the greatest improve- ment was made in what she calls the "maturity" tests — the A and a-t tests. Dividing the group into four divisions on the basis of ability shown in the first year's tests, she found the greatest im- provement made by the quartiles in the following order : second, third, fourth and first, a condition not in accordance with the generally accepted view at the present time. To the extent that individuals are adequately tested and to the extent that the functions 1 8 Changes in Mental Traits with Age * are not in such a high state of efficiency as to preclude much im- provement, to this extent we expect the children of greater ability to make the greater improvement in a given period of time. Burt (1909-10) re-tested a group of elementary boys of about twelve and thirteen years, eighteen months after the first test- ing. He does not state just how many were re-tested, but in all probability it was 25, certainly not more than 30. He found that the order of the boys was not materially changed in the second tests. A "dull" boy who stood twenty- fifth in 1908 in the combina- tion of six tests, in 1909 made the same score made by the fourth boy in 1908, yet he still ranked twenty- fourth. Burt says, "The data may be summarized most briefly by expressing the improve- ment or deterioration for the set of boys re-tested as a percentage of the average calculated for the same set of boys from the original experiments" and gives the following results: "Touch — 3%; Compar- ing Lines 8%; Dealing 15%; Card Sorting 6%; Alphabet Sorting 4%; Memory -9%; Spot Pattern -7%; Dotting-3%; Mirror3i%." The second tests were found to correlate almost as highly with the first as the first ones did among themselves; i. e., r = .$i to .76. Burt concludes that the capacities tested "appear to constitute a relatively permanent endowment and consequently it seems legitimate to assume that they depend upon innate differences in the individuals concerned." Bobertag (1912) examined 83 normal children, using the 1908 Binet-Simon tests, and re-tested the same individuals a year later. He correlated early and late scores using Spearman's rank formula. He found p =.95, P.E. = .024. He calls attention to the tests being too easy at the earlier ages and too difficult at the later ages, the curve being much like the practice curve, rather than a straight line. This is in agreement with the findings of other investigators. Moore tested 252 norma] English boys and 239 normal English girls, ages four to thirteen. At four the IQ was 109; at thirteen, 86. Such investigations are interpreted upon the assumption that mental growth continues, and that the tests themselves are not as well selected as they should be. Bloch and Lippa (1912) tested 71 feeble-minded children at Kattowtz by the 1908 Binet tests, re- testing the same individuals a year later. They conclude that the mental development of the feeble-minded follows closely that of normal children, only remaining Historical Survey of Experimental Data 19 from two to four years behind the normal, and finally remaining at a much lower level. Dr. F. Kuhlmann, Director of Research at the Minnesota School for Feeble-Minded, has re-tested every two years since 1910 all inmates over three years of mental age and under twenty years of chronological age. His results have not yet been published. In a letter to Dr. Leta S. Hollingworth, quoted by her in Psychology of Subnormal Children (1920, p.105), he says, referring to prelimi- nary tabulations made a few years ago, "On the whole the IQ for a given case remains constant, with a slight tendency on the average to decrease after the ages of nine and ten. To this general rule there are quite a number of individual exceptions. A good many cases deteriorate, for whom the IQ will then drop suddenly, and this may be at any age. In a smaller number of cases the IQ in- creases with age, very markedly in' rare instances, more or less frequently in a degree which may be accounted for possibly by an increasing familiarity with the mental tests through repeated ex- aminations. Also there seems to be the tendency for the mental ages to increase very slightly beyond the chronological ages of fifteen or sixteen." Berry (1913) tested 82 children (42 school children at Ann Arbor, Mich., chronological ages seven to twelve, and 40 mental defectives, chronological ages nine to twenty-four) by the Binet scale, re-testing them one year later. The school children who tested "below age" in 191 1, gained .96 years during the following year; those "at age" gained 1.02 years; those "above age" gained 1.17 years; average gain 1 year. The average gain of school children "above age" was 20 per cent more than that of the school children "below age" in 191 1. The defectives (mental ages four to eleven) made an average gain of .5 years during the year. The defectives under fifteen years of chronological age gained 50 per cent more that those over fifteen years of chronological age. Goddard (1913), using the Binet scale, made three annual testings of 352 feeble-minded at the Viiieland Training School. His results are summarized as follows: 109 remained absolutely the same; 232 varied not more than 2 points in the two years ; 22 gained more than 5 points (i. e., more than 1 year) in two years — all of these were younger cases; 19 lost 3, 4, or 5 points — all of these were older cases. 20 Changes in Mental Traits with Age Goddard also made three annual testings of 464 public school children, but the results are not reported in such form as to give any information on the problems of this investigation. All of the results, too, are subject to some error, due to the incorrect mental ages of the Goddard-Binet scale. (See Thorn - dike 1914-15, p. 189.) Jones (191 7) found the correlations of the total test average for each year by the Pearson product-moment formula for 203 Cincinnati children, tested at age fourteen, and re-tested at fifteen, sixteen, and seventeen, in the following tests: cancellation, four pages of digit-symbol substitution, immediate rote memory for digits, a sentence completion test, and opposites. The test average was found by assigning to each individual as his score in each test the number representing the decile division into which his actual score in that test placed him ; these decile numbers for all tests were averaged to give his yearly test average. This classifies each child by giving him a rank from 1 to 10 in each test; these ranks are averaged, and the averages are correlated by the Pearson formula. Giving these ranks throws away some of the refinement of the test scores. A better procedure would have been (1) to find for each test each individual's plus or minus deviation from the average of the same age in each test ; (2) to express these deviations in each test in terms of the variability, say, the average variability of ages fourteen, fifteen and sixteen, of that test; (3) to average these plus or minus sigma (or Q) deviations of each individual in all tests at each age; (4) to correlate these averages at the different ages. This procedure preserves the refinement of the original test scores, and at the same time makes possible a legitimate combining of results of several tests. Jones found the following coefficients of correlation: Second Year Third . Year Fourth Year First year average Second year average Third year average •74 .69 •71 .76 .76 •73 The correlations were found for the individual tests from year to year, as were also the partial correlations with school grade Historical Survey of Experimental Data 21 reached equalized or made constant. Two conclusions are of significance in connection with the problems of this study: (1) "We believe that the varying conditions of work in Cincinnati after the age of sixteen, and perhaps other factors, have operated to make the good slightly better, and the poor relatively poorer than they were at the age of fourteen" (p.84) . (2) One well-rounded testing of an individual probably gives his general intellectual rank for several years. Woodrow (191 7) carried out a practice experiment which is important in its relationship to a re-test experiment by Murdoch (1918). Woodrow devised and carried out in a thoroughly scien- tific manner an investigation upon 40 normal and 32 subnormal children of the same mental age (nine), to determine whether or not feeble-minded children show the same improvement