THE ACCOMPLISHMENT RATIO
A Treatment of the Inherited Determinants
of Disparity in School Product
By
RAYMOND FRANZEN
A.B. (Harvard), M.A. (Columbia)
Ph.D. (Columbia)
Teachers College, Columbia University
Contributions to Education, No. 125
Published by
Teachers College, Columbia University
New York City
1922
Copyright, 1922, by RAYMOND FRANZEN
PREFACE
The results of the experiment reported here have become so much a portion of my process of reasoning that duplication of material presented elsewhere is unavoidable. I wish in particular to recognize my indebtedness to the TEACHERS COLLEGE RECORD for permission to reprint here revised portions of an article which appeared in the November, 1920, number of that journal. I will warn here any reader to whom the intricacies of a full statistical account are irksome that the logic and conclusions presented in this study are incorporated in a more palatable and abbreviated form in Chapter IV of Intelligence Tests and School Reorganization (World Book Company).
The work presented here has been made possible by the cooperation and interest of the two principals of the Garden City public school during the period of my work there, Miss Gladys Locke and Mrs. Edna Maule. I also owe any success that this experiment may have had to the teachers who did the real work of “pushing” abilities to their limit. My indebtedness to Gladys Locke Franzen for help in expression and correction is surpassed only by what I credit to her encouragement and cooperation at its inception.
During the period in which this experiment was planned and executed it grew into a real problem through the advice of two of my teachers to whom I owe all such inspiration and knowledge as I possess—Edward L. Thorndike and Truman L. Kelley.
RAYMOND H. FRANZEN
Des Moines, Iowa, 1922.
CONTENTS
I. AN OUTLINE OF THE EXPERIMENT 1
The Use of Quotients and Ratios
The Derivation of Age Norms
A Method of Survey of Reading, Language and Arithmetic
II. STATISTICAL TREATMENT OF THE EXPERIMENT 17
The Quotients
The Ratios
Summary
III. THE PSYCHOLOGICAL CONCLUSIONS OF THE EXPERIMENT 43
The Neglect of Genius
Is Genius Specialized?
Current Psychological Opinion
Conclusions
PART I[1]
AN OUTLINE OF THE EXPERIMENT
THE USE OF QUOTIENTS AND RATIOS
Standardized measurement of educational product has won its way to a recognized place in the school life of this country. Many of our larger cities have research bureaus of tests and measurements, and advanced private schools have departments of measurement. The logic of the use of statistically derived evaluations versus the use of opinion, swayed as it is by the haphazard captions of emotion and condition, has become widely recognized. The case of scientific measurement in education has been argued and won. The objections to older forms of measurement have become the criteria of the value of the new.
Still administrators, although they have been convinced theoretically of its importance, find it hard to see just what measurement does for their schools. They often object that measurements are made, the tests are carried away by the examiner, and some time later they are presented with a neat series of distributions and are told where their school stands in relation to certain other schools or to schools in general. This is undoubtedly a very important piece of information; since a determination of the extent to which a goal has been attained forms the basis of the commendation or condemnation of the methods, curricula, and text-books employed in the process. But administrators want to know which of the various elements of school procedure are to be praised and which are to be blamed.
We cannot condemn or support a whole school system on the basis of composite results (unless all possible educational objectives have been measured, and show one common drift; or unless it is necessary that the system fall or stand as a whole) since then we should be throwing good and bad into a common discard. We must measure each thing separately. We must build our ideal system of education synthetically, taking the best methods from each of the prevalent groups of theories. There has been too much absolutism in education, too little of a realism that sees the good and bad in all and diminishes the bad and augments the good. If we adopt this point of view we become really empirical in our method, living through each educational experiment to incorporate it into a growing treasury of tested theory, not deducing success or failure from metaphysical or doctrinaire prejudice. In this administrators have been more scientific than those who measure. They have always objected that they wanted differential diagnoses. Here the answer to their needs must come through experimentation and it is only through nation-wide study and careful comparison and integration of results that methods of teaching can be scientifically established.
Three uses of measurement commonly stressed are: (1) Diagnosis of degree of attainment of goal; (2) selection of method of attainment of goal; (3) definitive outline of goals. We have seen that the first two are of little immediate value to the administrator. The first only gives him an accurate notion of where he stands in any one subject without pretending to tell him why; the second is a promissory note. Some day we shall be able to tell him the best methods for the attainment of his goal. The third has slightly more immediate value. Measurement splits up the goals of education, gives them concrete formulation, allows teachers to see an advance in the class in one function as separate from the rest; allows them, for instance, to distinguish more clearly than they otherwise would between oral reading and silent reading, or between addition and division. But this, too, is rather too general to appeal to administrative economy. One would find it very difficult to sell one’s services as a measurer to a school board or a superintendent on the basis of these three values. They answer that universities and scientific research give them as much as they want of these values. What an expert on measurement could add in interpretation of results would seem of small additional value to them.
Still there is a very marked function that such an expert can perform; but he must serve a fourth and fifth use of measurement while he serves a particular school. When he serves the first three he is serving the science of education and, unfortunately, no one school will pay him to do that. The uses of measurement that directly benefit any one school are: (4) Classification by information and intelligence and (5) diagnosis of individual disability. For the proper prosecution of these aims individual measurements and age norms are essential. Only with such equipment can we make the prognoses of future school behavior which the administrator so urgently needs.
