Chapter V: Adapting the Percentage Definition to the Binet Scale (1)

Sufficiently large random groups have not been tested with any development scale to make the determination of the borderline on the scale more than tentative. Such borderlines must be looked upon as temporary descriptions to be used in aiding diagnosis until more data are available. Nevertheless, the percentage method of procedure seems to be an improvement over other plans of stating the borderline. So far as the Binet 1908 scale is concerned, when we supplement Goddard's results with 1500 school children by the data for the lower limits of a random group of 653 15-year-olds which we tested, the limits on the scale for passable intellects defined by the percentage method will be found, I believe, not only more conservative, but more reliable than those in current use. Moreover the intended meaning of such borders becomes clear.

A. THE BORDER REGION FOR THE MATURE.

(a) INDICATION FROM A RANDOM GROUP.

The passing limit for adults is unquestionably much more important than that for children since any child who once passes this limit is assured, generally speaking, of social fitness so far as intellect is concerned. He has attained a position intellectually which is sufficiently good to enable him to get along without social assistance unless he is especially deficient in will. This borderline for the mature has been so thoroughly neglected that in none of the common published forms of the Binet scale, except the new Stanford Scale, is there an attempt to define it. This seems almost incredible in view of the general use of the Binet method in diagnosing feeble-mindedness. To be sure, there are discussions of this upper limit, as we shall see, but they have usually not been embodied in the actual directions accompanying the scales which get into the hands of amateurs. Most of these directions content themselves with describing borderlines for children with no caution about the final lower limit for social survival.

The borderline for the mature is the first difficulty which a court examiner will encounter when he attempts to obtain assistance from an objective system of measurement. Very little experience will convince one that it is not enough to describe the deficient ability of an adult in terms of years of retardation. It is widely agreed that at some age during adolescence practically all the mental processes are available that will be found in the mature. From that time the advance in ability is made by attaining greater skill in specific activities through training and by increasing knowledge, rather than through a native change in the form of thinking. If mental tests mainly reach capacity for thinking, as they aim to do, rather than amount of knowledge or skill in specific work, then we are conservative in using a randomly selected group at 15 years of age for approximating the borderline on the scale for the mature.

In connection with the new Stanford Scale, Terman says: “Native intelligence, in so far as it can be measured by tests now available, appears to improve but little after the age of 15 or 16 years. It follows that in calculating the I Q (intelligence quotient) of an adult subject, it will be necessary to disregard the years he has lived beyond the point where intelligence attains its final development. Although the location of this point is not exactly known, it will be sufficiently accurate for our purpose to assume its location at 16 years” (_57_, p. 140).

Yerkes and Bridges in connection with their Point Scale say, “it seems highly probable that the adult level is attained as early as the sixteenth year” (_225_, p. 64). Kuhlmann (_138_) used 15 years as the divisor in calculating the intelligence quotient of adults and Spearman thinks that the limit of native development is reached about 15 years (_184_). He says, “That mental ability reaches its full development about the period of puberty is still further evidenced by physiology. For the human brain has been shown to attain its maximum weight between the ages of 10 and 15 years” (_184_). For the last statement he quotes Vierordt. On the contrary Wallin thinks that we need more evidence for the correctness of these hypotheses before choosing a fixed age as a divisor for adults (_215_, p. 67).

We are not interested in determining a divisor for an adult intelligence quotient but in fixing a conservative borderline for the mature. Admitting that the mental capacity of those 15-year-olds at the lower limit may not be like adults, nevertheless adults would be more likely to be better than worse. Borderlines for the 15-year-olds, should, therefore, be safe for adults. Moreover, the lower limits with a truly random group of 15-year-olds would probably be more reliable than an assorted group of adults subjectively chosen from different walks in life and combined in an effort to represent a random mature group. The Stanford Scale utilizes such combination of selected adults. It seems, therefore, that we are justified in utilizing the lowest percentages of randomly selected 15-year-olds as a reasonable criterion for describing the limits for adult deficiency. Surely adults below this lower limit for 15-year-olds would have questionable intellectual capacity.