with practice as do normal children of the same mental age. The ex- periment involved sorting gun-wads upon which had been pasted the five geometrical forms of the Woodworth-Wells substitution test, and extended over a period of thirteen days. Both practice and control groups of normal and subnormal children were used. In both the amount of improvement by practice, and the amount of transfer or spread of practice, Woodrow found the feeble-minded showing the same improvement as the normal children of the same mental age. In contrast with this is the experiment of Murdoch, referred to above. Thirty-seven feeble-minded children of known mental age were tested by measuring their achievement in reading, arithmetic, spelling, handwriting, composition, language, and drawing; a year later 21 of them were re- tested and their rate of progress compared with that known to obtain in the case of normal children. The rate was found to be much less. The results led to the conclusion that what Woodrow found in the case of the simpler functions over a few days' practice was not true in the case of the higher or more complex functions over a longer period of time. It re- mained for Hollingworth to point out that there is no discrepancy or antagonism between the results of the two experiments, because in the latter one, at the end of the year the subnormal children are no longer of a mental age equal to that of the normal children with whom they were compared. This is but another way of saying that the rate of mental growth is slower in the case of the subnormals than in that of normal children. 22 Changes in Mental Traits with Age Terman (191 9) reports the results of re-tests of 315 children, ages three to fifteen at the time of the first test. The Stanford- Binet test was used. Some children were tested twice, others several times. The intervals between the tests varied from one day to seven years. Omitting tests which were less than a year apart, there are 349 comparisons of tests with re-tests at intervals of one to seven years. Terman summarizes the findings by noting (1) that the central tendency of change is an increase of 1.7 points in IQ; (2) that the middle 50 per cent of change lies between an increase of 5.7 points and a decrease of 3.3 points; (3) that the P.E. is 4.5 points; (4) that the correlation between earlier and later tests is .933; (5) that tests more than five years apart show a greater tendency toward an increase in I Q than is found in the case of tests at shorter intervals (though this may be due to some differences between the form of the test used in the earlier and that used in the later trials). Mental growth curves are given for several children. The slopes of the curves indicate that the higher the degree of intelligence the greater the mental growth per year. Baldwin and Stecher (1921) report the results of four annual testings of normal and superior children in the Observation School at the University of Iowa, by the Stanford Binet scale. The number of children tested is not given. The conclusions are as follows: 1. Considerable fluctuations of individual IQ's in successive years. 2. The average children remain average, and the superior children remain superior. 3. Superior children are more variable than average children. 4. Older children (chronologically) are more variable than younger children. 5. A general tendency for IQ to increase at later examinations, especially in the case of older children and children of superior ability. 6. The correlations at intervals of one, two, and three years by the Pearson formula are as follows : M2 = + .85 "3 = + 748 7-14 = + .780 The method of computing the correlations is not given, so we do not know if the age factor has been eliminated or made constant Historical Survey of Experimental Data 23 (by taking mental-age deviations from normal). If this has been done, these coefficients signify that the differentiation of children by levels of intelligence is relatively permanent, and are direct evidence that the average remain average and that the superior remain superior. Doll (1921) * reports the results of re-tests by the Goddard- Binet scale of 203 mental defectives at the Vineland (N.J.) Train- ing School, covering at least a five-year period for each individual. He also gives re-test data from a group of superior children attend- ing the Ethical Culture School in New York City. 4. DATA RECALCULATED FOR DIRECT COMPARISON WITH RESULTS OF MINNESOTA RE-TESTS The results of the following investigations I have recalculated and turned into suitable form for comparison with my own data: Dr. Gilbert (1894) at Yale University made one of the most careful and extensive early studies of differences in mental traits between children of different ages, from six to seventeen. Approxi- mately fifty school children of each age and sex were tested in the following mental traits: (1) Delicacy of discrimination of weight — "muscle-sense"; (2) delicacy of discrimination of colors; (3) force of , suggestion — size-weight illusion ; (4) voluntary motor ability — tap- ping; (5) fatigue in tapping; (6) reaction time ; (7) reaction with dis- crimination and choice; (8) time — memory. Ten trials were made by each individual in each test. The median for each age and sex in each test, and the average deviation (mean variation) for each age and sex in each of the last five tests, are given; in the first three tests the average deviation is given f 01/ boys and girls together only. Netschajeff (1900) tested 687 St. Petersburg school children, ages nine to eighteen, in eight memory tests — objects, sounds, numbers, and words referring to sound, sight, touch, feeling, and abstract relations — of twelve each. He gives the average perform- ance in each test for each age and, sex. No variability is given. Lobsien (1901) tested 462 Kiel children, ages nine to fourteen and a half, in eight memory tests, seeking to be more accurate than Netschajeff. 1 This monograph came to hand too late for a summary of it to be included in this report. 24 Changes in Mental Traits with Age Pyle (1913) gives age-norms (average and average deviation) for each sex and age from eight to eighteen in the following tests: (1) Logical memory; (2) immediate concrete memory; (3) immediate abstract memory — Whipple's lists in this test and in number two ; (4) digit-symbol; (5) symbol-digit; (6) word building — aeirlp; (7) word building — aeobmt ; (8) uncontrolled association ; (9) opposites ; (10) genus-species; (11) part-whole; (12) cancelling .4's. His tests, with few exceptions at seventeen and eighteen and one at fifteen, were given to from forty to eighty subjects of each age and sex. All tests were given at the different age-levels to the same group of subjects, so that the twelve test-norms for thirteen-year-old boys mean that a particular group of thirteen-year-old boys took all twelve of the tests and made the average scores given for each test. Pyle (1920) extended his investigations to a great many more subjects; in the case of city children he tested from one hundred thirty to four hundred fifty of each age and sex, from eight to sixteen, and from fourteen to ninety-eight of each age and sex at ages seven- teen and eighteen; in the case of the country children he tested twenty-one to one hundred ninety-nine of each age and sex from eight to eighteen. Very nearly the same tests were used as in 1913. The average for each age and sex is given for each test, but no variabilities are given. Bickersteth (1914-15) , of Oxford University, carried out a carefully devised and very carefully administered series of tests upon six differ- ent groups of school children. The ones that are of special interest and value in connection with my own data are the twelve tests given to 550 girls in Oxford higher elementary schools, ages five to sixteen, and five tests (Nos. j, 4, 5, 6, and 12) given to 600 boys and girls, ages nine to thirteen, in the Yorkshire Dales elementary (rural) schools. The first group numbers from eighteen to seventy at each age; the second group numbers eighteen to seventy-four for each age and sex. Each test was given twice, the testings for each child in each test being one week apart. Bickersteth groups the tests as follows: I. Motor Tests: (1) Power of sustained effort — tapping; (2) fa- tigue in tapping. II. Tests of Discriminative Selection: (3) Alphabet cancellation; (4) number