Grade norms cannot be used to make individual diagnoses. Though we can see by them which children are below and which above the level that in their grade they should attain, we cannot see just what administrators most need to know; namely, whether the retardation and acceleration are justified or not—how many children are working at maximum. More than that, computations based on grade norms are very inaccurate in individual cases because the variability within any grade is so great. As it becomes necessary to use new norms for such purposes it is important to have them in terms that are directly comparable to intelligence mensuration.[2]
First in importance is an interpretation of the meaning of an Intelligence Quotient. Too often it is stated as a number and left as a number with the belief that somehow or other that is a tag which carries its own divine implication. Its importance lies in its diagnosis of power of adaptation, and it has a high correlation with the maximum possible rate of school progress. Just as a pure information test diagnoses the neural bonds that have been formed in any one field, so an intelligence test diagnoses the ability to form bonds, to meet a new situation and form satisfactory habits—power to learn. It may be thought of as a diagnosis of the neural chemistry of the individual. As such it is not concerned with the connections or quantity, but rather with the quality of the neural tissue.
As an intelligence quotient is actual mental age divided by chronological age—which is the normal mental level of the child’s age-group—so it is the rate at which the child has progressed to mental maturity. It is his potential rate of progress. It is a division of what is by what normally would be. Then, when we use IQ we express the various degrees of power of adaptation due to various degrees of fitness of neural equipment to form bonds, by means of a diagnosis of the rate of formation of bonds which everyone forms sooner or later in an environment such as ours. It is conceivable that we might test this same power without testing the presence of such bonds at all. Such a test would detect directly the quality of the neural equipment irrespective of quantity or conformation.
A ten-year-old child whose mental age is ten has progressed at the rate which is normal, and his IQ is 1.00. A very exceptional ten-year-old child whose mental age is fifteen has progressed just one and one half times as fast as the former, and his IQ is 1.50. Another exceptional ten-year-old child whose mental age is five has progressed at just one-half the rate of the first, and his IQ is .50. What we mean, then, by an Intelligence Quotient is the rate at which a child grows to the mental maturity of human beings in the world as it is.
For purposes of presentation of a problem one can here assume (an hypothesis the value of which will here be determined) that each child can attain this rate of progress in each of the elementary school subjects. The degree to which this is true is the degree to which the IQ is a valid index of power to deal with school subjects. This assumes that inherited special disabilities in the school subjects are uncommon, that school progress is determined by the interplay of intelligence and environment, and that so-called interest characteristics which aid in development are the result of an earlier interplay of intelligence and environment. The degree to which educational product of children can be made to approach this intelligence will allow us to judge how far these factors are inherited, since differences that are removable must be learned, not innate.
We can the more readily see the significance of viewing a child’s equipment in terms of educational and mental age, when we conceive of a Subject Quotient. This is a quotient resulting from the division of the age level reached in the test in question by the chronological age of the pupil. It is a measure of the rate of progress of the child in the school subject under consideration. Thus a ten-year-old child with ten-year-old ability in Thorndike Reading Scale Alpha 2 would have as his reading age divided by chronological age, 1.00. This may be called his Subject Quotient in Reading or his Reading Quotient. The division of what is by what would be if the child were normal gives the percentage of normality, the actual rate of progress. Since the IQ is the potential rate of progress and the SQ the actual rate of progress, the ratio of SQ to IQ gives the percentage of what that child could do, that he has actually done. Thus a child with an IQ of 1.32 whose reading quotient (his RQ) is 1.10, though he is doing work which is above normal, is not doing work which is above normal for him. His RQ⁄IQ is 1.10⁄1.32, whereas if he were progressing at his optimum rate it would equal 1.32⁄1.32. This RQ⁄IQ is the same quantity as RA⁄MA. We may call this a Subject Ratio and the average of Subject Ratios an Accomplishment Ratio. We could, if the absolute association between reading age and mental age were perfect, measure the approximation to ideal educational performance of any one child in any one elementary school subject through the approximation of this Subject Ratio to 1.00. As we will see later, Subject Quotients approach the Intelligence Quotients when special treatment is given; that is, the correlation of SQ and IQ becomes nearer 1.00 and the difference between the average IQ and the average SQ approaches zero. It is safe then to expect these Subject Ratios to be at least 1.00 before we pronounce satisfaction with the school product.
There is certainly a significant relation between IQ and SQ, and the more perfect the educational procedure has been, the more it has called forth all that the child is capable of, the higher it will be. To determine whether the quotient in any school subject can be greater than the Intelligence Quotient in any significant amount, it will only be necessary after we have perfect age norms by months to get that quotient amongst enough pupils whom we know to be working at maximum. What is significant here is that the more nearly any such quotient reaches or exceeds the Intelligence Quotient the more nearly has the child been brought up to what he is able to do under the best conditions. The Accomplishment Ratio is the degree to which his actual progress has attained to his potential progress by the best possible measures of both.
This would be a mark of the child’s effort, a mark of the concentration and interest that the child has in the school work, and as far as no inherited traits or capacities other than intelligence affect school work it is a measure of the efficiency of a child’s education thus far. If there are such other innate bases, it is also a measure of those inherited traits and capacities or their predisposition, such as concentration, effort, written expression, etc. At any rate it is a measure of the child’s accomplishment, and so of the effort and concentration as they really are at present working under those school conditions. It is an index of achievement irrespective of intelligence.
A very convenient graph representing the same facts and easily interpreted by the teacher may be constructed thus:
Age Scale +------------------------------------------------ Mental Age | Reading Age +----------------------------------------- Chronological Age | Spelling Age | Arithmetic Age +----------------------------------------------------------
Here it can be easily shown that Spelling Age, Reading Age, Arithmetic Age, etc., are in some definite relation to both Chronological Age and Mental Age. Using the Mental Age line as a goal, these records may be kept constantly up to date. Another use of the Accomplishment Ratio is as the medium in which the children may keep records of their own work. As it is a mark in terms of intelligence, dull and brilliant children may compete on a parity to bring their Accomplishment Ratios as high as possible.