The borderline for the mature being the crucial feature of a developmental scale when used for detecting feeble-mindedness, it seemed imperative to us that some effort should be made to obtain records with a random group of older-age children or adults. Goddard's results with school children were not significant above eleven years of age since the personal examinations were confined to children in the sixth grade or below. The twelve year old group in the sixth grade clearly omits the best 12-year-olds, so that the percentage method would have no significance applied to his figures for children above 11 years of age. Moreover it was obvious that the group of _public school_ children 15 years of age or older would not give a picture of the lower end of a random group since many children drop out of school at 14. On the average those that leave are undoubtedly of lower ability than those who remain.

The most valuable data on the borderline for the mature would come from mental examinations of large random groups of adults. The impossibility of gaining the consent of adults for such examinations puts this plan out of consideration. Perhaps the next best method would be to examine all the children of 15 and 16 years of age in typical communities. It happened that we could approach this result in Minneapolis since we there had an excellent school census made from house to house covering all children under 16 years of age. The Minnesota law requires school attendance until 16 years of age unless the child has graduated from the eighth grade. Under the able direction of Mr. D. H. Holbrook of the attendance department the census of children of school age had been made with unusual care. All the children living in each elementary school district in the city were listed in a card index regardless of whether they were attending public, parochial or private schools, or had been excused from attendance for disability or for any other reason. Since we only needed to be sure to examine the lowest few per cent. of the children in ability this group of 15-year-olds could be tested by examining all those children in typical school districts in the city who had not graduated from the eighth grade. A third of the 15-year-olds were still in the eighth grade or below. Neither the compulsory attendance law nor the census would have reached the 16-year-old adequately. In most states even the 15-year-olds would have been above the compulsory school age.

There were 653 children, (322 boys,) 15 years of age living in the seven typical districts which were selected objectively for study. Among these there were 196 who had not graduated from the eighth grade. All of these latter children were examined, except one who could not be tested as she was in a hospital on account of illness. Quite a number of the children were in parochial or private schools, two were followed to the state industrial school and a number were examined at home. In order to be sure that we had not missed any institutional cases in these districts the complete list of Minneapolis children at the State School for Feeble-Minded was gone through to get any of low ability who might have been missed.

The seven districts in which the children were to be studied were chosen, with the idea of avoiding any personal bias in their selection, by taking them alphabetically by the name of the schools, except that no district was taken where the normal school attendance of the district was affected by inadequate school facilities so that children had to be transferred either to or from that district to other schools in order to meet crowded conditions. It happened fortunately that none of these schools represented extreme conditions in the city. The average percentage of children in the 69 elementary schools of the city retarded in school position below a standard of 7 years in the first grade, 8 in the second, etc., was 24.1% with a mean variation of 6.5%. The percentages retarded in the schools studied were as follows: Adams, 22.7; Bryant, 21.1; Calhoun, 21.7; Corcoran, 29.4; Douglas, 20.4; Garfield, 18.6; Greeley, 26.4.

Kuhlmann's adaptation of the 1911 scale (_135_) was used as a basis for the examinations, supplemented by the 1908 scale wherever tests had been changed so that other forms of the tests were found in either Kuhlmann's (_136_) or Goddard's (_110_) adaptations of the 1908 scale. Since test results with the 1908 scale provide the most data for describing the borderline for the immature, our plan was to use the 1908 form of a test first when the procedure had changed. The supplementary directions were arranged for each age so that the testing could proceed methodically and the results be scored under either the 1908 or 1911 scale with the least possible disturbance of each test. Over a third of the children were tested by myself. The rest were tested by three advanced students in psychology. It is a pleasure to express my thanks to these assistants, Miss Rita McMullan, Miss Lucile Newcomb and Miss Florence Wells. Besides having had brief experience in dealing with exceptional children, they practised testing under my observation until the tests could be given smoothly and I was convinced of their ability to follow directions intelligently and make full records with reasonable accuracy. The results of the tests were all carefully gone over and scored by me. So far as I can judge, the results are quite as accurate as any other published tables, although one must always consider the possible effect of errors of testing. Separate rooms were provided at the schools or homes so that the child could be alone with the examiner during the testing.

In attempting to define the borderlines on these scales we might either state the exact scale position in tenths of a year below which 0.5 and 1.5% of the cases fall, or we might merely attempt at present to state the borderlines in rounded terms of years on the scale. The latter plan is the one I have adopted for several reasons. The main reason is that I wish to emphasize that these are still rough boundaries. Besides that, however, a study of the results shows that the cases do not distribute by separate tenths of a year so that exactly these percentages could be picked off, without a questionable smoothing of the curves while the rounded years approach these limits fairly well.

