V- \rA.~ THE RELATION OF QUICKNESS OF LEARNING TO RETENTIVENESS BY DARWIlSr OLIVER LYON, A. M. REPRINTED FROM ARCHIVES OF PSYCHOLOGY NO. 34 Submitted in partial AilflUnent of the requirements for the degree ef Doctor of Philosophy in the Faculty of Philosophy, Columbia University NEW YORK 1916 THE RELATION OF QUICKNESS OF LEARNING TO RETENTIYENESS BY - DARWESr OLIVER LYON, A. M. KEPRINTED FROM ARCHIVES OF PSYCHOIiOGY No. 34 Submitted In partial ftilfilnient of the requirements for the degree ef Doctor of Philosophy in the Faculty of Philosophy, Columbia University NBW YORK 1916 Press of The new Era printing Company Lancaster, Pa. Gift -s^ OCT 22 «? PREFACE The present work is the outgrowth of experiments on memory that I have been conducting since the year 1906. My studies have had in view several problems under the general head of memory, and some of the results have already been published as follows : ' ' The Relation of Length of Material to Time Taken for Learning, and the Optimum Distribution of Time," Journal of Educational Psychology, 1914, 5, 1-9, 85-91, 155-163. The problem of the present study has been in view from the start, but has not been included, except incidentally, in the articles which are enumerated above. Acknowledgments are due first of all to Professor Cattell, to whom I am especially indebted for the numerous suggestions and for the many valuable hints and criticisms given me in the treatment of the results. For similar reasons I must also thank Professors Thorndike and Woodworth. To Professor E. Meumann, formerly of the Uni- versity of Leipzig, I am indebted for his numerous suggestions and for the opportunity given me to perform certain experiments on the students at the University of Leipzig. The numerous professors, superintendents, principals and teachers who have made this work possible are too numerous to mention. I am under particular obligation, however, to Alfred E. Rejall, formerly professor of philosophy and psychology of the State Normal College at Albany, N. Y. ; and also to Mr. Frank Lawrence Glynn, superin- tendent of the State Trade School of Bridgeport, for numerous cour- tesies extended me, as well as for his expert opinion on all matters per- taining to vocational instruction. The author also extends his thanlcs to the following for permis- sions and privileges granted : Joseph F. Scott, superintendent of New York State Reformatories and Prisons; Hon. John J. Barry, com- missioner of correction of the City of New York ; Dr. C. Macfie Camp- bell, of Bloomingdale Hospital, White Plains ; Dr. Frederic L. Wells, of McLean Hospital, Waverley, Mass. ; Dr. August Hoch, director of the Psychiatric Institute on Wards Island. The writer also desires to acknowledge his indebtedness to all those who served as subjects in the various experiments, and especially to those who were so obliging as to undertake the 40-nonsense-syllable, and other long tests. iii CONTENTS Chapter I Historical 1 Chapter II Methods Employed ,• 17 The Problem Stated 17 Methods of Experiment 17 Materials Used 22 Methods of Scoring 24 Classes of Subjects Tested 33 Chapter III Eesults 34 The Tables 34 Time of Initial Learning 37 Interval between Learning and Reproduction 40 Amount Retained 41 Intellectual Standing 52 Social Standing 53 Age 54 Sex 55 Chapter IV Summary and Recapitulation of the Main Results 56 Appendix Some of the Materials Used 59 THE RELATION OF THE QUICKNESS OF LEARN- ING TO RETENTIVENESS CHAPTER I HISTORICAL The history of scientific inquiry concerning the relation of The Quickness of Learning to Retentiveness, and, for that matter nearly all experimental work on memory, dates back only thirty-four years. Before 1880, experimental psychology had confined itself largely to reaction times and sensations, but with the publication of Ebbing- haus's ''Uber das Gedachtnis"^ in 1885 experimental work on mem- ory acquired an impetus that has ever since been on the increase. The material chosen by Ebbinghaus for his experiments consisted of about 2,300 nonsense-syllables made and selected as follows : From the simple consonants and the eleven German vowels and diphthongs he formed all the meaningless syllables possible by placing a vowel or a diphthong between two consonants. These lists of nonsense-syllables were then shuffled and drawn by lot. Ebbinghaus preferred these "nonsense-syllables" to words because of their relative simplicity. The remark is often made, however, that nonsense-syllables are not simple, and that on the contrary, they are in some respects as com- plex as words. Ebbinghaus himself remarks that something more simple would be desirable for the reason that the learning of nonsense- syllables involves not only the sense of sight and hearing, but the muscular sense of the vocal organs (tongue, lips, etc.) . Moreover, not only do nonsense-syllables not possess equivalent tendencies to set up association processes, but certain lists of syllables that may appear equally difficult to one individual, may appear very unequal to another. However, with all their faults, nonsense-syllables are pre- ferred by many psychologists to words, prose, or poetry for testing the "organic memory." Words are apt to form associations too easily, especially with some individuals ; and prose and poetry are far from being homogeneous in that they are constantly changing in character. This is especially the case with those individuals in whom 1 An excellent translation of this monograph has recently been made by Euger & Bussenius, vmder the title "Memory." It comprises Educational Ee- print No. 3 of Teachers College, Columbia University. 1 2 BEL AT ION OF QUICKNESS OF LEARNING TO BETENTIVENESS "interest" is so necessary that material not "interesting" to them is practically impossible of memorization. Though it is true that many of the nonsense-syllables used by Ebbinghaus were such as to allow numerous associations, his experiments were so conducted as to pre- clude the forming of these associations to a considerable extent; in fact, with Ebbinghaus they were seldom formed. Another advantage in the use of nonsense-syllables is that they afford an almost unlimited number of combinations of a similar character and quantity. Never- theless, nonsense-syllables have so many objections not carried by digits that it is a question as to whether the latter would not be better for the testing of "organic" or "rote" memory. Ebbinghaus gave much careful attention to details of method. His method was to repeat the syllables aloud until he could voluntarily recall them. He considered that he "knew" them when he was able to repeat the series correctly, in a given time, after the first syllable had been supplied, A series was read through once from beginning to end without stopping, and then upon the first syllable being sup- plied the attempt was made to repeat the entire series, stopping how- ever, at the first hesitation. At this first hesitation, the remainder of the list was read and the entire repetition was started again. The syllables were read and repeated at the rate of 150 per minute and in a uniform tone. The rate was secured by timing the reading by ' ticking of a watch or by the strokes of a metronome. Upon a series being completely memorized, Ebbinghaus made a pause of 15 seconds for noting the results, after which he immediately started in on an- other series. No attempt Avas made to form logical associations, the speed being so great as to practically preclude this. Ebbinghaus took great care that all the conditions would be such as to favor atten- tion ; his environment was such as to favor concentration and in case of ill health the experiment was deferred. Though Ebbinghaus did not specifically attack the problem of retention as related to speed of learning, some of his results are fundamental in considering this problem. It should be understood that he experimented only upon himself as subject, and that his re- sults have therefore, in the first instance, only individual validity; but it should also be remarlced that he tested every point in many trials, and that he was, undoubtedly, an unusually steady and trust- worthy subject for experiment. One of his results that is pertinent to our study concerns the effect on retention of varying amounts of time devoted to the original learning. He found, as we should naturally expect, that the greater the number of repetitions, within certain limits, the better the reten- tion. To determine the effect of many repetitions upon retention he EISTOBICAL 3 repeated a series of 16 syllables a definite number of times, and then noted how many repetitions were required 24 hours later to complete the learning-. He found that about one third of the labor was saved by the repetition of the day before. Thus we may say that three repetitions to-day save one to-morrow, or, in other words, for every three times a person repeats such a list to-day, he will save one repe- tition 24 hours later. This was true, whether the number of repeti- tions on the first day was barely sufficient, more than sufficient, or less than sufficient to enable the series to be immediately recited. In a general way, this same result applied also to the retention of series of differing length, learned at first to the point of correct recitation. As would be expected, it required a longer time to learn a long series than a shorter one. Ebbinghaus found that, as a rule, he could repeat a series of seven syllables after a single reading ; about 17 readings were required for a series of twelve syllables, and nearly 30 readings for a series of sixteen. But, on testing twenty-four hours later, he found that the longer series were the better retained. The additional work which the long series demanded in learning produced an enduring effect, much as if it had been devoted to the over-learning of shorter series. Ebbinghaus found that the value of a repetition for purposes of retention was greater when the learning was distributed over several days than when it was concentrated into a single study period. Thus, in one series of experiments, he learned 12-syllable series on one day, and relearned them on the three succeeding days. The average num- ber of readings required for an errorless recitation was 17.5 the first day, 12 the second day, 8.5 the third day and 5 the fourth day. In another experiment he continued reading 12 syllables beyond the time necessary to learn them, *. e., the number of repetitions was greater than that needed for an errorless repetition. Thus if the series was re- peated only eight times on one day they were not known the following day ; nor could they even be recognized as the list studied. If given 68 repetitions, however, they could be recognized the next day, al- though the series could not be given, for, on relearning the series 24 hours later, 7 repetitions were required. On comparing the two facts ' as given above it will be noticed that in the first case 38 repetitions, distributed over three days, needed on the fourth day only five repe- titions ; while 68 readings on one day needed, even on the very next day, seven repetitions. Ebbinghaus 's studies on the rate of forgetting are especially well known. He found that while it is relatively rapid at first, later it goes on more and more slowly, and in his judgment nothing once learned is ever absolutely forgotten. He found after an interval of 4 RELATION OF QUICKNESS OF LEARNING TO EETENTIVENESS one hour so much has been forgotten that more than half the time originally expended must be again applied to the work in order to relearn it. After eight hours almost two thirds of the labor must be repeated. From this point it would seem that the process of forgetting proceeds more slowly. After twenty-four hours two thirds of the original labor must still be performed, i. e., the "impression of the whole" retains about one third of its original strength. The change now becomes still slower, for even after six days one quarter is still retained, and after a month one fifth. "It is noteworthy" says Burnham, "that, while the impression made by nonsense-syllables is so evanescent that a series once perfectly learned is forgotten after an interval of twenty minutes, a residuum of some sort persists for a long time, so that even after a month the same series can be relearned in four fifths of the time originally required. A general statement of the results is as follows : The ratio of what is retained to what is forgotten is inversely as the logarithm of the time." Thus far we have considered only those experiments of Ebbing- haus in which the material used was nonsense syllables.. We will now turn our attention to the experiments in which he used logical trains of thovgJit. For this work Ebbinghaus used stanzas from Byron's "Don Juan." He found that the time taken to learn a stanza was only one tenth as long as that needed for a list of nonsense syllables of the same number as the number of syllables in the stanza. In other words, material connected by the bonds of sense and rhythm needed only one tenth the number of repetitions required by material vot so connected. Not only was the meaningful material more speedily learned, but it was also better retained. As tested twenty-four hours after learning, by his "saving method,"^ the retention was as follows : No. Readings Re- No. Readings Re- Per Cent. Material Learned quired to Learn quired to Relearn Retained 12-syllable series 16.5 11 33 24-syllable series 44 22.5 49 36-syllable series 55 23 58 Stanza of "Don Juan" 7.75 3.75 52 Meaning, therefore, affects the speed of learning and the retention in the same way, favoring quick learning and tenacity of retention. Another factor that affects the two in the same way is the speed of reading. Ebbinghaus reports experiments^ in memorizing stanzas of Schiller's translation of the ^neid at the rate of 200, 150. 