Mainly we have advanced formal education. We have in many ways promoted the abilities to read, write, spell and figure. But our philosophy of education has advanced far beyond that. We have other aims in education, and consequently other methods and modes, which also must be measured and judged. We wish to promote such qualities as stability, self-reliance, concentration, and ambition. It does not necessarily follow that we must measure these things directly, although every one vitally interested in measurement cherishes the hope that we may some day measure their behavioristic correlates,—“For the quality of anything exists in some quantity, and that quantity can be measured.”
“Some of us might be entirely willing to rest the case after asking whether in practical school life anyone ever saw a teacher thoroughly confident of teaching ideals but neglectful of reading and arithmetic. The fact is that the conscientious teacher always gives attention to both and the successful teacher is able, without omitting one, to cultivate the other. The theoretical possibility of thinking of the two results separately has little significance in dealing with real teachers and real schools. Good reading is a school virtue; and when one has measured good reading he has measured more than the trivial or formal side of education.”[3]
This I believe to be true, but I also believe that through measurement we can actually promote those other more ethical ideals in education. Through classification by information and by intelligence we gain a marked increase of attention, concentration, ambition, and other objectives, measured in part by Accomplishment Ratios. More discussion due to a greater homogeneity promotes powers of inference and insight; being only with equals promotes self-confidence and honor, and in many cases prevents a regrettable conceit among supernormals; having work to do which is hard enough prevents habits of indolence and carelessness so commonly found among intelligent children.[4]
It is a well-known fact that much work must be done in classification to get homogeneity or real conditions of teaching. As it is, most teachers are talking to the middle of their classes. When they do they mystify the lower quarter and bore the upper quarter; they talk to the upper quarter and mystify the lower three quarters; or they talk to the lower quarter and bore the upper three quarters. When a child is bored or mystified his Subject Quotients become less while his Intelligence Quotient remains constant. Then his Accomplishment Ratios become less as long as he remains in a position where he is being mistreated educationally. This, then, is the proper measure to see whether a child is classified properly or not. At the Garden City public school I changed as far as I was able the conditions of education of each child in that subject wherein his Accomplishment Ratio was markedly below 1.00. The concentration and effort of the child were obviously low and my attempt was to change conditions and to promote habits of consistent work. When the Accomplishment Ratio increased I knew that the child was profiting, that he was working. Our objective was to increase Ratios of all children, not to attain any set standard.
This Accomplishment Ratio would, to my mind, be an ideal school mark. Besides the inaccuracy of marks to-day, which are accurate marks only of the teacher’s opinion, biased as it is by the personal equation of her character with that of the pupil, there is another fault of prevalent school marking. It is based on average work. The mark is the link between education in the school and education in the home. It gives the parents an index of the child’s work and allows them to encourage or discourage the child’s attitudes. Such indices have no real significance when they are based upon average development, as the parent is generally mistaken about the ability of the child.
Marks given by a teacher are satisfactory only for a normal child with normal age for the grade. Brilliant children are over-praised for work which, though over the ability for the group, is under their own ability. Marks given to stupid children are misinterpreted by parents so as greatly to prejudice the effort of the child. Though his work may be such as to merit encouragement his mark may be very low. Teachers’ marks are, aside from their inaccuracy, just, only in a group that is perfectly classified; just, only when the children are all of the same ability and all possess the same initial information. So far as they are unjust they are subversive of our aims, as they then transmit a faulty message to the home and disrupt the continuity of school and home education.[5]
Such marks as are here advocated would correct this feature of our present system, as well as the inaccuracy of our present marks. It is a mark which evaluates the accomplishment of the child in terms of his own ability. A brilliant child would no longer be praised for work which in terms of his own effort is 70 per cent perfect, in terms of the maximum of the group 90 per cent. The teacher gives him a mark of 90 while we mark him 70. A stupid child who does work which is marked 70 in terms of the maximum of the class but 90 in terms of his own, a limited ability, is no longer discouraged. His effort is evaluated, and the praise which he receives from home is merited and consequently economical, since the resultant satisfaction cements the bonds of concentration and attention. Such a mark is an actual index of the effort that child is making and consequently forms the proper link between the school and the home.
Parents would need no great instruction in the interpretation of these marks, since they have always acted as though the other marks were these, and since these also are in percentage form. The only kind of mark they can understand is an Accomplishment Ratio. I found that the parents of the children at Garden City were more attentive to such marks than to others, and acted upon them more readily. Of course the parents of the very intelligent children, who are used to marks above 90, are surprised at first when you tell them that your mark of the child is 80; but upon explanation, which should in all cases precede the first report to the parents, they immediately see the value of such grading. It is fortunate in this connection that the greatest amount of explanation is necessary about intelligent children, as one usually deals then with intelligent parents.
THE DERIVATION OF AGE NORMS
In this study age norms were derived empirically, both regression lines being taken into consideration. From the point of view of statistics it becomes imperative, in order to use the technique here advised, to have the average age of a score—since we are going to predict age from score—to translate crude scores into indices of maturity in each subject under consideration. We are in error in the use of grade norms, if we find the average score of a grade and then, when we obtain that score in practice, say that the work is of that grade. To be able to say this we must know the average grade of a score. This takes in an entirely different cross-section of data. If we get the average score of all children in grade 6, then we can predict what a 6th grade child is likely to get, but we can say nothing about a child who is not in grade 6. In order to decide that a 4th grade child has 6th grade ability, we must know that he has such ability that all children who share this score make an average grade of 6.[6] It would be wise then to get the regression of score on age as well as the regression of age on score, since they are not identical, the correlation between score and age being less than unity.