It seems to me that it is best at present to be carefully conservative in describing these borderlines, so that I have chosen them from the available data at the nearest rounded age position which is reasonably sure not to catch more than these limiting percentages. Throughout the tables I have also followed the published directions for the 1908 scale in classing the person in the intellectual age group in which he finally scores all or all but one of the tests. I recognize, of course, that this is an arbitrary limit; but it is the limit fixed by the usual printed directions going with the 1908 scale, which is the only one thus far standardized for the immature on the percentage basis. For those who wish to calculate other borderlines or reconstruct the individual tests of the scale I have provided the complete data for each individual both for the 1908 and 1911 scales in Table XXI, Appendix I. The table also gives the exact ages and school grades of each child.

The summary of the results with the tests for those testing under XII is given in Table III. Life-age[11] at the last birthday and not the nearest life-age is used in the table. The children were all between their 15th and 16th birthdays. Following the directions published with the scales, the basal age for calculating the results in the table is taken as the highest at which all or all but one test are passed for the 1908 scale, and the highest at which all were passed for the 1911 scale. Two-tenths is allowed in the table for each test passed above the basal age and 0.1 for an uncertain answer. The children were tested by the long method, beginning with the mental-age group at which the child could pass all the tests and continuing to that age group in which he failed in all.

TABLE III—TEST BORDERLINES WITH RANDOMLY SELECTED MINNEAPOLIS
15-YEAR-OLDS

_Percentages of 653 living in these districts, 196 of whom had not
graduated from the eighth grade and were tested. Scored by the Kuhlmann
and Goddard 1908 Binet scale and by the Kuhlmann 1911 scale._

───────────────┬───────────────────────────┬─────────────────────────── │ 1908 Scale │ 1911 Scale ───────────────┼───────────────────────────┼─────────────────────────── Scored below │ Pass all but one in basal │ Pass all in basal age │ age │ ───────────────┼─────────────┬─────────────┼─────────────┬───────────── │ Per cent. │ Cases │ Per cent. │ Cases ───────────────┼─────────────┼─────────────┼─────────────┼───────────── IX.0 │ 0.0│ 0│ 0.0│ 0 IX.8 │ 0.2│ 1│ 0.5│ 3 X.0 │ 0.3│ 2│ 0.5│ 3 X.8 │ 1.1│ 7│ 1.2│ 8 XI.0 │ 1.2│ 8│ 2.0│ 13 XI.8 │ 10.0│ 65│ 8.1│ 53 XII.0 │ 10.4│ 68│ 13.0│ 85 XII.8 │ 23.6│ 153│ 29.1│ 190 XIII or XV │ 23.6│ 153│ 29.7│ 194 ───────────────┴─────────────┴─────────────┴─────────────┴─────────────

Thrown into percentages of the group of 653 children living in these districts, it is evident that a test score of XI raises any person above the group of intellectual deficients. The percentage that tested this low, _i. e._, under XI.8, with the 1908 scale, was 10.0 (65 cases) and this would probably be increased if those who had graduated from the eighth grade had also been tested. The percentage testing under the same position in the 1911 scale is 8.1 (53 cases). With the 1911 scale there were 32 additional cases testing XI.8 or XI.9. The table indicates that 0.2% of the 15-year-olds tested below IX.8 with the 1908 scale, and 0.5% with the 1911 scale. This defines our scale borderline for the mature who are presumably deficient as below test-age X. These positions are near enough to the lowest 0.5%. The group testing of uncertain ability, age X, (strictly speaking between IX.8 and X.7 inclusive,) includes 0.7 to 0.9%. We thus approach fairly well the rounded age positions which exclude 1.0% above the lowest 0.5%. The total number testing in presumably and uncertain groups is thus 1.1%, 7 cases out of 653, for the 1908 scale and 1.2%, 8 cases, for the 1911 scale. This is to be compared with the percentage definition that the lowest 1.5% are either presumably deficient or uncertain.

At present we are entitled to assume that adults testing below XI, _i. e._, below X.8, are so low in intellectual development that it is a question whether they have sufficient equipment to survive socially. Fine discriminations with the Binet scale are not possible with our present knowledge. So far as our information goes, if we use the percentage method of defining intellectual deficiency, we may say that adults who test X are in an uncertain group in intellectual ability, with the probability that they will require more or less social care, while those who test IX are deficient enough to need continuous care unless the evidence of the test is contradicted by other facts or is accounted for by the existence of removable handicaps.