120 and 100 iambics per minute. At these rates, he learned the same number 2 See below, p. 20. sGrundzuge der Psychologie, " 2d ed., 1911, pp. 672-673, EISTOBICAL 5 of lines in 138, 148, 160 and 180 seconds respectively, thus proving that the amount of time required varied inversely as the speed of reading. To be sure, a greater number of repetitions is required with the rapid than with the slow rates. He concludes that the fastest rate of reading is the most economical as concerns the act of learning. In order to test the retention as well, he relearned the stanzas twenty- four hours later, using now for all the constant rate of 150 iambic feet per minute, and found that the stanzas which had been originally read at the greatest speed and learned in the least time were also, on the whole, slightly better retained than those that had been read more slowly. He repeated the retention test after eight days, with the same result. In 1887 G. E. Miiller and F. Schumann,* stimulated by the work of Ebbinghaus, set out to repeat his experiments on a more elaborate scale, making, however, certain changes in method and material. Their labors extended over a period of five years (1887-1892 inc.). The only fundamental difference between their experiments and those of Ebbinghaus was that they did not let the subject know the purpose or result of the various experiments, a thing obviously impossible where the experimenter uses himself as subject. The material used consisted of nonsense-syllables similar to those iLsed by Ebbinghaus, but selected with greater care, and instead of being read directly from the sheet of paper on which they were written and where they could all be seen at once, they were read from a revolving drum through a slit in a screen. The drum from which the syllables were read was allowed to revolve at different rates in the various experiments. The three rates used were such that the syllables appeared at intervals of 0.731, 0.615, and 0.572 seconds, respectively. Thus the intervals were so short that no time was given for a second perception or for the formation of mnemonic acids. As explained before, the material used by Ebbinghaus was far from being homogeneous, and had he not read them at so rapid a rate many of his nonsense-syllables would have been highly undesirable because of their easy associations. Miiller and Schumann invented a convenient plan for constructing nonsense- syllables of a more homogeneous sort than those used by EbbinghaiLS. Ebbinghaus left the make-up of the syllables wholly to chance, while Miiller and Schumann laid down certain rules making the series of syllables ' ' normal " or " extra normal. " A ' ' normal ' ' list of syllables had all the initial consonants, all middle vowels, and all final con- sonants different, respectively, from the syllable immediately pre- * ' ' Experimentelle Beitrage zur Untersuehung des GedacMnisses, ' ' Zeitsch. fur Fsych., 1894, 6, 81, 257. 6 BELATION OF QUICKNESS OF LEARNING TO BETENTIVENESS ceding or following. The initial consonant of the first, and final con- sonant of the second syllable in any one of the trochaic feet into which the series was divided in reading, were never the same. Syl- lables forming well-known words were never allowed to come together. A series of syllables was called "extra normal" when no two syl- lables used on the same day had two letters the same. The most important results of Miiller and Schumann's experi- ments, bearing on the quickness of learning, may be stated as follows : 1. The association between syllables in the same foot is much stronger than that between adjacent members of different feet. The suppression of rhythm in memorizing lists of nonsense-syllables renders the task much more difficult, nearly twice as much time being required. 2. The syllables first learned are not necessarily those presented the earliest. Frequently those syllables at the end of the set are the first the subject is able to reproduce. The syllable first learned is that which first attracts the attention strongly. This may be because cer- tain associations arose easily or it may depend on circumstances purely accidental, i. e., the syllable may have appeared just when the attention was at its "height," and thus the syllable having gained the "ascendency," kept it, since the attention naturally centered on it every time. 3. The first of any two successively and simultaneously experi- enced syllables tends to call up the second. If they are associated only through intermediate syllables, the association is stronger if both are accented. The second syllable in a trochaic measure tends to call up the first, and this tendency seems to be stronger than the tendency to call up the first syllable of the next sueceeding measure.' 4. Under certain conditions, syllables with associations already established prove more difficult to memorize in combination with new syllables, than when such associations are lacking. The previous asso- ciations press in on consciousness and disturb attention in various ways. 5. The ease of memorizing seems to depend upon the amount and character of the work that has immediately preceded, aside from the factor of fatigue, which, of course, is all-important. 6. The ease with which series of such syllables are learned de- pends not alone on the subjective differences, but also on objective conditions, which, however, may lead to subjective differences. Colegrove in his book entitled "Memory" briefly sums up other 5 We should not, however, infer from this that every presentation alirays tends to call up the one preceding but we should take it that when any element of a complex presentation is supplied it tends to call up all the others. HISTOBICAL 7 results of Miiller and Schumann 's work as follows : A syllable series can be learned more easily (1) if two or more successive syllables have like initial consonants; (2) if two syllables rhyme; (3) if two suc- cessive syllables or initial syllables of two successive rhythms have the same vowel or diphthong; (4) if the beginning consonant of the first syllable and the end consonant of the second syllable of a rhythm, or the end consonant of a syllable and the beginning consonant of the next syllable are the same ; (5) if two or more syllables form a word. On the other hand, consonants difficult to pronounce or an accumula- tion of diphthongs impeded the act of memorizing. A series in the trochaic rhythm is memorized more easily than a series in the iambic rhythm. As regards retention, Miiller and Schumann found that the per- son who memorized a series of nonsense-syllables in the shortest time also relearned it in the shortest time after 24 hours. This was to be expected, since what is forgotten can be relearned more quickly by a quick learner than by a slow learner. But the slow learner saved more time, both absolutely and relatively, than the fast learner, when the relearning was compared with the original learning. Whitehead, in "A Study of Visual and Aural Memory Proc- esses,"® sets out to answer the following questions, among others: (1) What is the relative quickness of the visual and the aural senses when employed in the memorizing of nonsense-syllables constructed like those of Miiller and Schumann ? (2) What is the relative power of retention for matter memorized visually compared with that mem- orized aurally? Or, put otherwise, what is the relative rate of for- getting for material memorized in the two ways ? Whitehead answers the above questions as follows: "(1) Of our thirteen subjects ten showed themselves able to memorize most rapidly from visual presentations and two from auditory, while one gave am- biguous results. This outcome is without much doubt to be correlated with the fact that so much of our memorizing, whether it occurs in the verbatim form, or merely as the assimilation of meaning, is brought about through visual process. (2) Matter memorized aurally appears to be retained slightly better than that memorized visually. It requires less repetition by 32 per cent, to learn anew from visual presentations matter memorized visually a week previous, and less repetition by 40 per cent, for aural memorizing of the same kind. The difference is insignificant in view of the total number of cases. It seems to be simply a special case illustrative of the general prin- ciple already mentioned that the greater the number of original repe- titions the less the number necessary for learning anew." Psych. Bev., 1896, 3, 258. 8 EELATION OF QUICKNESS OF LEAENIN^ TO BETENTIVENESS In regard to individual differences in retentiveness, Whitehead considers that the slow learner both releams in shorter time and retains a larger amount, than the fast learner. An examination of his results however, does not entirely support this conclusion. As Pyle very correctly says, "If we eliminate the results from one of his sub- jects (the eleventh in the first table, p. 267) as being an error (for it shows a relearning time longer than the time for original learning), and add the relearning times for the fast six and the slow six, respec- tively, we find without exception that the six who had learned in the shortest time aLso relearned in the shortest time. In fact, if we rank the two series for learning and relearning, for the various tables, from the best to poorest, we find a fairly high degree of correlation between quick learning and good retention." Jost, in his article entitled "Die Assoziationsfestigkeit in ihrer Abhangigkeit von der Verteilung der Wiederholungen,"^ takes up the distribution of repetitions as a factor of the strength of associa- tion. At first he uses the method of "complete memorizing"; then he uses the method of "right associates." and finally the two in con- junction. By the first method he finds that ten readings of a series of nonsense-syllables on each of three successive days make the mem- orizing of the series on the fourth day easier than do thirty readings on the day immediately preceding, although the difference is small. By the method of right associates he finds that when twenty-four repe- titions are distributed equally on three, six and twelve days, respec- tively, the most extended distribution (that of two repetitions a day), gives the best retention.^ Jost emphasizes especially the matter of repetitions, and explains the value of rests between readings by the theory that the repetition of an older association has a greater value, relatively, than the repetition of a younger one. In her article entitled "Experimentelle Beitrage zur Lehre vom okonomischen Lernen,"^ Miss Lottie Steffens considers the problem of the most "economical" method of learning, more especially for logical trains of thought. The two methods of study which she com- pares are the "piecemeal" and the "entire" or "mass" methods. The former is that usually adopted spontaneously by a person who has a long passage to learn, and consists in dividing the passage into parts, and reading each part separately till it can be recited, finishing up by a few readings of the whole passage. The "entire" method 7 Zeitsch. f. Ps\jc}wJ., 1897, 14, 436. 8 The question naturally arises, however, as to whether some other distribu- tion might not be still more favorable. This problem, viz., the optimum distribu- tion of time is considered in greater detail in my article cited in the preface. 9 Zeitsch., 1900, 22, 321, 465. HISTOEICAL S consists in reading the whole passage through and through till it is learned. The ''entire" method, though not appealing to the subject at the outset, is shown experimentally to give the quicker learning, as well as the better retention. These experiments were repeated by Pentschew,^^ with children as well as adults. He confirmed the advantage of the ' ' entire ' ' over the "piecemeal" method of study in adults, and also in children so far as concerns the learning and retention of meaningful material. With nonsense syllables, however, children did better by the "piece- meal" method, probably because, with children, the learning of non- sense demands so much effort that fatigue and disinclination creep in unless the syllables are studied in small groups. Ogden, in his paper entitled "Ueber den Einfluss der Gesehwin- digkeit des lauten Lesens auf das Erlernen und Behalten von sinn- losen und sinnvollen Stoffen,"" obtain results much the same as those of Miiller and Schumann. He finds that the fast learner rarely requires more time for his relearning than does the slow learner, but usually less. Ogden used both logical as well as nonsense material and his results were practically the same for both. He found that although the curve of relearning is as a rule nearly parallel to the curve of initial learning, it showed as a rule some flattening, that is, individual differences in time of relearning are not as great as are the differences in time of initial learning, Henderson^- found that in general those who learn quickly are able later to recall a greater percentage of what they have learned than the slow learners. In other words he finds that the power to learn readily correlates with the power to remember what has been learned. In his experiments, however, he did not allow his subjects to completely learn the material, and for his material he used only prose. His method, briefly, was as follows : He requested his subjects to read twice a selection taken from "The Dutch Homestead" by Irving. Three minutes was allowed for this. The subjects were then requested to write down as much as they could remember. Two days later they were again called upon to write down as much as possible, and after a lapse of four weeks a third recall was requested. His subjects varied from ten years up. He found that the older subjects learned somewhat better than the younger and explained this as due to their greater capacity to understand. This capacity, however, seemed to 10 ' ' Untersuchungen zur Okonomie und Technik des Lernens, ' ' Arch. f. d. ges. Psychol, 1903, 1, 417. 11 ArcMv. f. d. ges. Psychol., 2, 93. 12 E. N. Henderson, "A Study in Memory," Psych. Eev. Man. Sup., No. 23, ]903. 10 EELATION OF QUICKNESS OF LEAENING TO EETENTIFENESS have no influence on the relative retention. Henderson's results can not be held to apply to nonsense-syllables or other meaningless mate- rial ; and even with respect to connected prose, the material used, his results are not directly comparable with those of experiments in which complete memorizing has occurred. Radosavljevich,^^ conducting experiments in Meumann's labora- tory upon both adults and children, found better retention for mean- ingful than for nonsense material, thus confirming the result above quoted from Ebbinghaus. He also confirmed Ebbinghaus's result that long series of nonsense-syllables were better retained than short series, when each had been studied to the point of correct recitation. Practise increased the speed of the first learning and of relearning, but the first more than the second, indicating that memorizing and retention are two distinct facts of memory, possessing their own peculiar laws and conditions. The slower learner showed a greater "saving" in relearning, and he concludes from this that the slow learners retain better than the rapid learners. Adults learn more rapidly than children, but (again according to the "saving" method) retain less of what they have learned; and the younger children, similarly, learn more slowly but retain better than older children. Extensive experiments upon "The Relation of Facility of Learn- ing to Tenacity of Impression" have been conducted by Miss Gamble since 1908, and are not yet published in full at the date of this writing.^* Her experiments were designed to answer the following questions : 1. Do the persons who learn with the greater degree of facility retain for a given time the larger fraction of the material severally mastered ? 2. In the case of individual subjects, does the rate at which mate- rial is presented affect the fraction of the initial learning time which is saved in the relearning? 3. When the learning time is lengthened by the difficulty of the material is the relearning ti-me relatively short or relatively long ? 4. How may retention best be gauged ? Two sets of experiments were made : the first set bore only upon the first and fourth of the above questions and was made bj^ the method of retained membersy^ The other set, made by the method of 13 "Das Behalten und Vergessen bei Kindern und Erwachsenen nach experi- mentellen Untersuchungen," Leipzig, 1907. 