We will note in passing that the data to establish these norms, except those of reading, are not as complete as may be desired, inasmuch as it was difficult to get test scores where the age in months also was available. However, the general data behind the grade norms could be used to keep the results from any crude error; and the averages were obtained for every month from 8 years to 14 years, with a corresponding refinement in intervals of score, which made still more improbable an error in the general tendency of the regression lines. Then all the distributions, when grouped by years, were corrected for truncation; that is, the tendency for the brighter children of the older group to be in high school (the data were from elementary schools only) and the duller children of the younger group to be in the lower grades where they could not be reached was recognized and corrected by finding the average, standard deviation, and number of cases which would have existed if these forces of truncation were not operating. This was done by the use of the other one half of the figures comprising Table XI of Pearson’s Tables for Statisticians and Biometricians. Dr. Truman L. Kelley pointed the way to its derivation.
These norms differ somewhat from those derived from the grade norms by translation of grade into average age for the grade. This is because the norm for a grade is the average score for a grade. Hence the norm of age 10 obtained in this way is the average score obtained by a grade whose average age is 10. Then the data used to obtain this average are made up of diverse ages, all of one grade, instead of all of one age and diverse grades. Even then, we would have only an average score of an age which approximates what we want, but is not as reliable to use as average age for a score.
A METHOD OF SURVEY OF READING, LANGUAGE, AND ARITHMETIC
The following procedure was employed in the experiment. The experiment was carried out in the public school at Garden City. Two hundred children were given the tests. The instructions, shown below, were followed in November, 1919, and in November, 1918; in June, 1919, and in June, 1920, with the exception that no arithmetic test was used in November, 1918, and June, 1919. The Binet tests were given by the author; all of the others were given either by the author or the principal who was careful not to deviate from the directions in any way. In June of both years the author gave instructions for a test in one room, and then left the teacher in charge and went on to the next. This could be done in June of each year as the teachers were then fully acquainted with the experiment and their coöperation was assured.
DIRECTIONS
I. Administer and score the following tests according to standard instructions. Give all tests to grades 3 and above.
Woody-McCall Mixed Fundamentals in Arithmetic Thorndike Reading Scale Alpha 2 Thorndike Visual Vocabulary Scale, A2 Kelley-Trabue Completion Exercises in Language Stanford-Binet Tests (given by the author)
II. Translate the scores into year-month indices of maturity by means of the following table. (Use Mental Age for the Binet.) Assume rectilinear development, that is, that the amount of score which equals the development of one month is the same as the amount of score which equals the development of any other month. Then interpolation and extension are allowable. Use the table in this way: Find in the table the score made by a child (for instance in the Woody-McCall); find the age to which it corresponds, then call this age the Arithmetic Age of the child. For instance, if the score in Woody-McCall is 20, his Arithmetic Age is about halfway between 10 and 11 or 10 years 6 months.
=====+============+=======+=============+============= Age |Woody-McCall|Alpha 2|Visual Vocab.|Kelley-Trabue -----+------------+-------+-------------+------------- 8—0 | 12.00 | 4.50 | 3.60 | 4.30 9—0 | 15.16⅔ | 4.98 | 4.32 | 5.00 10—0 | 18.33⅓ | 5.46 | 5.04 | 5.65 11—0 | 21.50 | 5.94 | 5.76 | 6.35 12—0 | 24.66⅔ | 6.42 | 6.48 | 7.05 13—0 | 27.83⅓ | 6.90 | 7.20 | 7.70 -----+------------+-------+-------------+-------------
III. Arrange these Arithmetic Ages of all the children of your school in order from high to low with the names opposite the scores in the extreme left-hand column of the paper. At the right have parallel columns of the grades. Check the grade of each child in these columns. You will then have a sheet like this:
================+======+===================
| | Grade
| +---+---+---+---+---
Name |Arith.| 4 | 5 | 6 | 7 | 8
| Age +-+-+-+-+-+-+-+-+-+-
| |B|A|B|A|B|A|B|A|B|A
----------------+------+-+-+-+-+-+-+-+-+-+-
Gertrude Smith | 180 | | | | | | | | |#|
| +-+-+-+-+-+-+-+-+-+-
Saul Sampson | 176 | | | | |#| | | | |
| +-+-+-+-+-+-+-+-+-+-
Ed Jones | 176 | | | | | | | | |#|
| +-+-+-+-+-+-+-+-+-+-
George Calut | 172 | | | | | | | | | |#
| +-+-+-+-+-+-+-+-+-+-
Ida Henry | 172 | | | | | | | | | |#
| +-+-+-+-+-+-+-+-+-+-
Raymond Teller | 172 | | | | | | | | | |#
| +-+-+-+-+-+-+-+-+-+-
Ed Hoard | 172 | | | | | | |#| | |
Etc.
Do the same with each of the tests. It is clear that, independent of the unreliability of the test, if your school were perfectly classified all the 8th grade children would come first on each relation sheet and then the 7th grade children, etc. You have now a picture of the overlapping of your grades. Regrade in reading and arithmetic. Draw horizontal lines across these relation sheets at the points of delineation. Divide your total number of children by the number of teachers available and then make a class division by the number of pupils, that is, call the upper one-sixth of the total number of pupils grade 8 in this subject, the next one-sixth, grade 7, etc. Teach all grades of arithmetic at the same time and all grades of reading at the same time. You can now send each pupil to the grade in which he belongs in each subject.
IV. Call each derived age a Subject Age (SA). Divide each subject age by the chronological age of the child. This will yield what may be called a Subject Quotient (SQ), previously called an Educational Quotient (EQ).[7] Dividing the Reading Age by the Chronological Age, you arrive at a Reading Quotient. This RQ is the rate at which the child has progressed in reading. We have the same kind of quotient for intelligence (Stanford-Binet IQ). This IQ is the potential rate of progress of the child.