It is perhaps not necessary to call attention to the fact that X and XI are used here merely to refer to positions on the Binet scale without regard to what per cent. of ordinary 10-and-11-year-old children attain these positions. For example, XI does not imply that most of the children of eleven years of age are above this borderline. Table IV, to be given later, suggests that hardly two-thirds of random 12-year-old children pass this position on the 1908 scale and not half of the 11-year-olds. Thorndike regarded X.8 as normal for a child of 11.6 years of age. (_200_)

So far as the determination of intellectual deficiency is concerned we should note with emphasis that placing the limit of passable intellects at XI for adults almost entirely removes the common objection to the Binet scale on account of the difficulty of the older age tests. The older age tests become of little consequence because the best of the deficient group have a chance at tests in at least two groups above those of mental age X, so that they can increase their score by passing advanced tests as they could not if they had to test XII.

As a check upon the borderline for those presumably deficient, it is important to note that the only case which tested below this borderline with the 1908 scale was a girl in the 4B grade. She tested exactly IX with each scale and was the only child in the group who was below the fifth grade in school. There can be no question that she was mentally deficient. On the other hand in the group which tested X or above there are several cases which it would be unjust in my opinion to send to an institution for the feeble-minded without some other evidence of mental weakness. Half of them, for example, are in the seventh grade. In Minneapolis this is not as significant as it might be in other cities, since pupils are rarely allowed to remain more than two years in the same grade whether they are able to carry the work of the next higher grade or not. Pupils in higher grades may not always be able to do even fifth grade work.

The evidence from the institutions for the feeble-minded indicates that less than 5% of their inmates test XI or over. Of 1266 examinations at the Minnesota School for Feeble-Minded, 3.8% (_154_); of 378 examined at Vineland, 3.2% (_113_); of 140 consecutive admissions examined by Huey at Illinois, 5.7% (_129_). To be sure, a goodly number of these inmates are not eleven years of age, but a majority of them are at least that old and many are older. Of 280 children in the Breslau _Hilfsschulen_, Chotzen (_89_) found none reaching XI, and only six who tested X. These few cases in institutions reaching XI or over may well come within our class of those feeble-minded through volitional deficiency.

Goddard's description of the children at the Vineland school for feeble-minded who tested XI with the 1908 scale hardly sounds like an account of social deficiency. He says:

“In the eleven year old group we find only five individuals, but
they are children who, for example, can care for the supervisor's
room entirely, can take care of animals entirely satisfactorily, and
who require little or no supervision. They are, it is true, not
quite as expert or trustworthy as those a year older, and yet the
difference is very little and the two ages can probably be very well
classed together” (_113_).

The studies of groups are more important for fixing our general rules than individual examples. We must always expect to find exceptional cases where the brief intellectual tests given in an hour or less are not adequate, especially if the testing has been interfered with by the person's emotional condition at the time or by deliberate deception. A number of illustrations have been reported of successful adults who have tested X under careful examinations. Such, for example, are three cases of successful farmers tested by Wallin (_215_) and a normal school student tested by Weidensall (_59_). There are two examples of persons testing IX with the Binet scale and yet earning a living. Such is the case related by Dr. Glueck of the Italian immigrant making two trips to this country to accumulate wealth for his family by his labor (_109_), and the case of the boy reported by Miss Schmidt (_179_). These cases should make us cautious, but they are so rare that it seems best to treat those testing IX at least as exceptions.

The group studies confirm our suggestion that a borderline of X or below will bring in for expert consideration nearly all adults who are feeble-minded from a lack of intellectual ability, while testing IX is a fairly clear indication of such serious deficiency as to justify isolation. That testing X, in the absence of other evidence of conative disturbance, places the case only in an uncertain region so far as isolation is concerned is best indicated by the fact that 1.1% to 1.4% of these 15-year-olds tested this low. We have good evidence that many in special classes, which contain only about the lowest one per cent., afterwards do float in society with or without social assistance. They cannot be presumed to require isolation, as I showed in the previous chapter. It is better to say at present that those testing X require evidence of their deficiency before isolation, except in special classes, is justified. The test diagnosis alone is too uncertain, even when there are no removable handicaps.