cancellation; (5) combined number and alphabet cancellation. III. Memory Tests: (6) Memory for narra- tive — logical memory; (7) memory for related words; (8) memory for unrelated words. IV. Tests of Analytic and Synthetic Apper- Historical Survey of Experimental Data 25 ception: (9) Spot-pattern test. V. Tests of Attention: (10) Sustained voluntary attention — dotting; (11a) Discs — concentrated attention ; (116) Discs and sentences — divided attention. VI. Reasoning: (12) Analogies. Woolley and Fisher (191 4) in Cincinnati have carried on a very significant investigation at the Vocation Bureau. They have tested those who apply for work permits, and have re-tested many who come back for new permits, and they have sought out and re- tested as many others as they could. Such re- tests have been very nearly a year after the previous tests. Data are published for seven hundred fifty who were tested at fourteen and again at fifteen. The data are given in terms of the median and Q for each age and sex in each test. For purposes of telling about changes in individuals the central tendency and variability of the differences between each individual's score at fourteen and his score at fifteen would be preferable, but the central tendencies of the same group at fourteen and again at fifteen are much better than the same data for different groups at the different ages. The following tests have been given: (1) Tapping; (2) fatigue in tapping; (3) card-sorting; (4) cancellation of A's; (5) memory for digits, seven-, eight-, and nine-place; (6) memory span; (7 a, b, c) substitution, digit-geo- metrical forms; (8) substitution, memory digit-geometrical forms; (9) sentence completion ; (10) opposites. Under Dr. Woolley's direction this investigation has been con- tinued now for more than five years. Not only have the tests been very carefully given and the results carefully tabulated, but there has been also a large enough number of individuals re-tested to make it the most extensive experimental investigation by annual re-tests of normal children, ages fourteen to eighteen, that we have up to the present time. Below are given the numbers of each age and sex for both the school group and the working group. (This is the group reported upon in the 1914 publication for ages fourteen and fif- teen, while the school group is a control group which has been used as a check against the mental development which takes place with those who go into industry.) The data are for re-tests of the same individuals in all cases with the following exceptions : nearly one-half of the school group of the ages, fourteen, fifteen and sixteen, had left school by seventeen and eighteen and were replaced by a new group, judged to be practically 26 Changes in Mental Traits with Age Ages 14 15 16 17 18 Boys: School 430 294 289 178 66 Working . . 420 388 346 309 304 Total 550 682 635 487 370 Girls: School ... .330 255 240 165 79 Working . 327 285 296 244 204 Total 657 540 536 409 283 Total Boys and Girls 1,507 1,222 1,171 896 653 the same as the original group whom they replaced. The original data from which I have calculated the gains from ages fifteen to eighteen are soon to be published by Dr. Woolley. Dewey, Child, and Ruml (1920) have carried out one of the most scientific experimental studies in educational psychology. Individual tests have been given to fifty boys and fifty girls of each age from nine to thirteen in the New York public schools. The children are all Jewish. A random sampling of the three thousand normal children attending the schools from which the children tested were selected, was obtained in the following manner: The age-grade distribution for the whole school in per cents was found. The fifty children of each age and sex were then selected from the different grades of the schools so that for any age or sex the grade distribution was of the same proportion as for all the children of that age and sex in the whole school. Children in special classes were not selected. A wide range of tests was given. Space does not permit any description of them. Those interested in the scientific testing of school children should refer to the book by these authors. The results of the following tests are compared with my own data: (1) Cart construction; (3) narrative pictures; (4) identification of forms; (5) instruction box; (6) needle- threading; (7) nail-driving; (8) picture-completion; (9) problem box; (11) memory for objects; (12) Knox cubes; (13) Healy puzzle A ; (15) Healy puzzle B; (16) card sorting; (17) cancellation of A's; (18-19) substitution; digit-geometrical forms ; (21) memory span — digits; (23) steadiness of motor control — right hand. The average Historical Survey of Experimental Data 27 of each age-group is given for each test, as are also given the stand- ard deviations, and the P.K.t.-obt.av., and P.K.t-obt.S.D. The re- gression equations are also given for each test. The results of the different tests have been analyzed by means of the partial correlation method to find those tests which do not correlate highly with each other. Such tests have been used to form a maturity scale, due weights being assigned (by the regression coefficients) to the different tests included in it. IV STATUS OF THE SUBJECTS BY AGE AND SEX In considering the status of the subjects tested it is desirable to note their distribution by grade at each age for each sex. Such distribu- tion will throw some light upon the interpretation of the results obtained from the tests. Figs, i-a to 7-b present graphically these distributions. The fourth grade was chosen as the lowest grade in which to give the entire series of tests, while the ninth grade was the highest grade attended by pupils of the Training School. For various reasons it was impossible to test any pupils after finishing the third year of the junior high school at the Training School. Keeping these facts in mind, an examination of Figs. 1 -a to 7-b will show clearly that the groups tested at the earliest and latest ages vary from a true random sampling of normal school population in the following significant respects: (1) By beginning the testing with the fourth grade, the nine-and-ten-year-olds of less ability (as measured by grade reached in school) have been lopped off. To have a true random sampling of school population we should have some children of nine and ten years of the third grade, and some second-grade children nine years of age. This is of still greater significance when we recall that the tests were given during the last month of the school year in a school which makes annual promotions, does not have A and B divisions of grades, but which divides the pupils into two sections according to ability instead, so that grade four really means fourth A, or advanced fourth. It is readily apparent that children who finish the fourth grade before their tenth birthday in a school in which practically all are six years old before entering the first grade, are on the whole superior nine-year-olds. Those finishing the fifth grade are, of course, still more so. Figs, i-a and i-b show by their skewness this variation from random sampling. (2) At the older ages there is a cutting off of some children of superior ability. Many children who are just short of their sixteenth birthday have completed the ninth grade. The same is true of a much smaller number who are not yet fifteen. These two facts must be considered when we discuss the rate of im- provement from year to year. There are other significant facts Status oj the Subjects 29 Fig. i-a — Boys 9 yrs. old Fig. i-b — Girls 9 yrs. old r 1 I I I I I ' __J l it ! 1 r- Fig. 2-a — Boys 10 yrs. old 4- Fig. 2-b — Girls 10 yrs. old r— -1 1 1 I ■ 1 r- L -1 1- Fig. 3-a — Boys 1 1 yrs. old Fig. 3-b — Girls 11 yrs. old --1 ' * ' (. ' 7 ' S ■ 1 ' Fig. 4-a — Boys 12 yrs. old 4- Fig. 4-b — Girls 12 yrs. old ..r 1 1 1 1 ■ ■ ....-■ Fig. 5-a — Boys 13 yrs. old Fig. 5-b — Girls 13 yrs. old r > 1 1 j r 1 1 1 v. ... . . - Fig. 6-a — Boys 14 yrs. old Fig. 6-b — Girls 14 yrs. old , 1 v- ' j r • i. • 7 Fig. 7-a — Boys 15 yrs. old V ' i> Fig. 7-b — Girls 15 yrs. old Figs, i-a to 7-B Grade Distribution of Subjects by Age, and Sex Note. Age means age on last birthday. 30 Changes in Mental Traits with Age disclosed by these graphs to which attention will be directed in the later discussion. The results of the tests have been compiled so as to show the status by age and sex in each test. The average, the standard deviation and the P. K.t.av. — obt. av. and the P.E.t.S.D.