V. The ratio of any Subject Age to Mental Age[8] may be called a Subject Ratio (SR), previously called an Accomplishment Quotient (AccQ).[7] This Subject Ratio gives the proportion that the child has done in that subject of what he actually could have done, and is a mark of the efficiency of the education of the child in that subject to date. The goal is to bring up these Subject Ratios as high as possible. When they are above .90, the child may be considered as receiving satisfactory treatment, providing norms for subject ages are reasonably accurate. (This figure, .90, applies to a Subject Ratio obtained by using a Stanford-Binet Mental Age.) An Arithmetic Ratio based on one arithmetic test and one intelligence test only is not as good as one based on three arithmetic tests and three intelligence tests. If Subject Ratios go far over 1.00 the chances are that the Mental Age diagnosis is too low. The average of the Subject Ratios of a child may be called his Accomplishment Ratio.
In the application of the above instructions, whenever opportunity offers for classification of both subject matter and intelligence (which means many teachers or a large school), use a Relation Sheet (for instance for Arithmetic) and then have additional columns at the extreme right for intelligence headed A, B, C, and D. If a child’s IQ is in the upper quarter of the IQ’s of your school, check in the column A opposite his name; if it is in the upper half but not in the upper quarter check in B, and so on with C and D. Then you will be able to split each group; for instance, the one which is defined as 8th grade in arithmetic ability, into four sections, each of which progresses at a rate differing from the others. The A section will progress most rapidly, B next, C more slowly, and D most slowly.
As Garden City was a small school, adjustment of procedure to individual differences in intelligence, besides the grouping for subject matter, was done mostly by pushing children. Children were advanced whole years (the grade they “belonged to” was the one in which geography and history were taught; this was their home grade) besides the readjustment made by the special regrading in reading and arithmetic. A special treatment class was formed where pronounced negative deviates were given special attention. Regrading was also instituted for spelling. Children were promoted whenever it was considered advisable; teachers were switched from subject to subject whenever that was considered advisable by the principal and the author. The Thorndike Arithmetics and other new texts were introduced to some extent. Any change possible was made in order to bring EQ⁄IQ as high as possible. That was the goal. The purpose was not to prove that any certain educational procedure would tend to promote abilities more rapidly than others, but that abilities could be promoted to the level of intelligence—that intelligence is substantially the exclusive inherited determinant of variety of product among school children. (It is to be understood that intelligence may be, and probably is, the summation of thousands of inherited factors,—neutral elements, here merged in the broader behavioristic concept of intelligence.)
SCIENTIFIC QUESTIONS INVOLVED IN CLASSIFICATION
If we were able to negate other influences upon disparity of product, we could conclude that these were not inherited. Hence it would be our burden as educators so to manipulate education as to prevent their operation. We will attempt to analyze the determinants of individual differences in product in these children, to see which influences besides intelligence are part of the inborn equipment which is not the province of education, but of eugenics, to correct. No absolute validity is held for any of the conclusions stated here. The subject is, at best, vague and complicated; but our conclusions can be used as the basis for a good guess in school procedure. We can judge general tendencies from the educational experiences of the two hundred children whose abilities for two years are here charted.
The importance to educators of the subject in hand is excuse enough for its treatment. All educational procedure points a prophetic finger toward the classification of pupils and a reduction of the individual differences of product to the inherited bases of these differences.
Classification, however, needs some more accurate psychological foundation than the mere awareness of individual variance. We must know:
1. What tests to use.
2. How to use them.
3. Whether abilities in reading, spelling, and arithmetic or their predispositions exist as special abilities, or whether children differ in these simply because of their innate differences of intelligence.
4. Whether individual differences in ambition, interest, and industry, in so far as they influence accomplishment, are due to special tendencies, or whether they are learned manifestations of a more general heritage.
5. How these proclivities, specific or general, are related to intelligence.
Points 1 and 2 are problems of procedure which must be evolved from our existent knowledge of measurements and statistics. Points 3, 4, and 5 are problems which must be solved from the evidence resulting from an experiment in classification using these methods. Points 4 and 5 introduce the vexed question of whether there is a “general factor” or some general inherited cause of disparity in school product other than intelligence. Should reading ability prove to be the result of certain inherited abilities, or predisposition to abilities, we could not use a measure of mental ability alone as the guide to what a child could attain in reading. If intelligence, however, were the only inherited prognostic factor of school achievement, we could mark the education which had functioned in the child’s life by the percentage which the actual accomplishment of the child was of the maximum accomplishment of which he was capable at that stage of his mental development. So, too, if interest in particular subjects and ambition are not mainly the result of rewards and punishments of early life, but are themselves significantly rooted in the nature of the child, we could not condemn or commend curricula and methods upon a basis of the ratio of resultant accomplishment to mental ability, but must include a measure of this potentiality. The practical queries whether or not a child can do reading as well as he does arithmetic, whether his ambition and his honesty have their origin in the same strength or weakness, can be answered only when these problems are fully solved. The immediate consequences of knowing that a child can usually be taught to read if he does other tasks well is of obvious import. It would be of great service, too, to know whether lack of application can be corrected so as to bring concentration to the level of the other traits. If a child is normal in other ways and not in his tendency to respond to the approval of others by satisfaction, can this “drive” be increased or reduced to the average, or are individual differences in specific original tendencies basic to development of character, and if they are, how much influence do these differences exert upon school accomplishment? In order to classify children and comprehendingly watch and control their progress we must know the relation of achievement to the inherited bases upon which it depends. We must be able to state a child’s progress in any one school subject in terms of the potential capacity of the child to progress. We must know the inherited determinants of disparity in school product.
PART II
STATISTICAL TREATMENT OF THE EXPERIMENT
In the discussion and tables which follow:
Q stands for Quotient, which will mean a Subject Age divided by a Chronological Age. R stands for Ratio, which will mean a Subject Age divided by a Mental Age.
AQ means Woody-McCall Arithmetic Age divided by Chronological Age, and AR means this AA divided by Mental Age.