14 The rather brief summary of her work here given has been made from notes taken during the reading of a paper by her at the Washington meeting of the American Association for the Advancement of Science (December, 1911). 15 This method will be found described below on page 18. EISTOBICAL 11 complete memorizing (Erlemungsmethode)^^ bore upon all four questions. In the first set of experiments Gamble used as subjects 350 college students and as material words, letters and figures. The method of presenting the material and the method of ascertaining each subject's degree of retentiveness differed somewhat from year to year, but the procedure may be roughly outlined as follows : The material was read 4 or 5 times to the subjects and 5 or 6 weeks later was again presented. The subject's tenacity was gauged by the two methods: The first was comparable to what I have called "Method 1,"^^ retention being gauged by the amount of material that could be reproduced without a fresh presentation. The material was then read once to the sub- jects, after which another reproduction was called for. This is prac- tically the same as what I have called ** Method 2,"^® The material was then read several times to the subjects after which still another reproduction was called for. In some respects, as far as results go, this is very much the same as my "Method 3,"^^ although complete relearning was not allowed. On the basis of the results obtained by Method 1, the subjects were arranged in two scales according to their facility in learning and according to their retentiveness as measured by the fraction retained of the amount originally learned. Each scale was divided into quarters. Gamble found that those who fell in the first quartile as regards facility in learning, fell in the first quar- tile as regards retentiveness in sufficient numbers to show a marked correlation between quickness of learning and tenacity of impres- sion. ^^ She recognizes the fact that some subjects who learn a very small amount in the first experiment appear to have retained a rela- tively large amount, merely because the amount learned the first time was so small that almost anything retained must be a large fraction of it. The results secured by what I have called ' ' Method 2 ' ' were of doubtful significance but the results obtained by "Method 3" showed, as might be expected, a marked correlation between facility in learning and relearning, 16 This method will be found described on page 2. As used by Gamble, it was practically the same as the method used by Ebbinghaus except that with her the presentations were aural instead of visual. 17 See below, page 18. 18 See below, page 19. 19 See below, page 19. 20 Were there no correlation whatsoever it is obvious that, by chance alone, about 25 per cent, of those standing in the first quartile of "primary learning" would stand in the first quartile of "retentiveness." As a matter of fact, how- ever, Gamble found that the percentage waa about 45, — i. e., 20 per cent, more than chance alone could account for. 12 RELATION OF QUICKNESS OF LEARNING TO RETENTIVENESS In the second set of experiments mentioned above (those made upon subjects by the method of complete-memorizing) facility and tenacity were gauged by the time (in seconds) of learning and re- learning. The material consisted of nonsense-syllables. The time which elapsed between learning and relearning was either one or two weeks, differing with different subjects. In these experiments Gamble found a slight correlation between quickness of learning and reten- tiveness. This, however, she found by what we might term the ' ' abso- lute" method of comparison, i. e., a comparison of the actual time taken for relearning with the actual time taken for the original learning — not dividing the one into the other and, therefore, not a comparison of percentages. Gamble thus found that, when facility and tenacity are measured on an absolute time basis, those who learn quickly are apt to relearn quickly. Gamble found that when a series of nonsense-syllables was learned and relearned at the same rate of presentation the fraction of the learning time saved in relearning is greater if the presentation rate is neither very slow nor very fast. When the series are learned at different presentation rates but relearned at the same rate, the frac- tion of the learning time saved is greater for the series which were originally learned at the slow rate of presentation, unless the absolute learning time of the "slow series" is very small. Series which are hard to learn are more often hard than easy to relearn. In attempting to answer the question, how retention may best be gauged, Gamble admits that no single method is satisfactory. She objects to a method of reproduction without fresh presentation for the reason that if a long time has elapsed since the series was learned, very many of the subjects can actually reproduce no units whatsoever, although the series may have left subliminal impressions which differ from subject to subject. Though she thinks the method of relearning is valuable to use in conjunction with others, she points out the im- possibility of distinguishing the revival of old impressions from a genuine new learning. In the paper here summarized she reached no definite conclusions in regard to the best method of testing retentive- ness. Pyle, in studying "Retention as Related to Repetition,"-^ used for material passages from an elementary book on nature study, con- taining 40 "ideas" each. Each passage contained on an average 150 words. The subjects taking part in the experiment were twelve graduate and senior college students. Pyle's method of presenting the material to the subjects was as follows: The experimenter read the material to the subject. After the 21 Jovr. of Ed. Psych., 1911, 2, 311. HISTORICAL 1 3 first reading, the subject gave orally as many ideas as he could recall. The experimenter checked up the record, recording the number of ideas correctly reported. Then the material was read a second time, and a second report was given by the subject and checked up by the experimenter. The experiment was continued in this manner until the subject reported, in his own words, every idea. The experi- menter having before him a copy of the material divided off by vertical lines into forty units, found it easy to check up the reports as given orally. After the lapse of 24 hours, the subjects were called upon to repro- duce, in writing, as much of the material as possible. The written ''ideas" were marked either ''right" or "wrong," "ideas" that were partially correct— that is, that had a "kernel" of truth— being marked as correct if they closely approximated the correct idea* rarely, half-credit was given when the variation from the correct meaning was considerable. The material was divided into such small units, each significant adjective, adverb or expression being set off as a separate unit, that this point gave little trouble,— a subject either reported the idea or he did not. The results of Pyle's most extensive set of experiments are shown in the table below. Only four subjects were here used, but each of them memorized 21 passages (of 40 "ideas" each). Subject C To Learn Repetitions Av. Dev. (No . of Ideas) ^tention Av Dev 4.7 2.24 37.5 2.0 F 2.9 0.78 38.5 1.7 K 5.2 1.40 •34.2 4.6 J 3.6 1.90 36.7 3.2 Ave, 4.1 36.7 The results as shown by this table show no great difference in amount retained between the fast learners and the slow learners. What little difference there is would seem to be in favor of the fast learners. It will be noted, however, that we can only say that they retain more absolutely. It is possible that had Pyle allowed his sub- jects to relearn the material previously memorized— obtaining his "amount retained" by dividing the time of second learning by the time of first learning— he might have found that the slow learners, although remembering absolutely less, could relearn what they had forgotten in a smaller percentage of their original learning-time than would be required by the fast learners. By the absolute method, however, Pyle is probably correct in his conclusion that "the slow learner certainly has no advantage in retention over the fast learner." It should be understood, however, 14 BELATION OF QUICKNESS OF LEARNING TO HETENTIVENESS that no general conclusions can be drawn from so few subjects, and although in general Pyle 's eight other subjects bear out the same con- clusion, they do not do so unanimously'-. However, Pyle 's later study^^ of 600 school children shows a high correlation of learning capacity, as measured by immediate memory, with retention, as determined by amount retained 5 weeks later. This extensive study confirms his earlier intensive study, and his conclusions may be stated as follows : A slow learner with more time and repetitions spent in learning does not retain more, absolutely, than the faster learner who uses less time and fewer repetitions. In 1911, Busemann, in an article entitled "Lernen und Be- halten,"-^ published results of several years' work on various aspects of the memory problem. Only a small portion of this work, however, throws light on the relation of quickness of learning to retentiveness. His experiments were performed on school children ranging in age from 12 to 18 years. As material, he used lists of various parts of speech (nouns, adjectives, etc.) and simple syllables. From his re- sults he concludes that of two individuals the one who takes the greater amount of time in memorizing a series of words will require less time, relatively, in relearning them. In performing his experiments Busemann used two of the various methods described below (page 18), the method of complete mem- orization (Ersparnisverfahren), and the method of right associates (Treffermethode). He does not feel that his experiments with the first method can answer the question as to whether the quick learner also forgets quickly. He considers the "Treffermethode" the one to use in answering this question, but does not feel that with this method he performed a sufficient number of experiments to warrant his making any general statement. His results, however, as far as they go, would seem to point against the assumption that it is the quick learners who forget quickly. In summing up his work on this subject he says "it has not yet been proven that a greater ability to learn corresponds to a smaller ability to retain ; — on the contrary it is prob- ably true that the good learner is at the same time a good retainer, ' ' Miss Norsworthy, in &n article entitled "Acquisition as Belated to Retention, "24 presents some very interesting results. The material she used as well as her method of experimentation were different from any that we have thus far discussed. As subjects she used 83 students in educational psychology. The material used was a German-English vocabulary of 1,200 words. Each student studied twenty minutes for 22 Jour, of Ed. Fsych., 1913, 4, 61. 23 Zeit. fur angewandte Psych., 1911, 5, 211. 24 Jour, of Ed. Psych., 1912, 3, 214. HISTOBICAL 15 five days, memorizing as many of the English equivalents of the Ger- man words as possible. Two days were then allowed to elapse, when each student reviewed the list of words that he had succeeded in "memorizing" during the previous five days. Two days more were then allowed to elapse, when the work was again reviewed. At the first meeting of the class after the above three study periods were over, they were asked to write the English equivalents of a certain 50 German words that were presented to them, and that had occurred in the list of German words they had succeeded in previously mem- orizing. From the results the percentage remembered could then be ascertained. One month after this test, another list of 50 words, chosen from those that remained, was presented to the subject with the request, as before, to write down as many of the English equiva- lents as possible. In like manner, the percentage remembered of these 50 German words was ascertained. Norsworthy found that the average per cent, remembered in the first test was 63, and that the average per cent, remembered in the second test, one month later, was practically the same, being 62, From these averages she found the deviation, either -]- or — , for each of her 83 subjects. The average deviation from the median for the six subjects learning 700 words or over, was + 14, whereas for the 13 subjects who learned only 300 words or under, the average devia- tion from the median was — 17. In other words, the quickest learners, who had mastered a vocabulary of over 700 words in a fixed time, retained a larger fraction than the slowest learners were able to retain of their much smaller vocabulary, learned in the same time. With the second test the difference was even more striking. The upper half of the class, in respect to size of vocabulary learned, re- membered in the first test, on the average, 70 per cent., the lower half only 52 per cent. The Pearson coefficient, for the whole class, between the number of words learned and the average per cent, remembered is .41 for the first test and .50 for the second test. In short, Nors- worthy finds a high positive correlation between rate of learning and retention — a correlation that is considerably higher than that obtained by any of the investigators whose work we have already examined. This, however, is probably due, not only to the method she used — the time remaining constant but the amount learned varying — but also to the nature of her material. This is not meant as a criticism. In fact it is probable that the use of such material as a German-English vocabulary, especially when used in the manner chosen by Nors- worthy, is far better, than the use of such material as nonsense- syllables, if we mean by ' ' memory ' ' such memory as occurs in every- day life and especially in the school room. 16 DELATION OF QUICKNESS OF LEARNING TO EETENTIVENESS Norsworthy's method of keeping the time constant, but allowing the amount learned to vary, has numerous advantages. It frees the learner from the responsibility of having to decide when he thinks that the material has been thoroughly memorized — "a responsibility that brings a very varying personal equation into the problem. It also frees the investigator from the burden of making a fair allow- ance for imperfectly learned material. ' '^^ In summing up the results of these various investigators, it is perhaps fair to say that they have found in the main, and other things being equal, the individuals who learn the quickest to remember the longest, i. e., to be the best retainers. Miiller and Schumann found that the quick learners forgot more, but were able to relearn what they had forgotten in a shorter time than the slow learners. An examination of their data shows that, relatively speaking, there is not much difference between the quick and the slow learner. ' White- head believes that the