— obt. S.D. have been computed for boys and for girls of each age in each test. These data are presented in Table I. The significance of the plus and minus quantities given after the averages and standard devia- tions will be made clear by the following explanation : The pupils tested represent very small samples of the larger groups — children nine years old, children ten years old, etc. The average achievement (or S.D.) of these small groups probably varies from the average (or S.D.) we would obtain if we tested the larger groups of which they are samples. The plus and minus quantities are the median deviations (called P.E.t.-obt.) of the true averages or standard deviations from the averages or standard deviations which have been found for the different groups actually tested, and tell us the chances are even that the true measure will differ from the obtained measure by an amount greater than the plus and minus quantity given after each measure; e. g., to the extent that the nine-year-old boys tested represent a random sampling of nine-year-old school boys, we know the obtained measure is the most probable one, and that in the number-checking test, for example, the chances are even that the true average will not be greater than 1 15.71 and less than 102.71 (109.21*6.50). To the extent that the sampling is characterized by a distribution which is skew in one direction or another, we must expect the true average to be greater or less than that obtained. Errors of simple sampling, as well as the form of distribution of the groups tested, must be taken into account in interpreting the data on yearly improvement. Status of the Subjects 3i TABLE I Showing the Average, Standard Deviation, P.E.t.av.-obt.av. and P.E.t.-obt. S.D. for Each Sex at Each Age in Each Test Boys Girls Age Average S.D. Average S.D. 1. Number Checking 9 109.21 ± 6.50 25-50 * 4-6o 116.08 ± 2.19 14.15 ± 1.55 10 101.75 2.67 19.41 1.89 117.97 2.51 21.68 1.77 11 "3-33 2.24 19.9 1.58 131.82 2.49 22.8 1.76 12 123.03 2.50 21.0 1.77 145-13 3-52 30.9 2-49 13 139.21 3-41 24.8 2.41 160.16 2.68 24-5 1.89 H 156.12 3-32 24.12 2.35 165-73 2.66 26.16 1.88 15 165.23 6.01 35-03 4-3i 169.21 3.21 25-19 2.27 za. Handwriting Quality (Ordinary Written Work) 9 65-00 =t 3.41 I3-36 ± 2.41 74.21 ± 1.87 12.06 ± 1.32 10 72.92 1.83 13.30 1.29 88.97 2.00 17-31 1.42 11 79-58 1-37 12.2 .97 93.68 2.58 23.6 1.83 12 86.41 1.92 16. 1 1.36 109.00 2.85 25.04 2.02 13 95-83 2-37 17.2 1.67 126.84 2.72 24.9 1-93 14 102.92 2.20 16.00 1.56 125-79 2.62 25-78 1.85 15 127.67 2.60 14.92 1.84 138.39 2.77 21.76 1.96 2b. Handwriting Quality (Writing Test) 9 70.71 ± 2.93 11.47 =±= 2.07 74-74 * 1-95 12.62 =* 1.38 10 74-17 1.76 12.80 1.25 91.32 2.22 19.22 1-57 11 83-45 1.60 14.19 1. 13 101.45 2.38 21.76 1.68 12 92.50 2.02 16.91 1.43 112.30 2.74 24.06 1.94 13 101.25 2-75 19.96 1.94 128.95 2-49 22.76 1.76 H 108.96 2.70 19.64 1.91 138.75 2-53 24.89 1.79 15 H7-33 3.22 19.52 2.28 146.96 2.40 18.82 1.70 2C. Handwriting Speed (Writing Test) 9 124.79 ± 7.17 28.13 10 125.12 3-34 24.27 11 136.73 3-29 29.25 12 150.87 3-51 29-45 13 159-71 3-78 27-45 14 164.17 4.21 30-55 15 172.30 3-90 22.40 * 5-07 131.28 * 5-8o 37-51 * 4.10 2.36 136.56 2.58 22.33 1.83 2-33 145-55 2.40 21.91 1.70 2.48 156.58 3-19 27.99 2.26 2.67 158.82 3-24 29.64 2.29 2.97 170.23 2-39 23-50 1.69 2.76 179-54 2.20 17.27 1.56 32 Changes in Mental Traits with Age TABLE I — Continued 2bc. Handwriting — Speed and Quality (Writing Test) 9 128.57 ± 4.96 19-45 =■= 3-51 140.13 ± 3.55 22.93 * 2.51 10 137.02 2.56 18.57 l-8i 157-99 2.73 23.61 1-93 ii 149.89 2.30 20.5 1.63 174-37 3-02 27.6 2.14 12 167.16 3-15 26.4 2.22 190.23 3.04 26.7 2.15 13 181.08 3-41 24.8 2.41 209.18 3.25 29.7 2.30 14 190.75 3-38 24.50 2.38 224.26 2.86 28.09 2.02 15 203.48 4-59 26.37 3-25 236.91 2.94 23.08 2.08 3. Spelling 9 25.21 ± 2.88 11.28 ± 2.03 32.13 ± 1.39 8.99. ± .98 10 25-93 1.69 12.31 1.20 32.45 1.22 10.57 .86 ii 28.81 1.68 14.96 1. 19 38.74 1-38 12.57 •97 12 35-34 1.89 15-57 1-33 41.41 1.62 14.2 1. 14 13 40.40 1.70 11.26 1.20 46.47 1.58 I3-69 1. 12 14 42.50 i-93 11.46 1:37 47.60 1. 61 13.09 1. 14 15 44-83 3-13 13.93 2.22 49.81 2.03 12.06 1.44 4. Visual Vocabulary 9 89.07 =*= 7-15 28.06 ± 5.06 102.76 ± 4.27 27-59 ± 3.02 10 85-33 5-41 39.27 3.82 104.50 4.30 37-13 3-04 11 103.42 4.17 37-i 2.95 115.32 4.30 39-3 3-04 12 126.16 4.72 39-6 3-34 126.13 4.05 35-5 2.86 13 135-71 5-44 39-5 3-85 135-79 3-93 35-9 2.78 H 138.87 5-87 42.61 4.15 143.82 3.28 32-30 2.32 15 H3-44 6.82 39.16 4.82 154.93 3-58 28.08 2-53 5a . Courtis Arithmetic — Attempts 9 17.07 ± 1. 16 4.56 ■*■ .82 19.82 ± 1.09 7.07 ± .77 10 21.46 .82 5-95 .58 23-65 .72 6.23 •5i 11 23.64 .60 5-34 -42 27.71 .87 7-92 .61 12 27.24 .81 6.72 -58 33.16 .89 7-83 -63 13 3i-°5 1.28 8.51 .91 37.18 1. 11 9-63 •79 H 34-92 1.29 7.66 .91 37-93 1 2 1 9-79 ■85 15 38.72 2.51 11. 17 1.78 39-56 1.67 9-93 1. 18 5 b. Courtis Arithmetic — Rights 9 9-79 * -78 3-o6 ± .55 9.18 ± .96 6.22 ± .68 10 9-50 .81 5-9i -58 13-91 -8i 7.02 •57 11 14.67 ■73 6.41 .51 18.61 .93 8.49 .66 12 17.79 .62 5-15 44 23-73 -98 8.61 .69 13 23-15 1.24 8.24 .88 26.21 1. 17 10.09 •83 H 23.00 1.48 8.77 1.05 28.17 1.24 10.09 .88 •15 26.50 i-93 8.60 1.37 27.18 1. 61 9-53 1. 14 Status of the Subjects 33 TABLE I — Continued Sab. Courtis Arithmetic — Combined Atts. Rts 9 13-78 * -95 3.72 =•= .67 14-25 ± .94 6.08 ± .66 10 15-65 .72 5-21 .51 18.53 •72 6.19 •51 ii 18.72 -65 5-8 .46 23.21 -83 7.6 •59 12 22.26 .68 5-6 .48 28.22 .92 8.05 -65 13 26.92 1. 19 7.9 .84 31-47 1.09 9-4 •77 H 28.97 1.36 8.08 .96 33-65 1. 18 9-55 -83 15 30-97 2.23 9-93 1-58 33-37 1-57 9-33 1. 11 6. Woody Arithmetic 9 74.21 ± 2.22 8.72 ± 1.57 75-03 ± 2.77 17.92 ± 1.96 10 79-75 2.70 19.61 1.91 90.21 2.20 19-05 1.56 ii 94.89 2.12 18.90 1.50 100.95 2.08 19.01 1.47 12 109.27 1.89 15-6 i-34 111.27 2.06 18.1 1.46 13 "5-4 2-49 16.5 1.76 114.09 1.98 17.1 1.40 14 116.94 2.47 14.66 1.75 116.27 1.92 15.60 1.36 15 121.39 2.62 11.66 1.85 117.56 2-57 15.26 1.82 7. Stone Reasoning 9 2-75 =1= .28 1. 10 =<= .20 3-45 ± .41 2.66 =*= .29 IO 3-43 •34 2-43 -24 3-83 •23 1.98 .16 ii 4-93 •34 303 -24 4-77 .21 1-95 •15 12 6.77 •38 3-i -27 6-39 •3° 2.6 .21 13 8.13 .48 3-2 -34 7.09 •37 3-2 .26 14 8.42 ■59 3-51 -42 7-65 •38 3.06 •27 15 9-74 ..86 3-85 -6i 7-83 .46 2.72 ■32 8. Composition 9 3.00 =t .16 .64 ± .12 3-39 * -13 ■84 ± .09 10 2.97 •13 •97 -09 3-99 .10 •85 .07 ii 3.21 .11 .98 .08 3-97 .10 ■93 .07 12 3-98 .12 .99 .08 4.24 .14 1.20 .10 13 3-46 •14 1.02 .10 4-75 .12 1.06 .08 H 4-49 .14 1.05 .10 5-28 .11 1. 12 .08 15 5-05 .16 .90 .11 5-55 •15 1. 14 .10 q. Opposites 9 8.36 ± .40 1-55 * -28 10.71 =*= -33 2.17 * .24 10 9-75 •39 2.82 .27 u-53 •33 2.82 •23 ii 11.03 ■38 3-4 -27 11.63 •35 3-2 •25 12 12.98 ■53 4-36 -37 11.68 43 3-77 •30 13 13.60 •58 3.82 .41 11.76 42 3-65 •30 14 12.87 •79 4-70 .56 12.89 49 3-97 •36 15 13-39 •93 4.12 .66 13.00 •56 3-34 .40 34 Changes in Mental Trails with Age TABLE I — Continued 9 12.10 10 12.27 ii 13.46 12 l6.06 13 17.70 H 20.70 15 17.96 9 20.79 10 20.88 ii 22.33 12 24-53 13 25-67 14 25.I3 15 26.30 9 14.64 10 I7.83 ii 19.17 12 20.28 13 22.62 H 22.46 15 23-50 9 18.07 10 14-50 ii 16.08 12 18.44 13 20.75 14 20.54 15 20.23 •56 .87 ■43 •41 •57 I-I3 1.20 14 49 39 32 36 57 56 ± 1 75 67 52 44 52 60 72 1.32 1.01 .81 •94 1.27 1. 21 1-43 10. Directions 1.85 =±= .40 14.04 4-63 .61 16.11 3-H ■3i 16.53 3.01 .29 16.37 3-29 •4i 17.70 5-31 .80 18.34 5-33 •85 19-43 11. Concrete Memory 4.46 ± .80 20.24 3-59 •35 22.26 3-5 .28 23-63 2.69 ■23 24.70 2.6 •25 25.84 4.16 .40 26.64 3-32 ■40 26.57 12. . Abstract A. Temory 6.85 =±= 1.24 15-45 4-85 •47 18-35 4.6 ■37 20.16 3-72 •31 21.64 3-8 •37 22.53 4-33 ■42 23.11 4-13 •51 24.18 13. Italian Voc abulary 5-18 =■= -93 16.24 7-37 .72 16-35 7.2 ■57 18.26 7.92 .67 19.76 9.19 .89 23.24 8.76 •85 24.77 8.20 1. 01 23-79 62 43 45 33 5i 57 75 61 37 35 32 29 29 27 •85 ■46 •43 •38 •33 •37 .41 1.84 .81 •91 1.02 •94 •76 1. 11 3.06 ± •44 3-o8 ■31 3.62 •32 2.82 •23 3-8i •36 4.20 .40 4-33 •53 3-96 * •43 3-24 .26 3-2 •25 2-77 .22 2.64 .20 2.84 .20 2.10 ■19 5-5i =■= .60 3-93 •32 3-9° •30 3-33 •27 3.02 •23 3-6i .26 3.21 •29 11.92 =t 1.30 7.04 •58 8-33 .64 8-95 •72 8.57 .86 7-43 ■53 8.71 .78 14. Woodworth-Wetts Substitution 9 38.21 ± 2.05 8.06 ± 1.45 47.71 ± 1.67 10.81 ± 1. 18 10 40.25 i-37 9-95 -97 48.35 1.22 10.53 .86 11 44.78 1.27 1 1.3 .90 50.39 1. 