VQ means Thorndike Vocabulary Age divided by Chronological Age, and VR means this VA divided by Mental Age.
RQ means Alpha 2 Reading Age divided by Chronological Age, and RR means this RA divided by Mental Age.
CQ means Kelley-Trabue Completion Age divided by Chronological Age, and CR means this CA divided by Mental Age.
SQ means any Subject Quotient, that is, any Subject Age divided by Chronological Age, and SR means any Subject Ratio, that is, any SA divided by Mental Age.
EQ means the average of all Subject Quotients and AccR, the Accomplishment Ratio, means the average of all Subject Ratios.
All r’s are product-moment correlation coefficients, uncorrected. As the reliabilities (Table 4) are almost what the other coefficients are in June, 1920 (Table 5), it is apparent that the corrected coefficients, when Grade III is excluded, would all be very near unity at that time.
THE QUOTIENTS
In Table 1 are presented all the quotients for all periods of testing, grouped by children. The table, a sample of which is included here,[9] shows clearly how all SQ’s approach IQ as special treatment continues. The grades indicated in this grouping are as of June, 1920. Inasmuch as many double and triple promotions were made in an effort to get maximum product for intelligence invested, no conclusion can here be formed of the grade to which these children belonged at any time except June, 1920. The correspondence between IQ and the SQ’s in June, 1920 is further shown in Table 2. In this table the 48 children who took all tests at all periods are ranked from high to low IQ and their SQ’s are listed opposite. The high correspondence is readily apparent.
TABLE 1[10]
INTELLIGENCE QUOTIENTS FOR ALL PERIODS GROUPED BY CHILDREN
The children are arranged by grade as they were in June, 1920, and alphabetically within the grade. The periods of testing are lettered in their chronological sequence; a is November, 1918, b is June, 1919, c is November, 1919 and d is June, 1920. * = Zero Score
GRADE 3
=============+======+==========+==========+========+========== Intelligence| Test |Arithmetic|Vocabulary|Reading |Completion Quotient |Period| Quotient | Quotient |Quotient| Quotient -------------+------+----------+----------+--------+---------- | a | | | | 101 | b | | | | | c | 64 | 58 | | 43 | d | 106 | 88 | | 93 | | | | | | a | | | | 128 | b | | | | | c | 80 | 102 | | 81 | d | | 152 | 124 | 153 | | | | | | a | | | | 116 | b | | | | | c | 56 | 90 | * | 49 | d | 94 | 95 | 77 | 89 | | | | | | a | | | | 87 | b | | | | | c | 90 | 40 | 35 | 54 | d | 72 | 74 | 61 | 52 | | | | | | a | | | | 112 | b | | | | | c | 90 | 137 | 133 | 112 | d | 112 | 113 | 121 | 131 -------------+------+----------+----------+--------+----------
TABLE 2[11]
GROUP TAKING ALL TESTS AT ALL PERIODS ARRANGED IN ORDER OF MAGNITUDE OF INTELLIGENCE QUOTIENTS
=============+============+==========+==========+=========== Intelligence | Arithmetic |Vocabulary| Reading |Completion Quotients | Quotients |Quotients |Quotients |Quotients -------------+------------+----------+----------+----------- 146 | 111 | 154 | 164 | 150 142 | 129 | 135 | 137 | 136 141 | 109 | 118 | 107 | 121 139 | 124 | 141 | 124 | 134 138 | 101 | 112 | 105 | 106 | | | | 138 | 121 | 130 | 110 | 109 130 | 107 | 139 | 135 | 136 122 | 127 | 130 | 124 | 121 122 | 113 | 121 | 117 | 124 122 | 112 | 102 | 114 | 129 | | | | 121 | 128 | 125 | 128 | 128 120 | 100 | 116 | 102 | 119 118 | 117 | 123 | 114 | 125 117 | 131 | 111 | 118 | 124 117 | 106 | 122 | 112 | 111 | | | | 114 | 105 | 126 | 110 | 114 109 | 83 | 113 | 117 | 103 107 | 103 | 112 | 95 | 103 107 | 94 | 126 | 94 | 123 104 | 99 | 117 | 96 | 104 | | | | 104 | 103 | 110 | 94 | 116 103 | 108 | 113 | 112 | 106 101 | 100 | 114 | 109 | 106 100 | 90 | 103 | 92 | 92 100 | 109 | 118 | 108 | 113 | | | | 99 | 114 | 104 | 106 | 110 99 | 114 | 119 | 117 | 115 98 | 102 | 101 | 108 | 104 98 | 99 | 106 | 107 | 106 97 | 95 | 109 | 107 | 105 | | | | 97 | 108 | 101 | 102 | 105 97 | 95 | 104 | 89 | 110 96 | 90 | 104 | 91 | 91 95 | 84 | 99 | 93 | 100 95 | 90 | 107 | 99 | 105 | | | | 95 | 85 | 117 | 114 | 103 94 | 106 | 57 | 89 | 108 94 | 103 | 103 | 106 | 104 92 | 96 | 86 | 94 | 85 87 | 83 | 88 | 92 | 87 | | | | 87 | 95 | 96 | 94 | 102 84 | 85 | 87 | 93 | 87 83 | 106 | 91 | 87 | 104 80 | 77 | 91 | 80 | 84 80 | 84 | 75 | 79 | 84 | | | | 80 | 89 | 107 | 88 | 86 78 | 87 | 90 | 93 | 85 60 | 69 | 56 | 71 | 77 -------------+------------+----------+----------+-----------
The intercorrelations of the quotients of these 48 cases for all periods may be seen in Table 3 (page 21). The correlations with IQ and the intercorrelations of the SQ’s have increased toward positive unity or rather toward the limits of a correlation with tools of measurement such as we have used. This limit is a function of the reliability of the tests employed. It is customary to use a formula to correct for attenuation in order to find the percentage which the correlation is of the geometric mean of the two reliability coefficients. This is tantamount to saying that any correlation can go no higher than the geometric mean of the reliability coefficients of the tests used. It is better to assume that an r can go as high as the ∜(_r_₁₁⋅_r_₂₂) since an r can go as high as the square root of its reliability coefficient. Dr. Truman L. Kelley has shown that the correlation of a test with an infinite number of forms of the same test would be as the square root of its correlation with any one other form.