slow learner is a better retainer, but from the data he gives it is difficult to see just how he arrives at» this conclu- sion. Norsworthy, on the other hand, obtains a very high positive correlation. Working with a German-English vocabulary she finds that the last quarter of her class retain only two thirds as much as the first quarter. Ogden and Henderson working with meaningful material unite in finding that as a rule the quickest learner is the best retainer. Pyle is somewhat more conservative but says that the fast learner is certainly at no disadvantage in retention. With most of his subjects, Busemann finds that rapid learning means good retention. Gamble, dividing her classes into halves, quarters, etc., after much the same manner as Norsworthy, obtained in the long run a positive correlation. In the following pages, which deal with the special research that it is the object of this paper to present, an attempt will be made to prove that on the problem in question no general law or conclusion can be drawn from the use of any single material or method. We will endeavor to prove that not only do different methods give different results, but we shall endeavor to show that with the same data it is possible to draw contrary conclusions by dealing with the data in different ways. 25 Op. cit. CHAPTER II METHODS EMPLOYED The Problem Stated The experiments, which, with their results and the various meth- ods of dealing with same, it is the special object of this paper to dis- cuss, may be briefly stated as consisting in the learning, or "mem- orizing" of certain materials, allowing a definite number of days to elapse, and then measuring retention by one or more of the methods mentioned later in the chapter. In this way a fairly accurate idea was obtained of each subject's retentiveness, and by comparing this with the time taken for the initial learning, we arrive at a fairly accurate idea of the relation of each individual's quickness of learn- ing to his retentiveness. So varied were the materials used and so different the ages, con- ditions, intellectual standing, etc., of the subjects experimented on, that many* results were obtained that have been considered sufficiently valuable to warrant mention although they were not the especial ob- ject of the research, and in many cases have no direct relation to the problem. Besides the so-called "normal" subjects, state prison con- victs and asylum patients were tested. The latter, over 200 in num- ber, give results so complex in character that they shall be considered only very briefly. Our results obtained show not only the relation between quickness of learning and retentiveness, but also the relative amount of for- getting after different intervals; the relation between memory for logical trains of thought and for lists of syllables or digits ; the effect of age, sex and training on rapidity of learning and remembering; and a comparison of the amount actually retained by each subject with what he can reproduce after one reading. Methods of Experiment The main difficulty that one encounters in investigating such a problem as this is to determine which of the various possible methods and materials shall be used. To use all methods and all materials would involve too great a labor for any one experimenter. Three methods were used in this research. Since each method is frequently spoken of and referred to, it was deemed best to give each one some 17 18 RELATION OF QUICKNESS OF LEARNING TO EETENTIVENESS distinctive appellation, and I have named them "Method 1," ''Method 2" and "Method 3." Briefly stated these methods are as follows : Method 1. — Keproduction, as far as possible, of the material originally learned without fresh presentation. Method 2. — Reproduction, as far as possible after a single presen- tation. Method 3. — Supplying the subject with the original material and taking his time for relearning it. ■ We shall now consider each of these methods in detail. Method 1. — The subject was given, face downward, a sheet of paper on which were typewritten 20 nonsense-syllables.^ He was told that he could study these in any way he saw fit, but that as soon as he felt positive he could repeat them without error he should say "now" and come to the experimenter's desk. He was advised not to come up before he felt quite certain that he could repeat them without error, as the time consumed, if he failed to give a perfect reproduction, would be counted as part of his "time for learning." To avoid com- petition, each subject was taken separately, although where the op- portunity presented itself, several subjects were allowed to study in one room, and allowed to come to the adjoining room for their hear- ing. Instead of reciting his work, each subject was allowed, if he preferred, to write it down. The question will naturally arise : What was done when the sub- ject came up for examination and made numerous mistakes ? To this we can only say that such was seldom the case, it being thoroughly impressed on the subject's mind that he must be sure he could repeat his material perfectly before coming up for his recitation. Where several serious mistakes were made the subject was always sent back to continue his work of memorizing. But where only one or two minor errors were made it was thought best to deduct for these in as fair and scientific a way as possible, rather than send the subject back. This may not seem strictly accurate and scientific, but of two evils it was thought to be the lesser. Otherwise a subject whose time was 15 minutas for the nonsense-syllables might have been 30 minutes had he been sent back to correct the single minor error made. The material having thus been learned, a definite time interval was allowed to elapse after which each subject was called upon to re- produce in writing as much of the material as possible. It is in this reproduction that we have "Method 1." No especial directions were 1 In explaining these three methods we shall speak only of nonsense syllables. Other materials were also used, as will be explained below. 2 This varied in the different experiments from 1 day to 10 weeks. I I METHODS EMPLOYED 19 given for "Method 1," other than requesting that each subject write down as much of the original as he could remember, using the original words whenever he was able. He was also told that where he could remember nothing but the "gist" of the passage,^ he was to "put that down." MetJiod 2. — Method 2 was made to follow immediately upon Method 1. The directions read to the subjects for this method were as follows: "You have just tried to reproduce from memory a set of nonsense- syllables that you learned one week ago. You probably have a fair idea as to the correctness of your paper. I shall now read for you the original set of nonsense-syllables and shall ask you to again write out the list so far as you are able. ' ' This method, that I have designated as "Method 2," is to my mind one of the most satisfactory. Unfortunately it was not used with the first group of subjects (1907-08). MetJiod 3. — Method 3 was made to follow immediately on Method 2, The directions read to the subjects for this method were as follows : "You have tried to reproduce in writing a set of 20 nonsense- syllables that you memorized one week ago and which, after one hear- ing, you just now endeavored to reproduce. You undoubtedly have a fair idea as to the correctness of the paper you just handed me. I shall now supply you with the original set of nonsense-syllables with the request that you relearn them, saying "now" when you feel quite certain that you can reproduce the entire set. ' ' It will be noted, since in ' ' Method 2 ' ' the original material is read to the subject, that he does not enter upon "Method 3" with as much ignorance of the material, as if "Method 2" had been omitted. In view of this, in some of the later experiments, a separate series of syllables (or other material) was used for "Method 3," and this, of course, necessitated the memorizing of two distinct sets of syllables in the first place — one for Methods 1 and 2, and another for Method 3, The writer is aware that these methods are open to criticism. In the first place no one of the three methods is sufficient to answer the problem, and in averaging the results obtained by the three methods, it is a question which method to give the most weight. At the outset of these experiments. Method 3 was considered the most important, and Method 2 was ranked as being more important than Method 1. It was later thought, however, that the best way of arriving at each subject's general retentiveness was to count each method as equal. 3 We are here supposing the material was prose or poetry. 20 DELATION OF QUICKNESS OF LEAENING TO RETENTIFENESS We shall now, taking one method at a time, consider the chief criti- cisms that may be raised against it. Method 1. — It has the advantage of getting directly at the matter in hand, i. e., of obtaining from each subject exactly what has been so well retained that it can be voluntarily reproduced after a lapse of a certain period; but it has several disadvantages. The chief of these is that reproduction, without a fresh presentation of the mate- rial originally learned, reveals only the strongest of the original impressions — the so-called "supraliminal associations." It can be proved that many of the subjects have a considerable portion of the material once memorized on the "borderland," so to speak, — material that can be entirely recalled after one further reading. Were our investigation merely one dealing with the question of the relation of quickness of learning to reproductiveness, we would have to rank Method 1 higher than any other; but where ability to retain rather than ability to reproduce is the factor in question, it is obvious that we must take into consideration the various associations that are on the "borderland." Method 1 also has the disadvantage of giving results that are diffi- cult of measurement. Very frequently, in an attempted reproduction of material once memorized, the subject (if he is able to recall the various "topics" and "subtopics" and the "thought" of the passage in general) is apt to express this "thought" in a greater number of words than existed in the original passage. He is also very apt to introduce new thoughts, thoughts which he may or may not express in words that occurred in the original passage. This introduces several perplexing factors which are difficult of measurement. Method 2. — Its chief merit lies in the fact that it endeavors to do away with the above criticisms made against Method 1. To this end it endeavors to bring back the "subliminal" associations by reading the material once to the subject before asking for the reproduction. This one "reading" however, carries with it its own penalty. A single reading of a passage of 100 words consumes about one half minute and it is obvious that one half minute to a quick learner means much more than does one half minute to a slow learner. The second objection made to Method 1 naturally applies also to Method 2, although not to so great a degree, for this reproduction after hearing the passage read is less likely to contain new thoughts and extra words than if the passage had not been read at all. Method 3. — In utilizing the results of this method, the plan of Ebbinghaus Avas followed, the time for relearning being compared with the time of the original learning, and the time saved in relearn- ing, especially the per cent, of the original time saved, being taken as METHODS EMPLOYED 21 the measure of retention, while the time spent in relearning, ex- pressed as a per cent, of the time of the original learning, gives the complementary measure of the "amount forgotten." The chief dis- advantage to this method is that, in relearning, it is impossible to dis- tinguish facility in forming fresh associations from retention of sub- liminal associations. Another disadvantage is that it does not get directly at the amount and nature of the matter retained by each subject. It is thus a serious question if the method is a fair one to use in settling the question in hand. For with this method the sub- ject is not called upon to give exactly "what he rememhers" at the end of three weeks, but is first given the material to relearn, and then asked for a reproduction. A factor is thus introduced that is difficult of measurement, for this "relearning" may recall more to the mind of one subject than another, both of whom might otherwise have given equal results by the first method. It may, however, be justly contended that this factor is desirable since our problem is one dealing with retentiveness and not with ability to recall. Another criticism that may be made against Method 3 is this: it may be said that it is incorrect to rate two men as having the same degree of retentiveness, one of whom takes 25 minutes to learn a pass- age and three weeks later takes 5 minutes, while the other takes 10 minutes and three weeks later takes only 2 minutes. It may be true that these figures prove both men to have saved four fifths of the time originally spent, and that therefore the amount of the original that each has forgotten is one fifth, but this hardly seems fair, when we consider that the second man takes 07ily 2 minutes to do his relearn- ing as against the 5 minutes needed by the first man. Again it is possible that the first man had forgotten the material so completely at the end of three weeks, that not only was he unable to recall any of it, but he also retained practically none of it, and that the second learning was for him practically a memorizing of entirely new mate- rial, and that this time he took only 5 minutes because he was in exceptionally good condition. In fact when the material used con- sists of digits, we would expect the time for relearning to be, on the average, nearly as great as the original time.