14 10.4 .80 12 48.96 1.06 8.92 -75 55-41 152 13-3 1.07 13 55-54 1.32 9.62 .94 60.37 1.60 14.6 I-I3 H 57-00 1.88 1366 1.33 6345 1.52 14.90 1.07 15 61.63 2.24 12.86 1.58 62.93 1.70 13-33 1.20 Status of the Subjects 35 TABLE I— Continued IS- Letter-Digit Substitution 9 99-93 ±= 6.60 25.91 ± 4.67 128.08 ± 3.42 22.08 ± 2.42 10 105.96 3-88 28.18 2.74 138.44 3.33 28.75 2.35 ii 117.28 2.91 25.9 2.06 154.47 2.33 21.3 1.65 12 I35.84 2.29 19.2 1.62 168.33 3-6i 31-7 2.56 13 147.46 3-35 24-3 2.37 181.47 3.92 35-8 2.77 H 160.96 5-21 37-8i 3.68 188.95 4-07 40.07 2.88 15 170.17 6.00 34.46 4.24 192.50 4.16 32.61 2.94 16. Part of Omnibus 9 18.07 ± .80 3-i6 ± -57 15.92 ± .83 5-38 * -59 10 13-67 .86 6.28 .61 13.68 .80 6.88 •56 ii 11.81 •72 6.4 .51 12.76 .72 6.58 •5i 12 9.08 .83 6.87 .59 11.47 .70 6.11 •49 13 8.15 .86 5.69 .61 10.00 .62 5-39 •44 • H 8.87 1.04 6.16 .73 10.77 -79 6-43 ■56 15 9.72 1.49 6.65 1.06 10.00 .94 5.60 .67 17 . Trabue Language Completion 9 11.07 =*= -54 2.13 ± .38 11.50 =t .37 2.36 ± .26 10 11.42 ■37 2.72 .26 12.71 .27 2.36 ■19 ii 11.64 •30 2.7 .21 13-03 -23 2.07 .16 12 12.81 .26 2.17 .18 13-33 - 2 4 2.14 •17 13 13-96 •37 2.68' .26 13-79 -30 2.72 .21 H 13-79 .42 3-o8 .30 14.48 .22 2.12 •15 15 14.36 .48 2.63 .32 15-07 -32 2.48 .22 18 . Thorndike Reading — Alpha 2 9 5-55 ="= .09 •37 =*= -07 5.94 ± .12 •77 ± .08 10 5-58 .12 .84 .08 6.16 .09 .82 .07 ii 6.11 .09 .82 .07 6.40 .07 •63 •05 12 6.65 .09 .77 .06 6.72 .09 .69 .06 13 7.08 .10 •73 -07 7.07 .07 .64 •05 H 7-13 .09 •57 -06 7-33 -07 ■71 •05 15 7.19 .12 .71 .09 7-53 -08 ■65 .06 In Table II is given the number of boys and girls of each age, taking the tests. Table III presents data showing the per cent of the boys at each age equalling or exceeding the median girl's score for the same age in each test. 36 Changes in Mental Traits with Age TABLE II Showing the Number of Boys and Girls of Each Age Taking the Tests Tests I, 2a, 2b, 2c, 4, 8, Tests 3, 50, 5&, 6, 7, Test 10 11. 12, 13, 14, 15, 17, 18 9, 16 Ages Boys Girls Boys Girls Boys Girls 9 7 19 7 19 5 11 10 24 34 24 34 13 23 ii 36 38 36 38 24 29 12 32 35 31 35 25 24 13 24 38 20 34 15 25 14 24 44 16 30 10 25 15 15 28 9 16 9 15 TABLE III Per Cent of Boys at Each Age Equalling or Exceeding the Median of the Girls of the Same Age in Each Test Ages Test 9 10 11 12 13 14 15 1 . . 57-1 20.8 19.4 14. 1 16.6 41.7 40.0 2a . . 28.6 10.0 13-9 1 1-3 8-3 8-3 6.6 2b 42.9 10.8 8-3 12.5 9.2 6.6 2C . . 28.6 20.8 30-5 45-3 45-8 29.2 26.6 3 ■ 28.6 27.1 27.7 25-1 25- 21.9 33-3 4 ■ 14-3 41.7 33-3 59-4 58.3 54-2 53-3 5" 35-7 36.1 34-7 22.6 35-0 34-3 33.3 50 . . 71.4 33-3 30.5 22.9 45-0 28.1 44.4 6 . . 77.1 29.2 41.6 45-9 50.0 50.0 66.6 7 ■ 48.6 37-5 36.1 54-9 60.0 56.2 55-5 8 . 45-7 20.0 16.9 26.8 29.2 24.2 34-6 9 ■ ■ 7-i 20.8 52.7 57-1 66.0 75-o 66.6 10 30.0 15-4 22.9 41.6 33-3 79.0 41-7 11 57-1 39-2 33-3 43-8 50.0 52-1 53-3 12 57-1 53-1 43-1 52.5 53-3 54-2 46.6 13 85-7 50.0 37-5 35-6 47-9 33-3 31-3 14 . 25.0 29.2 33-3 21. 1 25.0 33-3 40.0 15 ■ ■ 28.6 12.5 5-5 3-i 16.6 25.0 40.0 16 71.4 58.3 38.8 33-5 35.0 25.0 33-3 17 40.0 37-5 28.3 44-3 54-2 52.1 50.6 18 14-3 38.3 - 30.6 28.1 37-5 46.6 36.0 V AMOUNT AND RATE OF YEARLY IMPROVEMENT I . METHOD OF TREATING DATA Each child's score in each test was subtracted from his score in the same test the following year. This difference represents his improvement in one year, and is positive or negative. For those tested three years the same procedure was followed, taking the difference between the first and second, and the second and third, tests. These improvements in each test have been grouped ac- cording to the ages of the children. May 15 was the median date of testing each year, and so ages have been computed as of that date. The age given on all tables is, in each case, the child's age on his last birthday; thus a child nine years, seven months and twenty-nine days old on May 15 is recorded as nine years of age. The median yearly improvement in gross score in each test, for each age and for each sex, has been computed and is given in Table V. Table IV gives the number of boys and girls making the improvements shown in Table V. TABLE IV Showing the Number of Boys and Girls of Each Age Making the Improve- ment Shown in Tables V, VI, and VII Tests 1, 2a, 2b, 2c, 4, 8, Tests 3, 5a, 5b, 6, 7, II, 12, 13, 14, IS, 9, 16 Test 10 Ages 17,18 Boys Girls Boys Girls Boys Girls q to 10 7 17 7 17 3 9 10 to II 20 24 20 24 9 13 II to 12 24 21 24 21 11 12 12 tO 13 16 20 15 20 9 9 13 to 14 13 27 10 23 5 14 14 to IS 14 24 9 14 6 9 38 Changes in Mental Traits with Age TABLE V- Median Yearly Improvement in Gross Score for Each Age, Test, and Sex Yearly I 2a 2b 2C 2bc Gain from Age B G B G B G B G B G QtolO 6.00 20.67 16.25 16.50 8-75 16.50 18.75 20.83 25-83 28.75 10 to II . 14.67 17-33 10.00 15.00 12.50 I7-50 22.50 10.00 22.50 26.00 II to 12 . 10.67 6.50 10.00 11.50 13.00 7.92 27.50 16.25 25.00 13-13 12 to 13 . 3.00 14.00 11.25 14.29 11.00 10.00 30.00 17-50 18-33 17-50 13 to 14 . 28.33 18.50 17-50 11.25 11.25 12.92 27.50 27-5o 25-83 22.08 14 to IS ■ 10.00 16.00 11.25 12.50 8-75 14.29 12.50 20.00 13-33 21.25 9 to 10 10 to II 11 to 12 12 to 13 13 to 14 14 to 15 Sa 5b Sab 5.00 5.00 22.50 16.25 4-50 7-33 4.00 6.67 4-50 3-33 8.67 31-25 20.00 5.00 4.67 7-33 6-33 5.00 4-33 5.00 15.00 13-50 4-33 8.25 3-67 4-75 3.00 3.00 4.00 10.00 12.50 4-25 4.71 5-33 3-50 4.00 4.67 3-56 10.83 6.50 7.67 5-25 2-33 5.60 4.14 5.00 1.67 6.67 10.00 4-50 5.00 5-75 10.00 6.00 7.20 5-33 5-75 4-33 4.80 2.00 otoio 10 to 11 11 to 12 12 to 13 13 to 14 14 to 15 QtOIO 10 to II 11 to 12 12 to 13 13 to 14 14 to 15 otoio 10 to II 11 to 12 12 to 13 13 to 14 14 to is 31-50 24-75 2.88 1.25 .650 ■950 3-38 3-50 5-oo 21-75 15.00 2.25 1.50 •500 ■450 2.40 1.70 3-25 11.25 10.13 1-33 2-15 •633 .600 2.17 2.19 1.88 4.88 9.00 2.63 1.83 .700 •340 1.90 1.38 1.50 10.50 6-75 i-33 1.58 ■350 •783 1. 00 1.79 7-50 7-5° 10.00 1.42 1.67 .700 .600 I-I3 2-33 1. 00 13 14 1.88 2.50 2.50 3-75 3-oo 1.25 15 3-50 2.25 5-5o 5-25 2.00 o-75 7-50 6-75 28.75 2.50 2.50 2-75 2.25 1.67 0.00 10.00 10.00 26.67 2-75 1.90 2.67 2.50 0.00 1.20 9.00 9-38 27.50 1.50 1.50 1. 00 2.00 1. 00 2.20 7.00 6-75 19.00 1.38 1.70 •50 2.10 2.00 2.00 1.50 7.69 22.50 2.00 1. 00 1. 00 3-50 1. 00 1.67 7-50 4.88 30.00 18.75 27.00 19-38 25.00 28.75 20.00 16 17 18 9-33 6.25 2.38 2-75 ■75o .800 5-57 3-88 1.50 1.50 .767 .700 3-67 3-38 2.00 1.44 •533 ■438 3-25 3-00 2.67 125 -500 .400 3-67 2-73 1-75 1.42 •440 .417 2.00 2.00 1. 00 1.60 .200 •367 1 This table should be read as follows: In Test 1 boys made a median gain in gross score of 6.00 from age nine (i. e., 9.0 to 9.9) to age ten (i. &, 10.0 to 10.9), etc. Rate of Yearly Improvement 39 Only a very rough idea of the course of improvement from one age to another can be obtained from Table V. In order to compare the results of the different tests with one another, in order to com- bine them into similar groups upon various bases of classification, and in order to compare my results with those of other investigators, it is necessary to employ some means that will overcome the effect of different-sized units in the different tests and of different numbers of persons tested in different experiments. The size of units presents itself concretely as follows: Is an improvement of 21.75 problems on the Woody scale more or less than an improvement of 5.25 prob- lems on the Courtis arithmetic tests? It is unnecessary to go into any discussion of the various methods which are possible. The method used by Norsworthy (1906), recommended by her and by Thorndike, Woodworth (1912), Sleight, and others, is the method which is quite commonly used in giving careful statistical treatment to educational and psychological data.. This method, which seeks to equalize units of different tests and to render data from diff- erent groups comparable, employs the procedure of dividing gross score differences of various kinds by the respective variabilities of the tests, groups, etc. Any measure of variability, average deviation, median deviation, semi-interquartile range, or stand- ard deviation, may be used. On the whole the use of the stand- ard deviation is probably better than that of other measures of dispersion. With my data the problem is to render different tests comparable, and to compare gains at different ages. I have not, however, divided the gross gains in each test at each age by the respective variabilities for each age and test, but have used the average of the standard deviations of ages eleven, twelve, and thirteen. We may think of gain at different ages in two ways at least: (1) Gain in relation to whatever ability, training, etc., the child at any age possesses; i. e., gain as a fraction of what he already is, or has. (2) Gain in relation to some more or less constant, objective thing, by which we can say the child from nine to ten improves 1.2 as much as from fourteen to fifteen, and 1.1 as much as from eleven to twelve, and mean this constant, absolute sort of thing, rather than the kind of gain implied in (1). It is for the purpose of finding out something about gain or improvement in this second sense that we have chosen to divide the different gains by a constant in each test and for each sex — the 4 o Changes in Mental Traits with Age TABLE VI 2 Yearly Sigma Gains in Each Test for Each Age and Sex— Data of Table V Divided in Each Case by the Appropriate Average S. D. Yearly 1 2a 2b 2C Gain from Age B G B G B G B G QtO 10 . .213 .792 1. 