The reliabilities and limits defining a limit as the fourth root of the multiplied reliability coefficients are in Table 4.
Correction for attenuation is often ridiculously high because the reliability coefficient of one of the measures used is so low. If an element is included in the two tests which are correlated, but not in the other forms of each test used to get reliability, the “corrected coefficient” is corrected for an element which is not chance. Whenever the geometric mean of the reliabilities is less than the obtained r, the corrected r is over 1.00 and hence absurd.[12]
Therefore we use here instead, a comparison to the maximum possibility in a true sense. Since a test correlates with the “true ability” √(_r_₁₁), ∜(_r_₁₁⋅_r_₂₂) is the limit of an r, its optimum with those tools. Although these limits apply, strictly speaking, only to the total correlations, since the reliability correlations are with all the data; we may assume that the same facts hold with regard to the correlations of each of the grades, that is, the reliability is a function of the test not of the data selected.
TABLE 3
INTERCORRELATION OF ALL QUOTIENTS FOR ALL PERIODS OF THE 48 CHILDREN WHO TOOK ALL TESTS
NOVEMBER, 1918
IQ VQ RQ S.D. M
IQ 19.12 105.15 ±1.32 ±1.86
VQ .72 20.54 102.52 ±.05 ±1.41 ±2.00
RQ .64 .64 19.09 95.90 ±.06 ±.06 ±1.31 ±1.86
CQ .63 .71 .77 19.34 99.44 ±.06 ±.05 ±.04 ±1.33 ±1.88
JUNE, 1919
IQ VQ RQ S.D. M
IQ 19.12 105.15 ±1.32 ±1.86
VQ .73 20.80 113.54 ±.05 ±1.43 ±2.02
RQ .65 .58 14.73 101.31 ±.06 ±.06 ±1.01 ±1.43
CQ .62 .68 .77 19.76 101.04 ±.06 ±.05 +.04 ±1.36 ±1.92
NOVEMBER, 1919
IQ AQ VQ RQ S.D. M
IQ 19.12 105.15 ±1.32 ±1.86
AQ .46 14.08 102.90 ±.08 ±0.97 ±1.37
VQ .86 .23 17.07 109.17 ±.03 ±.09 ±1.18 ±1.66
RQ .65 .56 .71 13.91 101.42 ±.06 ±.07 ±.05 ±0.96 ±1.35
CQ .79 .47 .83 .82 17.53 105.21 ±.04 ±.08 ±.03 ±.03 ±1.21 ±1.71
JUNE, 1920
IQ AQ VQ RQ S.D. M
IQ 19.12 105.15 ±1.32 ±1.86
AQ .73 14.10 101.79 ±.05 ±0.97 ±1.37
VQ .81 .60 18.89 108.94 ±.03 ±.06 ±1.30 ±1.84
RQ .79 .68 .87 16.43 104.94 ±.04 ±.05 ±.02 ±1.13 ±1.60
CQ .84 .77 .78 .84 15.87 108.08 ±.03 ±.04 ±.04 ±.03 ±1.09 ±1.54
TABLE 4
RELIABILITY COEFFICIENTS
One Form Two Forms One Form Two Forms of Each of Each with an with an Test Test (by Infinite Infinite Brown’s Number Number Formula) of Forms of Forms
_r_₁₁ _r_₁₁ √_r_₁₁ √_r_₁₁
Intelligence Quotient .888 .942 (by Brown’s Formula)[13]
Arithmetic Quotient .824 .904 .908 .951
Vocabulary Quotient .820 .901 .906 .949
Reading Quotient .866 .928 .931 .963
Completion Quotient .883 .938 .940 .968
Limits of the r’s = ∜(_r_₁₁ × _r_₂₂)
Nov. 1918, June and Nov. 1919 June 1920 IQ and AQ .925 .946 IQ and VQ .924 .946 IQ and RQ .936 .953 IQ and CQ .941 .955
The limits of the June, 1920 r’s are naturally somewhat larger than the others since two forms of tests (except the Binet) were used; the unreliability of the quantitative indices is therefore lower and hence the correlation with IQ may be larger.
The correlations in 1920 of another group—the whole school except Grade III—are reproduced in Table 5. Grade III was excluded since here there had as yet been little chance to push the r’s. Partials were obtained with these data (Table 6). Little faith may be placed in the relative sizes of these partials, much because the _r__{VQ.RQ} is here only .73 and, in the data presented in Table 3, it is .87. This is due to the fact that the data in Table 3 cover all periods (2 years) while those in Table 5 cover only one. This difference has comparatively slight influence on our general conclusions; but it makes a huge difference in the correlation of RQ and VQ when IQ is rendered constant, whether the one or the other set of data is used. Moreover, the whole logic of arguing for general factors by reduction of partial correlations from the original r has been called gravely into question in Godfrey H. Thomson’s recent work on this subject: “The Proof or Disproof of the Existence of General Ability.” Thomson shows that partial correlation gives one possible interpretation of the facts, but not an inevitable one. Thus we cannot say that because RQ and IQ and RQ and AQ are highly correlated, correlation of IQ and AQ is dependent upon RQ. We can say, however, that it is likely to be. IQ and AQ may be correlated by reason of inclusion of some element not included at all in RQ. The higher the correlations which we deal with the less we need worry about this, and of course correlations of unity exclude any such consideration.