* However, taking everything into consideration Method 3 has many merits and gives us information that neither Method 1 nor Method 2 is capable of. It also has the advantage of supplying us with a very easy and accurate measurement, namely, time. One objection carried by Method 3 is that it takes no allowance for 4 In several cases the second time was not only equal but even greater. This is aseribable either to a poorer mental condition of the subject or to distraction of some sort. 22 EELATION OF QUICKNESS OF LEARNING TO BETENTIVENESS the partial relearning that the preceding methods (1 and 2) have given. Method 3 is supposed to show,^ besides other things, the actual time that is taken for relearning the material. It is obvious, there- fore, that before starting Method 3, the subject should not only not have thought of the material during the period that has elapsed from the day it was originally learned, but he should not be allowed to "review" it just previous to starting Method 3. It is just these things, however, that methods 1 and 2 do — for in the one, the subject endeavors to recall as much of the material as possible, while in the other he is allowed a "review." This, however, is not a criticism against Method 3, per se, but a criticism against the way in which the method was here used. Rectification was made in two ways: either (1) a separate and distinct material was used for Method 3, or (2) — the time taken for the reading of the passage (in Method 2) wa.s added to the time given in column 3. [In some cases the time taken for the "attempted reproduction" was also added.] It will be noted, however, in those tables where this has been done, that the addition of a minute or two throughout column 3, makas practically no differ- ence in the final correlation. One criticism that might be made of all the methods rather than of any one method in particular, is that an investigation of this sub- ject, to be thorough, should involve the use of various time intervals. For example, instead of merely allowing 10 weeks to elapse between the time of initial learning and time of relearning, we should also use inter\'als of one day, one week, six months, etc. Proof that the length of the time intervals allowed to elapse should be seriously considered is seen in the fact that with most groups of subjects the correlation of quickness of learning with retentiveness depends partly on the length of the time interval. The complete solution of a problem of this nature should take into consideration all the mental performances of the subject, and should involve the use of all the senses, since each one may be said to have its own "memories." Limited experiments, such as these herein described, can answer the question only in a limited degree. Materials Used Five main kinds of material were employed on all of the regular subjects. Some of these were omitted or abbreviated in the case of the insane. The chief materials were digits, nonsense-syllables, words, prose and poetry. Four sets of each of these were employed. The specifica- 6 See column 3 of any of the tables. METHODS EMPLOYED 23 tions of the materials chosen, and their method of selection, are de- scribed below under their respective headings. (a) Digits. — In the regular set of experiments the number of digits used was 20. With one group of 16 individuals, series of 40 were also used. The method of procedure in making the list of digits was as follows : Small cards, bearing the digits from to 9 inclusive, were placed in a box and shaken up. They were then taken out, one at a time, and if the digit drawn violated none of the rules given below, it was written down as one of the list. In any case before drawing another digit, the digit previously drawn was put back in the box and the box shaken. Rules : 1. The digits must be drawn by chance. 2. No digit may be allowed to follow another that is one half as much, or twice as much, as the first, e, g., 6 may not follow 3, nor 3 follow 6. 3. No digit may follow another that is only one more or one less than the digit in question, e. g., 4 may not follow 3 nor 3 follow 4. 4. No three digits may be allowed to come together that have the same difference between them, e. g., 3-5-7. 5. No two digits may come together that have already appeared together in the list. 6. Since digits, like nonsense-syllables, words, etc., are generally learned rhythmically in groups of four, no digit may start a group that had previously been used to start a similar group, nor may the final digit of a group (of four) be permitted to stand if it has already been the final digit of a preceding group (of four), e. g., if 7-1-5-2 have occurred once as one group, no other group in the same series may start with 7 or end with 2. (&) Nonsense-syllables. — The diverse results that have been ob- tained by different experimenters using nonsense-syllables as mate- rial can be partly explained by the difference in the syllables selected, i. e., their degree of "nonsensity." The nonsense syllables employed by Ebbinghaus should hardly be called by this name as many of them are, in German as well as English, practically words. Those used by Miiller and Schumann were selected with greater care and are on the whole much better. A really good set of nonsense-syllables is ex- tremely difficult of formation. My own method of making the series of 12 and 20 was as follows : Out of a list of 90 nonsense-syllables,^ three competent judges 6 There are only about 90 fairly good nonsense syllables for English-speaking persona. 24 RELATION OF QUICKNESS OF LEARNING TO EETENTIFENESS selected forty-five that to their minds ''carried the fewest objections." These forty-five were then placed in a box and, by following certain rules similar to those laid down for digits, three sets of 20 were selected. Here, as with the digits, if the syllable drawn violated any of the following rules, it was thrown back and another selected in its place. The rules observed in the arrangement of the nonsense-syllables were as follows: 1. Syllables must be drawn by "chance." 2. Initial consonants may not be the same unless separated by two or more syllables. 3. End consonants may not be the same unless separated by two or more syllables. 4. Vowels may not be the same unless separated by two or more syllables. 5. The initial consonant of one syllable may not be the same as the final consonant of the preceding syllable. 6. There may be no repetition of the same syllable in any one series. (c) Words. — In the regular experiments only nouns were used. These were drawn by chance from 200, previously selected, and ar- ranged in lists of 20. Whenever the word drawn, made, with the preceding word, an association that was considered "quite obvious" by two of the three judges, the word was thrown back. Of the four sets of words used, two were formed entirely of words of three letters, (d) Prose. — Several passages of different nature and content were chosen, as follows : 1. A passage of 100 words from Kipling's "Kim" starting with "The diamond bright dawn." 2. A passage of 100 words from the preface of Haeckel's "Riddle of the Universe," starting with "The present study." 3. A passage of 100 words from Kant's "Critique," beginning with "Time is nothing but the form of the internal sense." 4. A passage of 100 words from Franklin's "Autobiography," beginning with "But I soon found." 5. Two sets of unconnected sentences, each set comprising in all 100 words. (e) Poetry. — Two selections, each containing four stanzas of four lines. Methods of Scoring The method of scoring the various reproductions of the material memorized — a matter of prime importance in an invastigation of this nature — will now be considered in detail. METHODS EMPLOYED 25 (a) Digits. — Method 3 needs no comment as to scoring. It is obvious that where complete relearning is used, the only measurement we have to consider is that of time. In methods 1 and 2, however, we must take into consideration the various mistakes, be they of omis- sion, insertion of wrong material, or wrong order. In my earliest ex- periments, I used the method devised by Ebbinghaus,^ scoring every omission as one error, every displacement from the correct position in the series by two or three places as 0.5 error, and every displacement by four or more places as one error. The subjects were then com- pared with respect to their error-score in series of each length sepa- rately, I found however, upon correlating the scores thus obtained, that my results were practically the same as when using the much simpler method used by Dr. Whitley.^ * ' The. chief difficulty, ' ' says Whitley, ' ' in comparing people 's work on memory, lies in the varia- ble methods of scoring, especially with regard to transpositions. If the order is 76431528 and a subject writes 7463 . . ., some experi- menters call it two errors because both the 4 and the 6 are in the wrong place ; other experimenters call it one error because by making one change — by 'lifting' the 6 over the 4, it is corrected. The latter method seems preferable. Supposing a subject were to write 87643152, eight errors would be scored by the first method since each numeral is misplaced ; by the latter method only one error is scored, since one change would set all right. ' ' Thus a misplacement is rated by Whitley practically the same as an omission. For example, a sub- ject writing 76-31528, would, by the first method, be scored one error for omitting the 4, but two errors if he placed it before the 6. By Whitley's method, however, he is, by counting misplacements and omissions as equal, scored only one error. This method as used by Whitley is the method that was used in scoring the results given in the following tables. Each numeral that was given correctly was scored 1, and if it was in the right place — either relative or absolute,^ it was scored 1 more. This method may at first sight seen crude, but many were tried and the more elaborate ones were discarded. 7 H. Ebbinghaus, ' ' Ueber eine neue Methode zur Priifung geistiger Fahig- keiten und ihre Anwendung bei Schulkindern," in Z. P., 1907, 13, 401-457. 8 "Tests for Individual Differences," Archives of Psychol., 1911, No. 19. 9 I counted a digit to be correct as to its relative position provided it was preceded by the correct digit. My reasons for using the preceding digit instead of the following digit in determining correctness of position are given in the fol- lowing sub-section entitled ' ' Nonsense Syllables. " If in place of a digit the subject merely drew a line thus indicating that he was aware of an omission, he was given credit for thus preserving accuracy of position for the digit following. 26 BEL AT ION OF QUICKNESS OF LEARNING TO BETENTIVENESS Examples of the Scoring of Seeies of Digits are Shown Below Series studied 5 0947152638047381629 Eeprod. by subj. A. F... 5 0947-5380473629 Score 2 2 2 2 2 2122222122 Total 28 Eeprod. by subj. J. M... 5 09471543680259646129 Score 2 2 2 2 2 2 2 112 2 112 2 Total 26 Eeprod. by subj. M. K.. 5094715263807-381629 Score 222 2 222222221 2 2 2 2 2 2 Total 37 (i&) Nonsense-syllables. — With nonsense-syllables also, Method 3 gives no difficulty as far as scoring is concerned, but with Methods 1 and 2 we encounter the same difficulties that confront us with digits, since omissions and misplacements are usually numerous. Here also I first tried several of the more elaborate methods includ- ing that of Ebbinghaus, but discarded them for one of my own make. This method, while easy and quick, proved, upon comparison with the results obtained by the more elaborate method, to be fully as accurate. Briefly stated the method is as follows : Each correct letter, provided the syllable is in the correct positio7i,^° receives a score of 1, and the syllable, for being in the correct position, receives an extra score of 1. Thus a perfect syllable in the correct position receives a score of 4. A syllable correct in itself, but not correct in position, receives a score of only 3. If the position is correct, and the syllable has two of the three letters correct" it is scored 3. If two of the three letters of the syllable are correct but the position of the syllable itself is not correct, either relative or absolute, it receives no score at all. There- fore, unless position is correct, the separate letters do not count unless all are correct.^- It must be remembered that, as before said, if a syllable is correct, but is not in the correct position, it gets 3 and only 3 counts, since each syllable that is in the correct position and also correct in itself receives a count of 4. The highest score, therefore, obtainable for a list of 20 syllables is 80. The subjects were told to draw a line under the last syllable in their reproduction if they felt sure that it tvas the last syllable. In this way the last syllable, even if it was not preceded by the correct syllable, was counted as being in the right position and given a score of 4 if it was correct and underlined. It was given a score of 4 since it had the correct absolute position. 10 "Correct position" here, as with di^ts, may mean correct relative posi- tion or correct absolute position. A syllable is in the correct relative position when it is preceded by the correct syllable, or by a syllable of which two letters are correct, provided these letters themselves be in the right order. 11 Provided these two letters themselves are in the correct order. 12 When, however, all three letters are written, but not in correct order, e. g., the letters reversed, — the syllable receives a score of 1, but if the position also is correct, a score of two. • METHODS EMPLOYED 27 The method of scoring is illustrated by the following example. ,iit of Syllables Studied Reproduction by Subject J. M. Scores vus VUS 4 YIF VIF 3 MIV JEP 3 JEP RIL VOB BOV 2 FEG SIR . WOF WOL 3 TIB TID 3 NUZ EOF JED KIB VEL ZID BOL SEF TAB KUV TEF NAD Total score 18 In explanation of this scoring, the following remarks may be added. VUS get 4 counts, being correct in everything. VIF gets only three counts, since although its position is correct, it starts with *'V" in- stead of "Y." JEP gets 3 counts ; had it been in the correct position it would have gotten 4, since, when a syllable is correct as to its letters, but in the wrong position it is credited with only 3 counts, — one for each letter, RIL receives no score at all, there being no such syllable. BOV receives a score of 2, for it contains all the letters that occur in VOB and, moreover, is in the correct position, i. e., where VOB should be. SIR receives no score at all. It is quite likely a pure guess, and put down merely to'secure correctness of position for the two following syllables. We are all the more led to believe this when we perceive that the next two syllables, WOL and TIB, have, in each, two letters correct, — their positions also being correct. (c) Words. — With words, method 3 also gives no difficultj^ time being the only measurement. With methods 1 and 2. however, a method similar to that used with nonsense-syllables was employed. A score of 1 was given if the position, whether relative or absolute, was correct. Here also correctness of the relative position was deter- mined by the preceding word. An extra count was given if any two letters^^ were correct, provided that the position of the word was 13 The same rule was used here as in the ease of the nonsense syllables and the two letters themselves had to be in the correct order. Reproduction by Subject M. K. TUB Score 3 2 JUG 2 EAT TAN MUG CAT 2 RUG 2 PEN 2 BED 3 GUN 3 28 BELATION OF QUICKNESS OF LEAENING TO BETENTIVENESS correct. If the word was wholly correct it received still an extra count, making a maximum of 3 counts for each word. The scoring is illustrated by the following case : Series of Words studied TUB PIN HEN BED LID GEM BUD CAR MAT ROD JUG FOG LAD SOD PEN CAT RAG BOX NET GUN Total score 19 This scoring may be elucidated by the following remarks. The first word TUB is given 3 counts, it having two letters correct, it also being the correct word and also being in the correct position. HEN is given a score of 2, it being the correct word but not in the correct position. For like reasons JUG is scored 2. RAT receives no score at all, although it has two letters, "-AT," that are correct (they being