07 1 •673 •524 •731 •653 .786 10 to II . .669 .664 .658 .611 •749 •775 .783 •377 II to 12 . .487 .249 .658 .469 .719 •346 ■958 .613 12 to 13 .106 •537 .741 •583 ■659 438 1-054 .660 13 to 14 . . 1.293 .709 I-I53 •458 .674 ■565 •958 1.037 14 to 15 ■ ■456 .613 •74i •509 ■524 .625 ■435 •754 QtO 10 10 to II , 11 to 12 , 12 to 13 13 to 14 14 1° 15 QtO 10 . 10 to II 11 to 12 12 to 13 13 to 14 14 to 15 to 10 10 to II 11 tO 12 12 to 13 13 to 14 14 to IS 2bc 5a 1.080 1.026 ■358 •370 .581 .440 .656 .941 .928 •239 .642 .807 •542 •729 1.046 .468 .310 •370 •387 .366 .631 .766 .625 •215 .296 .258 •338 .619 1.080 .788 •335 .263 .280 .176 1. 118 •557 .758 •358 .123 .172 .271 .656 5b Sab .606 •736 .700 .862 1.852 1.369 •927 I. Ill .698 ■778 .638 1.279 .830 •723 •556 •524 .466 .689 .661 .560 .427 .807 .386 .622 •519 .287 •492 .845 •353 .618 .644 •575 .617 •373 .427 .871 .000 ■932 .240 .441 ■553 ■456 10 II .661 .896 •875 .988 I-587 .610 1. 194 .501 •424 .621 .480 1. 03 1 .811 •853 •634 .566 .562 .618 •597 .811 .938 .702 .320 .492 •389 .476 1.217 •5ii •351 •737 ■259 •505 2.381 •974 .470 .702 .566 .292 .658 •317 •405 .682 .866 •552 •975 •557 .621 ■591 .581 •833 .709 .612 .647 .783 .871 .662 .522 •592 ■348 , 12 13 U 15 Qto 10 1.361 1-535 — .246 .087 •754 .528 1-257 ■633 10 to II .680 .657 .206 .000 1.005 •783 1. 166 .912 11 to 12 . . .660 .760 .000 -•139 .904 .726 1.202 ■654 12 to 13 .247 •584 .123 •255 .704 .528 .831 •844 13 to 14 . . .122 .614 — .246 .232 .150 .602 •984 .971 14 to is ■ ■ .247 1.022 -.123 -•193 •754 •374 1.312 •675 2 This table reads: In Test 1 boys from nine to ten improved .213 of the average S.D. of Test 1 of boys of ages eleven, twelve, and thirteen. Rate of Yearly Improvement 41 TABLE VI— Continued Gain from 16 17 18 9 to 10 1.476 1.036 ■944 1. 191 •974 1.230 10 to II . . .881 ■645 •595 .649 .996 1.076 II to 12 . . .580 .560 •793 .623 .692 •673 12 to 13 . . ■514 ■497 1-059 •54i .649 .607 13 to 14 . . .580 •452 .694 .614 ■571 .641 14 to is ■ ■ .316 •331 •396 .692 •259 ■564 average of the eleven-, twelve-, and thirteen-year S.D.'s of each test for each sex. The data of Table V have, therefore, been divided by the ap- propriate average S.D.'s; the results are given in Table VI. These results are now comparable, and we can examine this table to see the changes which have taken place with the group tested, from one age to another, but only in so far as we are safe in saying that the group has been truly tested. An inspection of Table VI shows the great variation in the amount of gain in the different tests at different ages. Much time could be spent developing more or less fantastic theories to fit the data of Table VI; e. g., if one compared Test 2a with Test 2b, the question at once arises, "How will we har- monize the great increase in improvement of the boys in Test 2a from thirteen to fourteen over that from twelve to thirteen, with practically no increase at the same time in Test 2b?" It could, of course, be said that the habits being formed in handwriting recitation practice (the thing tested in Test 2b, become so firmly fixed by age thirteen that they carry over into ordinary written work to a greater extent during the following year in than previous years, and so bring about a greater improvement in the quality of the handwriting in ordinary written work from thirteen to fourteen. This may or may not be true. My data do not seem to give valid grounds for such a conclusion. Again, comparing Test 5b Courtis, rights, with Test 6, Woody arithmetic, let us note the discrepancy in rate of gain from nine-ten to ten-eleven in the two tests. How do we account for the increase in rate in the one test and for the decrease in rate in the other? The same people were tested in both tests under as nearly the same conditions as we could probablv 42 Changes in Mental Trails with Age obtain. Here again, we might speculate over the difficulty of the problems in the two tests, or the length of time required in relation to attention, etc. And so on, with all the tests. I have compared the curves in the different tests (not given here) 3 by superimposition, and from doing this, as well as for other reasons, given later, believe our best interpretation of the data must be sought in another direction. To interpret directly from the results of single tests, most of them given but once in any spring (and hence not as reliable as if two tests of equal difficulty were given a week apart), and all of them given to a comparatively small number of children of each age and sex, is obviously unsound, even though often done. The unreliability due to few children tested can be seen in the even-numbered columns of Table I. I have computed the median deviations of the gains in each test at each age for each sex. These median deviations have been divided by the appropriate average S.D.'s; the results have been analyzed; these P.E.'s show clearly that we must group our data in some way to enable us to place more reliance upon it. Accordingly four bases of classification have been chosen, so that by grouping the results of the tests in these four ways all of the tests will be divided into a few large groups. This has the effect, in part, of giving a particular test twice; i. e., the different tests which belong to one of these large groups, when taken together, tend to give a more reliable result. The following bases of classification have been chosen: 1. Similar Functions. a. Tests of simpler or lower mental functions. b. Tests of memory functions. c. Tests of higher or more complex functions. d. Tests of informational functions. 2. Presence or Absence of High Scores. a. Tests in which practically no high scores are made. b. Tests in which some very high scores are made. 3. Influence of School Instruction. a. Tests of functions much influenced by school instruction. b. Tests of functions little influenced by school instruction. 3 Wherever reference is made to graphs or tables as not being given here, it means they are given in the original manuscript copy on file at Teachers College, Columbia University. Rate of Yearly Improvement 43 4. Ability Required to Make Initial Score. a. Tests requiring much ability to make an initial score. b. Tests upon which an initial score is easy to make. This chapter should, then, seek to answer two broad questions: (1) What changes are revealed at the different ages in the tests when classified in this fourfold way? (2) What light do the data throw upon the different theories and opinions as to mental develop- ment with age? Similar Functions. The tests have been divided among the four groups of similar functions as follows : 1. Simpler or lower mental functions: Test 1, number checking; and tests 2a, 2b, and 2c, the handwriting tests. 2. Memory functions : Tests 11 and 12, immediate auditory memory, concrete and abstract; and Test ij, memory for the English equivalents of Italian words. 3. Higher or more complex functions: Test 8, composition; test g, opposites; test 10, directions; test 14, substitution; digit-geo- metrical forms; test 15, substitution; letter-digit; test 16, the part of Omnibus test used; test 17, Trabue Language Completion; test 18, Thorndike Reading, Alpha 2 — the understanding of sentences. TABLE VII Average Gains, Four Groups of Similar Functions, in Terms of the Average S.D. of Ages Eleven, Twelve and Thirteen; for Boys and Girls Simpler Memory Higher Informational Ages B G B G B G B G 9 to 10 . . .615 •745 .770 .802 1.013 •951 1-034 .806 ioton . . ■7H .607 .580 •509 •845 .760 •875 .675 11 to 12 . . •705 .419 •532 .428 .726 .650 •5°7 •573 12 to 13 . . .640 •554 .294 •454 •675 •589 •434 .467 13 to 14 1.019 .692 •095 •479 .678 .683 .502 •4°3 14 to IS . . •539 .625 .269 ■392 •595 •542 •439 .407 4. Informational functions : Test 3 , spelling-columns Q, S, and U, of the Ayres scale ; test 4, Thorndike Reading A2 and B — visual vo- cabulary ; tests 5a and 5b, Courtis arithmetic, form B ; test 6, Woody arithmetic — -series A; test 7, Stone reasoning. 