TABLE 5
INTERCORRELATION OF ALL QUOTIENTS IN JUNE, 1920. ALL CHILDREN EXCLUSIVE OF GRADE 3 ARE HERE REPRESENTED
The P.E.’s are all less than .05
N = 81
Arithmetic Vocabulary Reading
IQ Quotient Quotient Quotient
Arithmetic Quotient .733
Vocabulary Quotient .837 .628
Reading Quotient .758 .694 .734
Completion Quotient .821 .770 .825 .801
I therefore draw no conclusions from the comparative size of these partials, nor do I get partials with any of the other data, and rest the case mainly on the high r’s between IQ and SQ’s in 1920; increase in correspondence of the central tendencies and range of the SQ’s by grade with the central tendency and range of the IQ’s of the same data; small intercorrelation of SR’s and negative correlation of AccR with IQ.
The general lowness of the partials (Table 6) does, however, indicate the great causative relation between IQ and disparity of product. The elements still in here are common elements in the tests and the mistreatment of intelligence.
TABLE 6
PARTIAL CORRELATIONS OF QUOTIENTS IRRESPECTIVE OF INTELLIGENCE QUOTIENTS
N = 81
Arithmetic Vocabulary Reading
Quotient Quotient Quotient
Vocabulary Quotient .04
±.07
Reading Quotient .31 .28
±.07 ±.07
Completion Quotient .43 .44 .47 ±.08 ±.06 ±.06
What happened by grade in 1918-1919 is summarized in Table 7. What happened by grade in 1919-1920 is summarized in Table 8. Since there were many changes in personnel from 1918-1919 to 1919-1920, we need expect no continuity from Table 7 to Table 8. For the continuous influence of the two years, see Table 3, which includes 48 children taking all tests at all periods.
TABLE 7
ALL CORRELATIONS, MEANS, AND STANDARD DEVIATIONS BY GRADE, SHOWING PROGRESS FROM NOVEMBER, 1918 TO JUNE, 1919
I stands for Intelligence Quotient
V stands for Vocabulary Quotient
R stands for Reading Quotient
C stands for Completion Quotient
GRADE r M S.D.
Nov. June Nov. June Nov. June
I V .467 .633 I 109.89 113.20 I 12.83 15.49 ±.12 ±.07 ±1.98 ±1.91 ±1.40 ±1.35
III I R .541 .492 V 96.11 109.90 V 21.21 18.69 ±.11 ±.09 ±3.28 ±2.30 ±2.32 ±1.63
I C .641 .386 R 82.26 101.40 R 22.58 15.85 ±.09 ±.11 ±3.49 ±1.95 ±2.47 ±1.38
C 86.89 108.40 C 22.76 15.79
±3.52 ±1.94 ±2.49 ±1.37
N = 19 30 -----------------------------------------------------------------
I V .724 .819 I 105.90 104.82 I 18.08 18.21 ±.07 ±.05 ±2.73 ±2.98 ±1.93 ±2.11
IV I R .665 .845 V 97.20 108.53 V 17.26 24.92 ±.08 ±.05 ±2.60 ±4.08 ±1.84 ±2.88
I C .596 .717 R 91.06 107.82 R 27.85 10.35 ±.10 ±.08 ±4.20 ±1.69 ±2.97 ±1.20
C 101.45 108.12 C 21.53 17.75
±3.25 ±2.90 ±2.30 ±2.05
N = 20 17 -----------------------------------------------------------------
I V .887 .822 I 101.64 99.42 I 24.76 17.63 ±.04 ±.05 ±3.56 ±2.73 ±2.52 ±1.93
V I R .799 .832 V 100.59 111.58 V 26.71 19.78 ±.05 ±.05 ±3.84 ±3.06 ±2.72 ±2.16
I C .818 .890 R 94.59 101.42 R 22.10 12.56 ±.05 ±.03 ±3.18 ±1.94 ±2.25 ±1.37
C 97.00 102.68 C 22.52 17.71
±3.24 ±2.74 ±2.29 ±1.94
N = 22 19 ----------------------------------------------------------------- I V .793 .772 I 109.90 115.90 I 23.45 24.38 ±.08 ±.09 ±5.00 ±5.20 ±3.54 ±3.68
VI I R .497 .726 V 108.00 126.80 V 30.20 25.25 ±.16 ±.10 ±6.44 ±5.39 ±4.55 ±3.81
I C .798 .891 R 103.10 107.20 R 13.77 20.62 ±.08 ±.04 ±2.94 ±4.40 ±2.08 ±3.11
C 108.90 117.10 C 15.23 18.81
±3.25 ±4.01 ±2.30 ±2.84
N = 10 10 ----------------------------------------------------------------- I V .625 .504 I 99.29 98.92 I 11.11 11.45 ±.11 ±.14 ±2.00 ±2.14 ±1.42 ±1.51
VII I R .622 .709 V 109.43 115.23 V 14.07 17.43 and ±.11 ±.09 ±2.54 ±2.95 ±1.79 ±2.31 VIII I C .782 .730 R 97.00 98.85 R 12.59 15.77 ±.07 ±.09 ±2.27 ±3.26 ±1.61 ±2.09
C 102.43 95.85 C 13.49 17.72
±2.43 ±3.31 ±1.72 ±2.34
N = 14 13 ----------------------------------------------------------------- I V .685 .680 I 105.07 106.88 I 19.34 18.45 ±.04 ±.04 ±1.41 ±1.32 ±1.00 ±0.93
I R .568 .626 V 101.12 112.67 V 22.83 21.58 TOTAL ±.05 ±.04 ±1.67 ±1.54 ±1.18 ±1.09
I C .639 .702 R 92.40 102.91 R 22.65 15.27 ±.04 ±.04 ±1.66 ±1.09 ±1.17 ±0.77