also in the word CAT). The word however is not in the proper position either relative or absolute and hence can receive no count at all. Words of this kind therefore receive a score of 2 or nothing for reasons given in detail under nonsense-syllables. The fairness of this rule is made clear when we realize that had the word RAT been pre- ceded by the word PEN, the chances of RAT having been a mere guess would be greatly lessened. TAN receives no count at all. To the next word MUG, one is tempted to give a score of 1 since it con- tains the two letters UG which are also contained in JUG. It would have received credit for these two letters had the word been preceded by ROD. Not being preceded by ROD it is given no count at all. That this is perfectly fair is in this particular case very conveniently shown by the appearance later on of the word RUG, which, although there is no such word, is given a score of 2, it being preceded by the METHODS EMPLOYED 29 correct word CAT. The two letters that are correct in this case are B-G and although separated by the wrong vowel " U " they are in the proper order. PEN receives a score of two, it having tAvo letters cor- rect and also being the correct word itself. BED receives a score of 3, 1 because it contains two correct letters, 1 because it is the correct word itself, and 1 because it is preceded by the correct word. In this case the "preceding" word is not wholly correct but it contains two correct letters and this naturally gives BED a higher scoring than it would have received had it been preceded by the word AXE, for example. The last word GUN receives a score of 3, it being in the correct absolute position for the reason that it is underlined, this proving that the subject knew it was the last word. (d) Prose. — The simplest method of scoring the prose passages is to grade the papers offhand on a basis of 10 (or 100) equaling per- fection. With this method, however, some examiners would not con- sider that "perfection" necessarily required the use of the identical words occurring in the original, nor might they consider that it re- quired a perfectly correct order of these words. With a certain amount of justification, they might say that the only thing necessary to get a score of 100 would be to have a perfect reproduction of the various ideas contained in the original passage, — in other words, a practically perfect impression of the "content" of the passage. This rather rough method of scoring has been used by several experi- menters. I used this method for a time, but soon gave it up for the more exact method of Henderson,^* somewhat modified. In scoring, Henderson divided his prose passages into "topics," "sub-topics," "details," and words. He was thus able to score his papers according to the number of "ideas" and "parts of ideas" that were retained. We shall first take up his method of scoring the smallest of the subdivisions, viz., words, and this is best given in a quotation from Henderson himself: "The scoring of words remem- bered might easily become a complicated matter. Doubtless, the re- producing of certain words means far more power of memory than that of others. I have used the following system. All words of the original that were reproduced in their former contexts were scored full value. Commonplace words, particularly articles, prepositions, and conjunctions, were not scored when reproduced out of their con- text. On the other hand, an unusual word was regarded as remem- bered, even though it appeared in the wrong context. Occasionally a word was evidently used because its sound was somewhat like that of one in the original. A half credit was here given. Words that 1* E. N. Henderson, ' ' A Study of Memory for Connected Trains of Thought," Psy. Bev. Monog. Supp., No. 23, 1903. 30 EELATION OF QUICKNESS OF LEARNING TO RETENTIVENESS were modified to suit changes in construction, etc., were given partial credit also. ' ' In defending his method of analyzing a passage into the various divisions mentioned, Henderson says:^^ "It must be confessed that this analysis has in it something arbitrary. To say that each of the detailed thoughts thus indicated is equal in value to every other is manifestly absurd. And this is time whether our estimate be based on relative importance to the thought in general or on relative diffi- culty of recall. But it must be granted that the same objection could be raised against any endeavor to compare two mental conditions quantitatively. However, as the mind of the subject traveled over the thought it was trying to reproduce, it may be conceived to have rested momentarily on each of the details indicated. In general, the better memories could be expected to retain not only the easily re- membered details, but also the ones harder to recall, whereas the poorer ones would retain only the former class. In such cases the scores given can not be challenged on the ground that the lack of equality between the units renders the ranking of the subjects arbi- trary. Placing different values on the ideas or analyzing the units differently might affect the ranking in cases where the loss of certain ideas is pitted against that of different ones, but seldom, I am con- fident, could one justify a valuation or an analysis so different from mine as to affect materially the ranking of a student. Hence, the general results of my investigation are, I conceive, not dependent on the peculiarities of my scoring. "The scores given have not been diminished, because of errors. They are records only of what was retained. I have taken the ground that the erroneous idea that contains the suggestion of the true one deserves a positive rather than a negative score. It indicates a thought corresponding, however inaccurately, to the earlier one. Such ideas are given a part of the value of an accurate memory. Some individuals, it is true, leave unexpressed the hazy idea that they fear is erroneous. They might suffer by comparison with cloudier minds that failed to discover the presence of the fog. However, a mind that feels a certain idea to be inaccurate is usually able to ex- press the part or phase of the thought that is accurate, and thus render a true account of what was in the memory. ' ' My own method of scoring is really nothing but a modification of Henderson's. The papers were first marked on a scale of 100 by three competent judges. The average of these marks was then taken and called "Judges' Mark." The papers were then scored by Hen- derson's method, the score, however, being converted into a scale of 15 Op. cit., p. 33. METHODS EMPLOYED 31 1-100. This was termed "Henderson's mark." The arithmetical ynean of these two "marks" was then taken as the final score. It was seldom that the two methods of scoring differed by more than 3. In one or two instances the difference was as great as 5, though this difference was mostly due to the presence of an introspective post- script that had been added by the subject, and which, while it could not be considered in Henderson's method, was evidently considered by the judges. It was frequently clear that the subject had a fair idea of certain "thoughts" that he was unable to express, — thoughts that were evidently not expressed in words sufficiently correct to obtain, by Henderson's method, as high a score as the judges deemed them worthy of, — for in these cases the "Judges' Mark" was inva- riably higher than ' ' Henderson 's mark. ' ' The results of this method of scoring can be seen in the following examples. Passage Studied. The diamond-bright dawn woke men and cows and bullocks together. Kim sat up and yawned, shook himself, and thrilled with delight. This was seeing the world in real truth, this was life as he would have it — bustling and shouting, the buckling of belts, and beating of bullocks and creaking of wheels, lighting of fires and cooking of food, and new sights at every turn of the approving eye. The morning mist swept off in a whirl of silver; the parrots shot away to some distant river in shrieking green hosts: all the well wheels within earshot were at work. Eeproduction by Subject A. F. The diamond bright dawn woke men and cows and bullocks together. Kim awoke, sat up, yawned and shook himself. This was life as it should be, this was seeing the world in real truth. The creaking of wheels, the lowing of cattle, the clanking of chains, the ringing of bells and new sights at every turn of the ap- proving eye. The parrots shot off to some far away river in shrieking green hosts; the and all the well wheels of industry were at work. Score, 72. Reproduction by Subject J. M. The diamond bright dawn woke men, and cows and bullocks all together. Kim sat up and yawned, shook himself, and thrilled with delight. This was see- ing life in real truth; this was life as he would have it. The blowing of horns, the lowing of cattle, the cracking of whips, and the creaking of wheels. (There was also something about parrots flying across the river, . . . and that everybody was at work.) Score, 49. Repeoduction by Subject M. K. The diamond bright dawn woke men, and , and bullocks together. Kim awoke and sat up. "This was seeing the world in truth, this was life as he would have it." The buckling of belts, beating of bullocks and blowing of 32 BELATION OF QUICKNESS OF LEARNING TO EETENTIVENESS horns, the cracking of fire and cooking of food and new sights at every turn of the approving eye. Score, 50, (e) Poetry. — The scoring of the poetry was practically identical with the scoring of the prose. Nothing, therefore, need be said unless it is that the "judges' mark" was more or less influenced by the qual- ity of the rhythm, rhyme, etc. For example, other things being equal, a word that rhymed with the appropriate preceding word was given preference over one that did not, even though neither of the words ap- peared in the original stanza. The result of the scoring is seen in the following examples : Selection Studied^^ And gentle Ellen welcomed her With courteous looks and mild: Thought she * ' what if her heart should melt, And all be reconciled ! ' ' The day was scarcely like a day — The clouds were black outright: And many a night, with half a moon I've seen the church more light. The wind was wild; against the glass The rain did beat and bicker; The church-tower swinging over head, You scarce could hear the Vicar! And then and there the mother knelt, And audibly she cried — Oh! may a clinging curse consume This woman by my side! Reproduction by Subject A. F. And gentle Ellen welcomed her, With tender looks and mild. Thought she, "what if her heart should melt And all be reconciled. ' ' The day was scarcely like a day, The clouds were black outright And many a night with half a moon I've seen the church more bright. 16 Other selections of prose and poetry, and other lists of digits, words and nonsense syllables, used as materials with some groups of subjects, are reproduced in the Appendix. METHODS EMPLOYED . 33 The , Score, 85. The church tower swinging overhead You scarce could hear the preacher. And then and there the mother knelt, and audibly she cried, * ' Oh, may a clinging curse consume, This woman by my side! " Eeproduction by Subject J. M. And gentle Ellen welcomed her With courteous looks and mild, Thot she, what if her heart should And all be reconciled. The sky was dark, the wind blew wild, We scarce could hear the vicar. (There was something about a mother praying that another woman be cursed.) Score, 39. Eeproduction by Subject M. K. And genter Ellen welcomed her, With courteous looks and mild, Tho't she what tho her Score, 23. The day was The clouds And many a night I seen more Classes of Subjects Tested 1. 40 grammar-school students. Modal age, 14. 2. 24 trade-school students. Modal age, 16. 3. 60 high-school students. Modal age, 17. 4. 24 state reformatory inmates. Modal age, 20. 5. 132 normal-college students. Modal age, 21. 6. 32 Columbia College seniors. Modal age, 22. 7. 14 Barnard College seniors. Modal age, 22. 8. 24 asylum attendants. Modal age, 25. 9. 12 workhouse inmates. Modal age, 30. 10. 24 clerks and business men. Modal age, 30. 11. 16 graduate students, instructors, and professors. Modal age, 32. 12. 24 prison inmates. Modal age, 34. CHAPTER III EESULTS The Tables. — To set forth in full the individual records of the twelve groups of subjects mentioned on page 33 would require an excessive amount of space, and I have accordingly limited the de- tailed presentation to two groups, one of 24 normal-college seniors, and the other of 17 students in a course in experimental psychology in the normal college. These subjects are all young women. Their records are given in Tables I.-X., which are self-explanatory, except perhaps for the columns numbered 5 and 6, 8 and 9, and 11 and 12. These give the average results for the quarters and for the halves of TABLE I 20 Digits. Normal-College Seniors. Gebls 1 Subject 2 Time of First Learning:, Min. S 4 5 6 Method Three Time After Percent, of Time One Week, SftTed or Amount Min. Retained. 7 8 9 10 11 12 Method One Method Two Score Per Cent. Score Per Cent El. W. . 2.25 .66 69 ■ 33- 40' Ed. W. . 3.00 1.16 61 34 39 H. B .. F. Wi. . . 4.50 . 4.56 1.75 61 1.25 73 -61 34 9 -28- 36 30 -35 - M. K. . 4.66 .50 89 37 40 G. L. .. J. M. . . 5.00 . 6.00 4.33 13 2.33 6r - 63 19 30 ' 27 ■27 34 = -34 F. K. . . 6.00 3.00 50 27 32 A. H. . . 6.16 2.80 55 24 37 -32^ E. W. . . 7.00 2.50 64 -65. 26 -26 . 30 C. C. .. . 8.00 2.00 75 20 27 H. M. . . 8.25 1.40 83 29 34 A. N. .. . 8.25 2.33 72' 23' 34' M. T. . . 8.25 1.16 86 30 41 F. Sc. . F. St. . . . 8.33 . 8.66 3.66 56 2.50 71 -70- 19 27 -23- 31 34 -36 - B. O. . .12.00 2.66 78 23 43 S. T. .. A. T. . ..13.00 .15.00 5.88 55 9.80 35^ - 71 18 9' 31 ■22 23' -36 E. S. .. .16.80 3.50 79 19 46 L. J. . . E. R. .. ..20.16 .20.16 2.40 88 2.00 90 -72. 26 33 -20. 40 47 -36 . E. T. .. ..21.50 5.00 77 8 22 J. Mc. . ..29.00 11.50 60 26 35 Aver. .. ..10.26 2.76 67 24 35 34 RESULTS 35 the groups, when the individuals are arranged, as they are in each table, in the order of their quickness of learning the material. Thus, in Table I., Colunm 5 informs us that the quickest quarter of the group in learning 20 digits saved 61 per cent, in releaming, the second quarter 65 per cent., the third quarter 70 per cent., and the TABLE II 20 Nonsense Syllables. Noemal-College Senioes. Girls 1 Subject 2 Time of First Learning, Min. 3 4 5 6 Method Thre« Time After Percent, of Time One Week, Saved or Amount Min. Retained 7 8 9 Method One Score Per Cent. 10 11 12 Method Two Score Per Cent M. K. . ..12.00 4.00 67^ 17- 49- El. W. . ..13.50 5.25 61 22 51 Ed. W. F. St. . ..14.00 ..24.25 7.00 5.50 50 77 ^68 52 15 -26- 62 41 ^47- A. T. . ..25.00 8.00 68 11 31 H. B. . A. H. . ..26.00 ..26.40 4.16 4.50 84 83' -71 40 37' -26 50 49' -44 F. Wi. . ..28.00 2.33 92 48 65 E. W. . ..28.00 7.00 75 18 38 E. S. . ..29.56 15.00 49 -75. 8 ^25, 17 - 42. F. Sc. . ..31.00 10.25 67 20 43 B. 0. . ..31.75 5.50 83 19 38 A. N. . ..32.00 9.16 71' 21' 15' M. T... ..33.50 13.40 60 7 18 H. M. . F. K. . ..34.00 ..34.00 8.80 6.40 74 81 -67- 18 21 -19- 40 30 ■26' J. M. . ..35.50 15.66 56 17 L. J. . . 