44 Changes in Mental Trails with Age But grouping tests as informational, does not imply that they do not test the higher functions. Division problems and the problems of the Stone reasoning test do test what we regard as higher or complex functions. In the same way increase in vocabulary is a mark of developing intellectual grasp, at least, up to a certain extent. The tests included under this heatding were chosen so as to have several tests more or less similar, in the group with the spelling, and the arithmetic problems in subtraction, etc. As already noted, the data of Table VI are comparable for the different tests. I have accordingly combined them into these four groups by averaging the S.D. gains . of Table VI for each age and sex. This gives Table VII. Let us take up these groups of functions in order. What changes are shown by the tests of the simpler or lower mental functions? 2. RATE OF IMPROVEMENT IN SIMPLER FUNCTIONS An examination of the data of Table VII shows that the amount of gain for boys at the different ages was about the same, with a decided increase in the amount at thirteen-fourteen. The gains for the girls show a less amount of gain at eleven-twelve than at any other period. While these figures are now comparable with each other, and we can say that in the tests given, these children made median gains that bear the relationships shown by the figures of Table VII, yet an examination of the data of Table VIII (in which TABLE VIII P. E. of Yearly Gains (in Terms of the S.D.) for Each Age and Sex in Each Group of the Similar Functions Simpler Memory Higher Informational Ages B G B G B G B G 9 to 10 •437 •465 1. 160 1.228 .422 •583 .466 •398 10 to II .632 .681 •730 .804 .558 •558 •391 .420 II to 12 . . .492 ■369 ■564 •775 •444 •436 .427 •355 12 to 13 . . .490 .468 .761 ■545 ■547 •534 •337 •323 13 to 14 . . •598 .472 .610 .651 .508 .520 .294 •327 ' 14 to is . . .616 ■458. .520 .727 .625 •550 •39° .427 Rate of Yearly Improvement 45 are given the median deviations in terms of S.D. of the different groups of tests) tells us that the ups and downs shown by the figures of Table VII for simpler functions cannot be regarded as absolutely representative even of the group tested. On account of this fact and in view of the errors of sampling it seems that the data give evidence of a steady rate of improvement for both boys and girls at all ages from nine to fifteen; that this improvement is positive at all ages and is on the whole probably about .6 of the average standard deviation (in these tests) of ages eleven, twelve and thirteen. In Fig. 8 I have shown the curves of changes at these ages. In plotting the changes I have used the same distance for .5 S.D. as for one year. This has been done because the gains from one year to the next, as shown by the differences between the average 95 •253 .236 -.080 .220 .052 •341 .031 .231 2 "Ox." refers to data from tests of girls in the Oxford higher elementary schools. Gain Shown by Other Investigations TABLE XIII 59 Average Yearly Gains in Tests of Higher Functions, in Terms of the Standard Deviation Gilbert Pyle ( 1913) Bickersteth Ox.' Dewey, Child and Ruml Ages B G B G B G G B G 8 to o •504 .216 .258 .250 •313 Q to 10 . . . . .648 .648 •259 .482 •503 •323 •3H •377 .174 10 to II . . .187 .389 •330 ■173 •450 .224 .410 .318 ■234 II to 12 .029 •259 .125 .358 .207 .414 .209 .226 .097 12 to I J .360 -.648 •434 .249 •394 •304 •174 -.025 .302 13 to 14 . — .101 .864 .071 .252 •193 14 to is .807 .144 •453 .199 .226 IS to 16 -.058 — .072 .203 .217 16 to 17 .144 •504 .069 .366 17 to 18 •332 .117 TABLE XIV Showing Yearly Gains in Memory and Higher Functions in Terms of Standard Deviation— Pyle (1920) Data Memory Higher Ages B G B G 8 to .198 .224 .292 .204 to 10 •279 ■151 •342 •390 10 to II •235 •354 .218 ■454 11 to 12 .163 •234 .262 •403 12 to 13 .069 .212 .258 ■35° 13 to 14 . .106 •093 .256 .241 14 to 15 •159 .082 .271 .266 15 to 16 — .014 .126 .207 .382 16 to 17 . . .250 .098 •425 •155 27 to 18 -•035 .019 .007 .169 ' "Ox." refers to data from tests of girls in the Oxford higher elementary schools. 6o Changes in Mental Traits with Age TABLE XV Showing Yearly Gains in Simpler, Memory and Higher Functions in Terms of 'Standard Deviation — Woolley Re-Test Data Ages Simpler Memory Higher B G B G B G 14 to is 15 to 16 16 to 17 17 to 18 •723 .097 .146 .408 .776 .005 •195 .440 •340 •5" .114 .028 .289 •463 .231 •057 ■390 .160 .021 — .001 .406 •154 .081 .110 Tables XII, XIV, and XV set forth the gains in memory func- tions. It will be noticed that Gilbert quite frequently finds the rate of gain to be negative. His data include one memory test — the estimation of a length of time equal to a two-minute period. The boys' gain from nine to twelve was nine times that from twelve to fifteen, but it is doubtful if any one would insist that such figures represent the course of improvement of memory, or even of time-memory. The girls' rate was more than twice as great during the first three-year period as during the second. Pyle (19 13) found negative gains for both boys and girls at one-third of the one-year periods between nine and fifteen. But in his 1920 data he finds with the larger groups no negative gains at any age between nine and fifteen ; furthermore the gains from year to year are more regular than with the smaller 191 3 group. This change toward greater regularity of gain from year to year, as we increase either the number of tests or the number of children tested, or especially as we increase both — this concomitant greater regularity of yearly rate is significant. However, the ratios of the total gain from nine to twelve to the total gain from twelve to fifteen, are the same practically in 1920 as in 1 913 — being about two to one. Bickersteth (Oxford girls) found no gain from nine to twelve in memory for related words; but these results are not conclusive because at every age some children made perfect scores. Dewey, Child, and Ruml found the boys' gains from nine to eleven more than three times as great as during the next two years, while the Gain Shown by Other Investigations 61 girls gained from nine to eleven one and a half times as much as from eleven to thirteen. The general evenness of Pyle's (1920) curves (not given here) between nine and fifteen is quite noteworthy. It is in marked con- trast with Norsworthy's gains in memory for related and unrelated words, and Smedley's data for growth of memory of digits. Tables XIII, XIV, and XV give the data for the higher mental functions. Gilbert's data represent one test, reaction with discrim- ination and choice, and show very great variations from year to year. Gilbert found negative gains for girls at twelve- thirteen and for boys at thirteen-fourteen. From nine to twelve boys gain two- thirds as much as from twelve to fifteen, while girls gain three times as much. Pyle's data for 1913 show positive gains at all ages but the rate from year to year is not even or constant; from nine to twelve, boys make an improvement about 70 per cent of that from twelve to fifteen; girls make nearly one and a half times as great gain from nine to twelve as from twelve to fifteen. The 1920 data, as compared with that of 1913, show the same greater evenness from year to year as in the case of memory. The boys' gains from twelve to fifteen are equal to those from nine to twelve ; the girls' gains during the nine-twelve period are one and a half times as great as during the twelve-fifteen period. It should be noted here that both boys and girls make slightly smaller gains from fifteen to eighteen than from twelve to fifteen. Bickersteth found boys from nine to eleven gaining 50 per cent more than from eleven to thirteen, while the girls gained about one-third more from eleven to thirteen than during the two previous years. Oxford girls from nine to twelve make 50 per cent greater gains from twelve to fifteen. Comparison of the