0. C. .. ..36.08 ..37.00 15.00 16.50 58 55' -68 29 12' -21 29 36' -33 E. K. . ..40.80 15.16 63 39 53 S. T. . . ..42.00 13.00 69 -69. 14 18 J. Me. . ..42.00 12.66 70 18 -23^ 41 - 40. G. L. .. ..44.16 4.50 90 46 52 E. T. .. ..45.00 15.40 66 6^ 38 Aver. .. ..31.06 9.34 70 ' 23 ' 40 lowest quarter 72 per cent. ; and Column 6 tells us that the upper half of the group, in respect to speed of learning, saved 63 per cent, in re- leaming, while the lower half saved 71 per cent. Table XI. sums up the results of Tables I.-V. in condensed form, and Table XII. does the same for Tables VI.-X. The column num- bers in these, as also in the following tables, correspond to those in the full Tables I.-X. It should be understood that the "upper half" and the "lower half, ' ' for each material, consist of those individuals who fell into the respective halves of the group in the particular material studied. 36 BELATION OF QUICKNESS OF LEABNING TO EETENTIVENESS The upper half does not, therefore, always include exactly the same individuals; and the average results, in Tables XI. and following, are obtained by combining the results of these various halves, and not by segregating the individuals who on the average learned the most or the least quickly. TABLE III 20 Words. Noemal-College Seniors. Girls 1 Subject 2 Time of First Learning, Min. 3 4 5 6 7 8 9 10 11 12 Method Three Method One Method Two Time After Percent, of Time Ten Weeks, S aved or Amount Min. Retained. Score Per Cent. Score Per Cent A. H. . .. 4.40 1.00 77- 43- 53" H. B. . . . 5.00 4.66 7 12 43 El. W. . G. L. .. .. 7.00 .. 7.66 3.88 4.66 43 39 -45- 35 11 -26- 50 39 -44- Ed. W. . . 9.00 3.08 66 31 51 A. N. . E. W. . . . 9.50 ..10.25 6.00 5.00 37 51' 22 -^0 20= 28 ■23 52= -44 A. T. . ..10.40 6.75 35 14 41 M. T. . E. S. . . ..11.00 ..11.00 7.50 8.75 32 21 -35. 20 17 -20. 40 39 -45. B. 0. .. ..11.25 6.75 40 27 49 J. M. . ..11.50 8.00 30 22 48' P. St. . ..11.66 6.88 41 ' 26 = 46 = S. T. .. ..12.00 4.40 63 3 21 P. Sc .. c. c. . ..12.16 ..13.00 4.00 3.75 67 71 -54- 22 32 -22^ 40 49 -37- M. K. . ..13.25 3.66 72 19 30 H. M. . P. Wi. ..13.33 ..13.80 12.25 4.16 8 70' .« -^ •- ^3^ -35 J. Mc. . ..14.00 7.25 48 16 31 P. K. . E. R. .. . 14.33 ..15.00 4.00 3.50 72 77 -68. 16 40 .18. 27 50 ^33, li. J. . .16.00 2.08 87 7 38 E. T. . ..28.50 13.00 54 9 17 Aver. .. ..11.88 5.62 51 21 39 Tables XIII. and XIV. give the condensed result for each mate- rial from two other groups of subjects, whose records are not pre- sented individually; while Tables XV. and XVI. present the results from all the groups in still greater condensation. The entries in Tables XV. and XVI. correspond to the average results from all materials combined, as presented at the bottom of Tables XI.-XIV. Another way of combining the results from the use of the differ- ent materiaLs is illustrated in Table XVII., which again is derived from Tables I.-V. The 24 individuals in the group were arranged in the order of their success in each test, and were given numbers indi- RESULTS 37 eating their rank or position in the group. The table gives the rank of each individual in each performance, and his average rank in speed of learning, in retention as measured by the saving method ("method three"), in recall ("method two"), and in recall after partial re- learning ("method two"). The average deviation of rank of each individual in each of these kinds of performance is also given. TABLE IV 100 Words (The Diamond Bright Dawn) Noemal-College Senior. Girls 2 Time of 3 4 5 6 Method Three 7 8 9 Method One 10 11 12 Method Two First Learning, Min. ..10.00 Time After Ten Weeks, Min. 1.33 Perce Saved R 87- nt. of Time or Amount etained. Scor 27 e Per Cent. Score Per Cent. 981 ..10.40 2.16 79 50 89 .13.00 1.00 92 42 99 ..13.00 4.40 66 -78- 46 -66- 50 -82- .13.75 4,00 71 56 85 ..14.33 4.25 70 77 73 .15.00 4.66 69' -68 49' -59 78' -80 . 15.25 6.00 61 14 68 .16.08 4.50 72 97 91 .17.00 11.25 34 -59^ 44 -53. 72 -79 J .17.00 5.40 68 93 87 .17.25 8.50 51 33 75 .18.66 6.50 65' 69' J 64" .19.50 10.00 49 62 52 .22.25 9.00 60 52 76 .23.25 9.50 59 1-64" 45 ^46 80 ^64' .24.25 5.56 78 39 " 37 .25.16 7.40 71 45 73 .26.08 4.00 85' -66 84 = 46 95' -67 .28.00 15.00 46 51 - 60 .29.80 17.00 43 32 54 .31.40 6.56 79 -68, 20 -47 89 ■70. .34.56 6.88 80 69 . 55 .45.16 11.75 74 76 67 .20.84 6.94 67 53 74 Subject Ed. W. . F. Sc. , , A. H. ,. E. S. ., El. W. . C. C. ... R. W. . . F. Wi. . F. K. .. G. L. ., H. B. . , J, M. .. F. St. . . H, M. , , A. N. .. B. O. .. A. T. . . M. K. . . S. T. ... M. T. . . L. J. ... E. R. ... J. Mc, .. E. T. ... Aver Finally, Table XVIII. is derived from the preceding table for a purpose which will be explained later. Time of Initial Learning.— An. examination of any of the tables will reveal the fact that the time of initial learning varies widely with the different subjects, and that these differences in learning are more marked than the individual differences in releaming. In other words, it may be stated as a general rule that with a given number of individuals, there will be a greater difference in their time of mem- orizing than in their retentive capacity. 38 RELATION OF QUICKNESS OF LEAENING TO EETENTIVENESS Generally speaking, with a group of 20 or 30 subjects, the time taken by the quickest learner is to the time taken by the slowest learner as 1 : 4. This, however, would seem to depend partly upon the nature of the material learned. Among the 24 Albany Normal Col- lege seniors (Tables I. to V.) it will be noticed that with digits the time of the quickest learner is to the time of the slowest learner as 1 : 13 ; that with nonsense-syllables the ratio is 1:4; that in the case of words the ratio is 1:7; that for prose it is 1 : 5 ; whereas for poetry TABLE V PoETEY. 100 Words (Gentle Ellen) Noemal-College Seniors. Girls 1 2 Time of First Learning, Subject Min. 3 4 5 6 Method Three Time After Percent, of Time Ten Weeks, Saved or Amount Min. Ketained. 7 8 9 10 11 12 Method One Method Two Score Per Cent. Score Per Cent. El. W. ... 2.08 1.00 52- 36" 59- H. B. ... 3.00 1.75 42 95 98 Ed. W. . . 3.25 E. W. ... 5.00 .33 1.40 90 72 ^65' 64 30 -56' 100 39 -72~ E. S. ... 7.00 4.50 36 11 36 A. H. ... 7.50 B. 0. ... 8.66 0.00 3.88 100 56' ^61 97 96' 100 '^^ 99' -73 G. L 8.80 6.16 30 28 50 A. N. ... 9.50 P. Sc. ...10.00 4.40 2.16 54 78 -57. 57 59 -63. 55 87 ■74. H. M. ...10.00 5.25 48 77 82 P. Wi. ..10.16 2.25 78 60 71 S. T. ...10.50 2.00 81^ 10' 35' E. R. ...10.56 3.80 64 78 92 M. T. ...10.75 P. K ...12.25 5.00 7.16 53 58 -62- 51 73 -43" 84 89 -65' M. K. ...13.40 5.08 62 23 44 E. T. ...13.75 C. C 14.00 6.33 3.08 54 78^ -65 24^ 46' - %' -57 J. M. ...15.75 6.25 60 36 47 J. Me. ...17.00 5.75 66 -68. 39 -37. 42 P. St. ...17.16 5.08 71 13 31 - 49, A. T. ...19.75 5.50 72 32 40 L. J 20.00 7.66 62^ 53 _ 68 Aver. ...10.83 4.00 63 50 65 it is 1 : 10. The difference in these ratios is, of course, largely a matter of chance. Take, for example, the table for words: here the slowest learner takes 28 minutes and 30 seconds, whereas the next slowest learner takes only 16 minutes. It is obvious that a much fairer form of comparison is that of comparing the average of the first four with the average of the last four. Doing this we find that the ratios are as RESULTS 39 1:3; words 1:3: prose follows: for digits 1:6; nonsense-syllables 1:3; poetry 1: 5.^ An individual who is a quick learner of one sort of material tends, upon the whole, to be a quick learner of other sorts also. This is seen most conveniently in the first part of Table XVII., which shows the ranks of 24 individuals in quickness of learning five sorts TABLE VI 20 Digits. Class in Experimental Psychology. Girls Subject B. B. ., F. Wo. , E. F. .. J. S. . . . E. C. .. I. S. ... A. D. .. B. C. ... El. F. .. A. Q. .. E. H. . . E. H. .. M. J. .. G. H. .. H. A. . . R. B. .. M. N. . . Aver. . . Time of First Learning, Min, . 3.40 . 4.50 . 6.00 . 6.50 . 6.50 . 8.00 . 8.56 . 9.00 . 9.80 .10.00 .11.00 .11.30 .11.80 .12.66 .14.00 .16.16 .24.25 .10.20 4 5 Method Three Time After One Week. Min. 0.75 4.16 0.88 2.75 1.33 1.66 9.66 1.33 0.50 3.25 2.40 2.25 1.33 4.80 0.16 1.66 6.75 2.68 Percent, of Time Sayed or Amount Retained. 78- 57 58 58 -80^ 82 81 7 8 9 Method 0n« Score Per Cent. 391 30 21 25 r24j ^25 24 10 11 12 Method Two Score Per Cent. 391 33 27 34 30 J 30 32 of material. Some individuals stand consistently high, and some con- sistently low. There is, however, a good deal of shifting from one material to another, and this shifting finds expression in the coeffi- cient of correlation between the ranking in two materials. As com- puted by the rank-difference method, the average correlation between the speed of learning any two sorts of material is, for this group of subjects, +.51. For the 17 subjects whose records are given in Tables VI.-X., the average correlation comes out a little lower, + .42. The shifting of an individual's rank from one material to another is partly due to the accidental factors inherent in a single 1 Even when we thus obtain our ratio by comparing the average of the first four subjects with the average of the last four, the P.E. is very large. It is :i noticeable fact, however, and one of some interest, that with every group of sub- jects the greatest difference (ratio) occurs with the digits. 40 BELATION OF QUICKNESS OF LEARNING TO BETENTIVENESS test, and partly, no doubt, to actual differences in the efficiency of the individual's powers of memorizing different classes of material. Interval ^between Learning and Reproduction. — This interval varied in different experiments, as indicated in the several tables. In the majority of my experiments the interval that was allowed to elapse for digits and nonsense-syllables was either three days or one TABLE VII 12 Nonsense Syllables. Class in Experimental Psychology. Giels 1 2 Time of First Learning, Subject Min. 3 4 5 6 7 8 9 Method Three Method One Time After Percent, of Time One Week, Saved or Amount Min. Retained. Score Per Cent. 10 11 12 Method Two Score Per Cent. J. S 6.08 0.75 88" 291 63" E. H. ... 6.75 B. B. ... 7.50 1.33 1.16 80 85 -84" - rn 72 E. F. ... 9.16 E. C. ...10.00 1.66 2.80 82. 72" - s: -37 60 J 48] - 55 G. H. ...11.00 5.56 49 -74_ 3n37 40 68h«J El. F. ...11.50 1.00 91 47 ■' B. C. ...12.00 2.16 82- 29 J 45- A. D. ...13.66 5.33 61] 20" 31" A. Q. ...14.00 3.08 78 1731 32 '28- 40 t ,„, 36 h^ M. J. ...14.25 5.16 64 18 I. S. ...16.00 1.66 90 J 42 J ■^5 12] 54 J F. Wo. ..17.00 9.16 46] -23 19" ■ 31 H. A. ...18.50 4.88 74 17 39 E. A. ...19.33 5.50 72 ■41. 21 "18. 19 ' 23. E. B. ...31.00 12.08 61 24 22 M. N. ...32.56 19.25 40. 10. 18. Aver 14.72 4.74 71 30 4. 42 week, whereas for words, prose and poetry it was much longer, being from three to ten weeks. In an investigation of this nature, where we are concerned primarily with acquisition as related to retention, we can of course choose any interval we wish. We might wait six months and still find a relation between learning and retention. That this relation would differ with the interval, however, appears probable from certain tests I have made where the longer interval gave a nega- tive correlation. I have not studied the matter systematically, and the data presented in this paper do not show any clear difference ac- cording to the interval employed. In general, we may suppose, the difference in amount reproduced by quick and slow learners tends to become less, since the amounts retained by all approach zero with time. BESULTS 41 Amount Retained Method 1. — Method 1 has already been described in Section 2 of the preceding chapter. It shows the amount that can be reproduced, after the lapse of a certain time interval, of the material originally memorized, — this reproduction being without a fresh presentation. By consulting columns 7, 8, and 9 of any table, it will be noticed that Subject B. B. E. F. E. A. F. W. E. C. B. C. A. D. A. Q. J. S. I. S, M. J. H. A. G. H. El. F. E. H. M. N. E. B. Aver. TABLE VIII 20 Words. Class in Experimental Psychology. Girls 2 Time of First Learning, Min. . 5.80 . 7.33 . 7.40 . 8.00 . 8.56 . 9.16 . 9.16 .10.08 .10.08 .12.00 .13.16 .13.50 .14.50 . 15.08 .15.33 .17.00 .19.00 .11.48 3 4 5 Method Three Time After Percent, of Time Ten Weeks, Saved or Amount Min. ~ ■ ' 2.08 «*l56 2.66 2.25 6.00 4.50 4.66 6.40 4.80 1.88 6.00 6.33 7.33 7.75 6.40 4.24 5.00 6.08 4.96 Retained. 64-^ 70 I 25 J 4445 30 r 52 J 81 50 52 46 47 58 72 71 68 56 50 .571 .63 J 61 7 8 9 Method One Score Per Cent. 28 28 ^ 15 ^21 231 19, 21 10 11 12 Method Two Score Per Cent. 53 47 ■37 37 33 J 42 35 in the case of all materials, both meaningless and logical, there ap- pears to be a positive correlation between quickness of learning and the amount retained. The score obtained by the first half- is in gen- eral better than that obtained by the last half. This is most marked in the case of prose and least marked with digits. In fact with digits, the score obtained by the last half is, in several cases, very nearly as high as the first half, and in the case of the high-school students (Table XIV.), the score of the last half is even better. In any case, however, the difference is small. With nonsense-syllahles, words, and poetry the difference is slightly in favor of the quick learners, al- though on the whole the difference is but slight. The probable error, 2 In the following pages we shall by "First half" or "Upper half" here- after understand the quickest learners, and by "Last half" or "Lower half" the slowest or poorest learners. 42 BELATION OF QUICKNESS OF LEAENING TO BETENTIVENESS however, is in most cases so high that the value of index of correlation is considerably lowered. Were it not that what correlation we do obtain is positive for every table the figures would have much less value. In the case of prose and poetry, a positive correlation is un- questionable. "With prose for example, the average score for the quickest learners is, as a rule, nearly double the score for the slow learners. The use of the Pearson method gives so high an index that the evidence is conclusive. Method 2. — Concerning Method 2, little need be said, — the indi- TABLE IX Prose. 100 Words ("The Present Study") Class in Experimental Psy- chology. Girls Subject B. B. . E. C. .. B. C. .. E. F. . A. Q. . I. S. . . H. A. . G. H. .. M. J. . E. H. . El. F. . M. N. . R. B. .. E. A. .. J. S. .. F, Wo. A. D. . Aver. .. Time of First Learning, Min. . . 7.00 ..11.16 ..12.25 ..14.33 ..16.08 ..17.50 ..19.00 ..19.33 ..20.00 ..20.40 ..21.56 ..25.25 ..28.16 ..28.40 ..30.00 ..32.66 ..39.50 ..21.33 3 4 5 Method Three Time After Ten Weeks, Min. 2.88 4.25 4.88 4.80 7.00 4.33 3.80 11.56 5.88 10.33 9.00 10.56 8.08 10.25 15.00 10.75 10.66 7.88 Percent, of Time Saved or Amount Betained. 621 62 63 59 66 J 63 7 8 9 Method One Score Per Cent. 57' 50 53 r21 21 51 21 10 11 12 Method Two Score Per Cent. 81 vidual differences being much the same as those observed by Method 1. With the exception of digits, the quick learners get the higher scores. Here again the greatest difference is with the prose and the least with the digits. The most noticeable fact with this method is that it gives the highest correlation of all, and that the correlation is high throughout, i. e., for all materials. The explanation of this is not hard to find. It lies in the fact that with Method 2, after the lapse of a certain number of days, the material is read once, and only once, to the subject, after which reading he is asked to write down as much as possible. Obviously, the quick learner will get more from BESULTS 43 this one reading than the slow learner and thus the index is made higher. Method 3. — So many factors are involved in this method that it calls for a more lengthy discussion than either of the two preceding methods. With this method the correlation is as a rule negative, both by the Pearson method and by the rather crude ''percentage Poetry. Subject B. B. .. F. W. . M. J. . E. F, . E. C. .. O. H. . E. H. .. E. A. . A. Q. . E. B. . A. D. . El. F. B. 0, . J. S. . I. S. . M. N. H. A. Aver. . TABLE X 100 Words ("To See a Man"). Class in Experimental Psychol- ogy. GntiiS Time of First Learning, Min. . 5.16 . 7.00 . 7.33 . 8.50 . 9.56 .11.25 .11.50 .11.80 .12.00 .12.16 .12.16 . 12.75 .13.00 .14.00 .14.00 .14.56 .14.75 .11.26 3 4 5 Method Three Time After Ten Weeks, Min. 3.56 2.50 2.40 3.50 4.33 8.08 2.66 5.08 2.50 0.00 6.56 6.00 3.50 0.33 4.25 5.25 5.50 3.88 Percent, of Time Saved or Amount Retained. 31" 64 67 59 55 28 77 57 791 100 46 53 73-^ 98 70 64 63 64 55 54 70 74 ^55 ^72 7 8 9 Method One Score Per Cent. 591 48157 68 I 10 n 12 Method Two Score Per Cent. 94 method. "3 With the percentage method we find that the quickest learners retain less than the slower learners for digits, words and, occasionally poetry. For prose, on the other hand, the quick learners retain more, while for nonsense-syllables they stand about even. To repeat: Method 3 gives results that by no means invariably agree with those obtained by the two preceding methods. This is due to the nature of the method, i. e., to the manner of computing the "percentage of time saved" and treating this as a measure of the amount retained. Whether this is fair to the quick learner is ques- tionable. According to Method 3, those who memorize prose most quickly retain it better than those who memorize it more slowly; 3 By this we mean the methods shovFn in columns 4, 5 and 6, where the per- centage of the first half of the class (comprising the quickest learners) is com- pared with the half of the class comprising the slowest learners. 44 BEL AT ION OF QUICKNESS OF LEABNING TO BETENTIVENESS this, indeed, agrees with the result by the other methods. With poetry the same relation often holds good, but the results are not uniform, and, as may be seen from Tables XI. and XII., the quick learners may, by this computation, forget even more, but in any case the difference is not marked. Taking prose and poetry together, how- ever, and assuming that they are illustrative of * ' logical " or " mean- ingful" material, we may say that the results obtained agree with TABLE XI 24 Normal College Seniors 1 2 3 6 9 12 Digits: Upper half 5.5 2.0 63 27 34 Lower half 15.0 4.0 71 22 36 Nonsense -syllables : Upper half 24.1 6.5 71 26 44 Lower half 38.0 12.1 68 21 36 Words : Upper half 10.0 5.5 40 23 44 Lower half ^4.8 5.7 61 20 35 Prose : Upper half 14.3 4.8 68 59 80 Lower half 27.3 9.1 66 46 67 Poetry : '' Upper half 7.0 2.8 61 59 73 Lower half 14.5 5.2 65 40 57 Average : Upper half 12.2 4.3 61 39 55 Lower half 21.9 7.2 66 30 46 The "time interval" here, as in Tables XIL and XIV., is 1 week for the digits and nonsense -syllables and 10 weeks for the prose and poetry. In Table XIII. the ' ' time interval " is 3 weeks for all materials. those obtained by Methods 1 and 2. Taking all three methods into consideration, we are entitled to say that with material that is logical in character, tJiose who learn quickly remember the longest. With digits, however, a material the memorizing of which is so- called **rote" memory, we find that the conditions are, so far as Method 3 is concerned, reversed, for here it is the quick learners who seem to forget the most. With digits the amount forgotten, as ascer- tained by Method 3, is always greater for the upper half of the class, and not only is this always so, but the difference between the two halves of the class is generally marked. This result is not strongly contradicted by Methods 1 and 2, according to which the difference is slight. At any rate we may say with some degree of certainty that, in the main, those who memorize digits slowly are more apt to retain BESULTS 45 them than those who memorize them quickly. This is just the oppo- site of the statement made for prose and poetry, and digits being an "opposite" form of material, so to speak, one might make the infer- ence that those who learn slowly remember long, if the material used is such as involves motor associations, but that they forget quickly if TABLE XII 17 Normal College Senioes _,..,! 2 3 6 9 12 Digits : Upper half 6.5 2.8 58 25 30 Lower half 13.5 2.5 81 24 32 Nonsense-syllables : Upper half 9.2 2.0 79 37 55 Lower half 19.5 7.3 65 23 31 Words: Upper half 8.2 4.2 50 21 42 Lower half 14.4 5.7 61 21 35 Prose : Upper half 14.6 5.4 62 51 79 Lower half 27.3 10.0 63 21 49 Poetry : Upper half 9.0 4.0 55 53 79 Lower half 13.2 3.7 72 50 76 Average : Upper half 9.5 3.7 61 37 57 Lower half 17.6 5.8 68 28 45 The difference between Tables XI. and XII. is probably due largely to the fact that the "materials" used are not identical. In this group of subjects only 12 nonsense-syllables were used. the material is logical in character, e. g., prose, and to a somewhat less extent, poetry. Such a statement, however, is true only in a very rough way. In the first place, nonsense-syllaUes, a material that is not only "un- meaningful" in character, but that involves the ''memorizing," so to speak, of motor associations, seems— so far as Method 3 is concerned— to side more with the prose than with digits. On the other hand, words, a material that, one W/Ould think necessitated the formation of logical associations, partakes (so far as Method 3 is concerned) of the nature of digits, for the "upper half" always retains less than the "lower half." Just why this should be is difficult to say, and I have no satisfactory explanation to offer. With prose and poetry our results by all these methods are quite uniform. As this material is essentially "logical" in character our 46 DELATION OF QUICKNESS OF LEARNING TO RETENTIVENESS results do not disagree with those obtained by Henderson,* Thorn- dike,^ and Pyle,* each of whom found that those who learn quickly retain more than those who learn slowly, for the material they used was not such as involved the learning of motor associations, as is largely the case \\dth digits and, with many individuals, even with words. Taking all three methods into consideration, however, and aver- TABLE XIII 20 Columbia College Men Students 1 2 3 6 9 Digits : Upper half 3.5 1.6 4& 18 Lower half 7.4 2.6 62 18 Nonsense-syllables : Upper half 8.0 3.7 52 22 Lower half 16.0 7.2 51 20 Words : Upper half 6.9 2.3 66 38 Lower half 14.5 3.0 79 35 Prose : Upper half 8.5 1.6 80 65 Lower half 13.8 4.0 72 51 Poetry : Upper half 7.9 1.6 81 73 Lower half 11.8 3.3 73 63 Ayerage: Upper half 7.0 2.2 66 43 Lower half 12.7 4.0 67 37 "Method 2" was not tried with these subjects. In this group of subjects only 12 nonsense-syllablea were used. The passage of prose was relatively easier than that used in Tables XI. and XII. hence the shorter time. aging the results we find that, with all materials, excepting digits, those who learn quickest forget the least. The contrary result ob- tatined with digits should not be considered in any way remarkable or contradictory, — the associations formed in memorizing digits being quite different from those formed in the momorizing of words and nonsense-syllables. Not that logical associations are invariably formed in the memorizing of nonsense-syllables, but when associations are formed they are of the same type as those formed in the memorizing of words. In short, the nonsense-syllable is first converted into a word, and the word is then ' * memorized. ' ' *^ *"A Study of Memory," Psy. Bev. Monog. Supp., No. 23, 1903. 5 "Memory for Paired Associates," Psy. Rev., 1908, 15, 122. 6 "Retention as Eelated to Repetition," Jour, of Ed. Psy., 1911, 2, 311. RESULTS 47 We have already considered the question concerning the degree to which the extremes at each end of a series should be considered, and, whether or not they should be taken at their face value. The method of averaging the two halves of each group, so that the average of the first half may be compared with the last half, tends, as we have already said, to "tone down" or lower the significance of these ex- tremes by immersing them with the remainder of the ''half -class" to TABLE XIV 60 High School Boys and Giels 1 2 3 6 9 12 Digits : Upper half 6.0 2.6 62 Lower half 14.1 3.1 74 Nonsense-syllables : Upper half 25.3 8.0 68 Lower half 38.7 10.9 68 Words: Upper half 9.5 4.8 48 Lower half 15.0 6.0 60 Prose: Upper half 15.4 5.2 68 Lower half 26.1 10.1 61 Poetry: Upper half 6.0 3.3 65 Lower half 13.6 3.7 61 Ayerage : Upper half 12.4 4.8 62 Lower half 21.5 7.0 65 which they belong. Arguments may be made both for and against this procedure. In the first place it may justly be contended that it is these very extremes that are most valuable — and that the compari- son of most worth would be that in which the first two or three indi- viduals were compared with the last two or three. On the other hand it is possible that it is precisely these extremes that are most to be suspected of error, and that the chance of error is lessened by talking the average or the median of each half of the class. Roughly speaking, the Pearson method may be said to do away with both of these objections, for, while it takes into consideration the actual amounts themselves, it tends to lower the significance of the extremes more than does the method of comparing the average of one half of the class with the other. The Pearson method was used with every group of subjects for determining certain of the correlations considered below. It is evi- dent that the data given in the tables supply material for the work- 21 28 22 31 30 48 23 35 25 44 23 36 57 74 38 60 61 84 51 80 39 55 31 48 48 BELATION OF QUICKNESS OF LEAENING TO BETENTIVENESS ing out of several correlations. Of these the four most important are : (1) Column 2 with 3; (2) Column 2 with 4; (3) Column 2 with 7; and (4) Column 2 with 10. These four correlations have been worked out for every group of subjects. Of the four correlations mentioned, the first, Column 2 with TABLE XV Several Groups JfO Grammar School Girls. Modal Age, 14 1 2 • 3 6 9 12 Method Three Method One Method Two Time of First Per Cent. Learning, Time of Re- of Time Score Per Score Per Min. learning Saved Cent. Cent. Av. upper half 13.2 5.0 60 37 55 Av. lower half 20.1 6.9 64 28 54 24 Trade School Boys. Modal Age, 16 Av. upper half 11.4 4.2 59 35 52 Av. lower half 19.2 7.3 60 26 41 60 High School Students. Both Sexes. Modal Age, 17 Av. upper half 12.4 4.8 62 39 55 Av. lower half 21.5 7.0 65 31 48 132 Normal College Women Students. Modal Age, 21 Av. upper half 11.2 4.0 61 39 56 Av. lower half 17.8 6.4 65 31 47 24 Asylum Attendants. Both Sexes. Modal Age, 25 Av. upper half 14.1 5.2 58 35 52 Av. lower half 18.3 7.2 62 28 41 12 Clerics and Business Men. Modal Age, 30 Av. upper half 12.2 4.4 61 37 49 Av. lower half 20.0 7.1 67 30 39 16 Graduate Students and Professors. Men. Modal Age, 32 Av. upper half 11.1 3.8 61 41 Av. lower half 16.9 6.1 63 33 The interval between first learning and relearning was, in the groups included in this table, one week for digits and nonsense-syllables, and ten weeks for words, prose and poetry. Column 3, is, with a few exceptions, positive. The exceptions are not confined to any one material though they occur mostly with the digit tables. The correlation is fairly high, averaging between .5 and .6. The second correlation — Column 2 with Column 4 — belongs to Method 3. Here, of course, the correlations tend to correspond to the relation shown by the two figures of Column 6 but this is not inva- BESULTS 49 riable. For example, with Tables I. to V. the correlations are all negative with the exception of prose— and here the correlation is so low and the P.E. so large that the index obtained is practically of no value. In fact nearly all of these "Method 3" correlations are ex- tremely low and their only value is to show that, so far as Method 3 is concerned, there is practically no correlation between the rapid learn- ing and retention. The third correlation— Column 2 with Column 7— belongs to TABLE XVI Several Groups 24 State Beformatory Inmates. Males. Modal Age, 20 1 2 3 6 9 12 Time of First Time of Re- Per Cent. Learning, learning, of Time Score Per Score Per A , ,„ ™^'^- Mm. Saved Cent. Cent Av. upper half 6.2 2.1 68 50 71 Av. upper half 12.2 3.9 70 43 62 32 Columbia College Seniors. Men. Modal Age, 22 Av. upper half 9.1 2.7 68 42 Av. lower half 12.9 5.0 70 35 U Barnard College Seniors. Women. Modal Age, 22 Av. upper half 7.0 2.2 66 40 Av. lower half H.g 4.5 60 33 12 WorJchouse Inmates. Men. Modal Age, 26 Av. upper half 10.3 4.5 68 '40 66 Av. lower half 16.0 5.4 69 32 54 24 Prison Inmates. Men. Modal Age, 34 Av. upper half 9.9 4.1 70 39 Av. lower half 14.3 5.0 72 37 _ The interval between the first learning and the relearning was, for the groups included m this table, three weeks for all materials. Method 1. The correlation is, with the exception of digits, alwavs positive, I. e., such as to show a correspondence between quickness of learning and retention, when the latter is measured by the amount re- called after the interval. It is not, however, a very high correlation, seldom going above .4 and averaging only .25. The fourth correlation— Column 2 with Column 10— belongs to Method 2. Generally speaking the index obtained agrees fairlv eloselv with that of Method 1. In view of the fact that the material is read once to the subject Method 2 allows a certain amount of relearning and .thus approaches Method 3. This is seen in several of the corre- lations obtained. Even though, as just stated, the general statistical relation between speed of learning and retentiveness is very loose, it might still be true that there was a class of quick learners who were poor in retention, 50 RELATION OF QUICKNESS OF LEARNING TO BETENTIVENESS Q e*«oc«oo^^oo«ooq'*'*«Doqoq^'*p«Dioe«oqp»oi> ^ XJ130J r-lt~(MCCI00(MrHOOl0^t--^C5-*C0O00e000r-llOCl?0 H OJi— li— IfMrH 1—' 1— lOJ t— I CQr-lOa i— I i— li— I •a S iDIOU CCic«5i-llO-<*-#C00>.— I^Ot- ^^ (M r-lr-li-l T-l r-li-<(Mi-l (Mi-I r-(Ca (Ml-( r-t C* rHi-HrHrHi-H tHrHfHi-l C{i-ICNlrHrH i^C{ ^ g^ t-(>-i r-i r-ii-ii-i i-icgrioioQ i-ioq jj l^TSia (MOj-*0'«*05«Oli3T-lrHirOt-U3C" S ^ q«]<>at« <; g^ rHr-l r-lrHi-liH iHr-lrHf-lT-<HfH>H r-lrH i-lrH>H 5 AJjaoj Ninii-(fooooooi*OTt ■g CMrH (MOaOQi— I (Mi— II— I i— I i— (i— Ir-ll— (r-l ^ spJO^ ooo5(Mcqrt.i-l ■5 aSaaSaO^ C'*IO^c«^c*oc«oo®«Orj'Cot»co»o'*'«*i'-ioo ^ i-l 1-1 rli-i (M(Nr-i (Mr-li-li-lOJl-IIN--l « S apjOM l0 10r-IOCO«Dt:~Oit-lrt*CM(MCOQ050i-iOOt^'^05fOOJOTj( ^ i-l T-l i-i i-i(Mcot^05iooOTt.ooC50r-i