Yorkshire Dales girls with the Oxford girls shows that from nine to eleven the former gain nearly two times as much as from eleven to thirteen, while the latter gain but 80 per cent as much from nine to eleven as from eleven to thirteen. Bickersteth 's gains at all ages are posi- tive. Dewey, Child, and Ruml found positive gains at all ages except from twelve to thirteen for boys. From nine to eleven the boys gain more than three times as much as from eleven to thirteen ; the girls' improvement is the same for both periods. The curves, showing the rates of improvement found in each of these investigations, are not given here; they show the effect of 62 Changes in Mental Traits with Age increasing the number of subjects and tests by a greater smoothness of the curves, and by the nearly constant rate of improvement from eight or nine to fifteen or sixteen; but increasing the number of subjects tested and increasing the number of tests given, is, other things being equal, getting more adequate measures of mental traits at different ages. Comparing all these data with my own, we see that the S.D. gains in the latter case are much greater than in the former; or, more exactly, they are from 1.5 to 6.9 times as much. It is reason- able to assume that the amount of growth from nine to fifteen is approximately the same for all the groups of children tested by these investigations, and that the differences in the size of the S. D. gains are largely due to the different tests used to measure the functions and to the possible masking of some of the changes which is involved in taking the differences of the central tendencies of different ages as the amount of growth from year to year. Pro- ceeding upon this assumption, I have put the total gains from nine to fifteen of the children I tested, equal to the total gains found in each of these investigations in the. same functions for the same ages. , The gains for each year have then been parcelled out so that the relative gain from year to year has been preserved, and the total gain from nine to fifteen is equal in all cases to the gain shown by my group. Where data are given for periods of time less than six years, the gains for the shorter period are put equal to the gains made by the Minnesota re-test group for the same years, and then parcelled out to each year of the shorter period. On the whole this has the effect of making the gains at each age more than those shown in Tables XI to XIV. This pro- cedure was not followed in the case of the Woolley data, because it is re-test material. The tables giving the data, as thus transmuted to this new basis, are not given here but a comparison of them with Table VII shows the following equalities of gains: 1. Simpler functions: Gilbert's girls from eleven to thirteen, Bickersteth's Oxford girls from eleven to thirteen, Pyle's girls from nine to eleven, from nine to twelve, and from twelve to fifteen, made the same respective gains as shown by my data; Pyle's boys from thirteen to fifteen, and Dewey, Child, and Ruml's boys from nine to eleven, and from eleven to thirteen Gain Shown by Other Investigations 63 made the same respective gains as do my own group. By one-year periods there are very few equalities of gains in all these data. 2. Memory functions: The boys tested by Gilbert and the girls tested by Pyle (1920) both made gains from nine to eleven the same as were made by my re-test group. Rejecting the results of the Italian vocabulary test does not make any difference in these equalities. 3. Higher functions: Gilbert's boys from nine to eleven, Pyle's 1920 boys from eleven to thirteen, Pyle's 1920 girls from nine to eleven made the same gains as are shown in Table VII. Attention should be called to the results of Netschajeff's eight immediate memory tests. No variabilities are given so the gains have been averaged. While the different tests are not comparable, yet they are similar enough that averaging the gains is not in serious error. The data show the following average gains : TABLE XVI Netschajeff: Average Gains in Memory Ages 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 Boys . . .11 .61 .21 .13 .90 .21 .16 -•17 Girls . . .20 .57 .62 .33 .10 .03 •56 .20 If we had the variabilities to use in making the gains in the different tests comparable, there is no doubt that the combined results would still show gains from nine to sixteen. One cannot safely generalize upon the results of each tes{: separately, because one test, requiring not more than three or four minutes, is not an adequate test of a function. Netschajeff's results have been used quite extensively, and some generalizations of doubtful validity have been based upon them; e. g., "The above eight series of twelve each . . . showed that each kind of memory here tested increased with age, with some slight tendency to decline at or just before puberty." Some of the tests actually do not show a decline in memory power at any age, though the rate of gain is decreased; there is no time between nine and seventeen when a positive gain is not shown by some one or more of the individual tests, while the average for each year is positive, except at sixteen- seventeen for boys. 6 4 Changes in Mental Traits with Age It should be observed that the boys from thirteen to fourteen made the largest gains, while my data show the smallest gains at this time; both are probably in error. There is in all probability greater improvement than shown by my data, and less than shown by Netschajeff's. Lobsien's eight memory tests (no variabilities are given) show the following average gross gains: TABLE XVII Lobsien: Average Gains in Memory Ages Q-IO IO-II 11-12 j 2- 1 4% Boys . . ... 7.25 10.68 2.76 8.19 Girls . . . . 4.82 16.00 3.08 8.82 The average of the gains is here more liable to error than is the average gross gain in Netschajeff's data. The irregular gains, shown by the data from both of these in- vestigations, are not symptomatic of the curve of growth of memory as we have seen from the data from more extensive investigations. TABLE XVIII Composite Average of Data From Tables VII, and XI to XV, Formed by Giving the Following Weights: Minnesota Re-Test Data 10; Woolley Re-Test Data 10; Gilbert 1; Pyle (1913) 3; Pyle (1920) 3; Bickersteth 3; Oxford Girls 3; Dewey, Child and Ruml 4 Simpler Memory Higher Ages B G B G B G 8 to •323 •503 .209 .091 .308 .252 q to 10 ■475 ■534 .491 ■523 .649 •569 10 to II ■519 •430 .428 •315 ■537 .471 11 to 12 .506 .318 .265 .250 .416 .418 12 to 13 ■395 ■375 .230 .316 .428 •359 13 to 14 •839 •517 .128 •363 •451 .487 14 to 15 •532 •537 •233 .267 •475 •390 15 to 16 •093 •059 .192 ■313 .163 .210 16 to 17 .189 •173 •159 .104 .108 .169 17 to 18 •472 •399 .051 .312 .063 .122 Gain Shown by Other Investigations 65 To get a better idea of the probable course of mental development from nine to fifteen I have combined the data of Gilbert, Pyle, Bicker- steth, Dewey, Child and Ruml, and Woolley. The averagesof thedata of Tables XI to XV have been found for the three groups of functions — simpler, memory and higher. In taking these averages the follow- ing weights have been assigned to the data from the different investi- gators: Gilbert — one; Pyle 1913 — three; Pyle 1920 — three; Bicker- steth — -three; Bickersteth's Oxford Girls — three; Dewey, Child and Ruml — four; Woolley Re-Test Data — ten; Minnesota Re-Test Data — ten. These composite averages are given in Table XVIII. The curves for these averages are given in Figs. 12 to 14 (page 66). We will consider the ages covered by my data — nine to fifteen. For simpler functions the two outstanding features of the curves of the composite averages are (1) the general regular trend of the curves showing a constant rate of improvement during these six years, (2) with an exception at thirteen to fourteen for boys — a TABLE XIX Number of Cases in Table XVIII at Each Age Age Boys Girls Total 8 459 509 968 9 696 781 1.477 10 900 901 1,801 11 984 919 1.903 12 887 1,084 1. 971 13 913 945 1,858 14 1.449 1,429 2,878 15 1,164 1,090 2,254 16 946 916 1,862 17 705 706 1,411 18 475 454 929 Total 9,578 9.734 19.312 No. of Boys No. of Girls Between Ages 9 and 75 6,993 7.H9 Total 14,142 66 Changes in Mental Traits with Age /.*■ ' g- j £Jo To^ii //-'/£. JMR'3 /3V? Ttf^S ~i&& Mc'7 H-H Fig. 12. Simpler Functions. (Composite Average — Table XVIII) ^=e~ . — -* -~-~x fe^. J6 «• °^*" — — — » ' *t & o 10-11 fi-'iS. t£-R /■?-/V l