As to the reliability of these borderlines, too much emphasis can hardly be put upon the fact that they have been determined for only a single group of 653 in a single community. They are undoubtedly not the exact borderlines, although they are the most probable percentage estimates we have at present and were obtained in a group that was as nearly unselected as it is possible to obtain. The method of selection was perfectly objective and excluded no feeble-minded children of this age living in these school districts.

The theory of sampling applied to percentages (_228_) enables us to say that the standard deviation of the true lowest 0.5% in samples of this size made under the same conditions would not be more than 0.28%.[12] That is to say, if our result were only affected by the size of our sample the chances are about two out of three that the border of the true lowest 0.5 per cent. would lie between the border of the lowest 0.22% and the lowest 0.78% of a very large sample. Assuming that the distribution in this sample represented that of communities generally, the chances would be two out of three that the true border of the lowest 0.5% for like groups in like communities examined under the same conditions would lie between IX.0 and X.6 or X.4 on the 1908 and 1911 scales respectively. Moreover, the chances that a case in the lowest 0.5% in this sample would be above the doubtful group in a larger sample, _i. e._, get above the lowest 1.5%, would be about 1 in 10,000. On the other hand, the chances that a case above the true lowest 1.5%, _i. e._, above the uncertain group, would get into the lowest 0.5% in a larger sample, _i. e._, be classed as clearly deficient intellectually, would be about 18 in 1,000.

So far as the theory of sampling goes it would seem that these borderlines for the mature are sufficiently accurate for correcting present practise. On the other hand, the conditions in Minneapolis so far as deficiency is concerned are probably better than in the country as a whole, so that the borderlines here described might very well exclude more than the lowest 0.5% and 1.5% in the country at large. But if we shifted the definition so as to exclude the lowest 0.2% and 1.1% (the percentages empirically found below the limits described), the borders on the Binet 1908 scale would not be changed from the rough measures IX and X which are as accurate as we should expect to define our limits with the present data.

(b) THE PRESENT TENDENCY AMONG EXAMINERS.

Comparing the suggestions as to the borderline for the mature which have heretofore been made, we find that they have gradually approached the boundary now suggested by the percentage method. In 1910 the American Association for the Study of the Feeble-Minded adopted a tentative classification in which the upper limit of the feeble-minded included those “whose mental development does not exceed that of a child of about twelve years” (_64_). This was based mainly on the fact that Goddard had found no case at the Vineland school for feeble-minded which tested higher than XII. Huey later than this found only two such cases at the institution at Lincoln, Ill., and Kuhlmann only ten cases at the Minnesota State School for the Feeble-Minded.

There was an early statement by Binet which referred to the practise in Belgium of regarding older school children as deficient when they were three years retarded in their school work (_77_, p. 41). This practise may have also contributed to this formulation by the American Association. Binet, however, regarded a child of the mentality of twelve as normal. In 1905, before his tests were arranged in age groups, he said:

“Lastly we have noticed that children of twelve years can mostly
reply to abstract questions. Provisionally we limit mental
development at this point. A moron shows himself by his inability to
handle verbal abstractions; he does not understand them sufficiently
to reply satisfactorily” (_76_, p. 146).

It is important to consider how the suggestion of XII as the upper limit of feeble-mindedness for adults got into the early practise in this country as the lower borderline for the mature. It is the most serious error which has marred investigations in this field. It seems to have been a case of repeated misunderstanding on the part of examiners for which nobody in particular was to blame. So far as I can determine nobody stated directly in connection with any scale what should be regarded as the lower borderline for the mature. Numerous examiners, however, in reporting their results, concluded that if the feeble-minded tested as high as XII then adults who tested XII were feeble-minded. They were somewhat encouraged in this fallacy by the fact that the 1908 scales suggested three years of retardation as an indication of feeble-mindedness, and the highest age-group of tests was soon shifted to fifteen years.

The trouble seems to have been that early workers failed to recognize that some of the feeble-minded in institutions, the purely conative cases, have passable capacity so far as the brief intellectual tests are concerned. To determine scientifically what is the borderline, we should study randomly selected groups from the general population and determine the positions on the scale below which practically all are socially unfit. Or, as Wallin has suggested, we should find out the degree of tested ability necessary for survival in simple occupations that are afforded by society (_216_, p. 224). These positions can only be checked by finding the conditions in institutions or special classes. They cannot be determined by tests of these abnormal groups alone. Besides the confusion arising from these feeble-minded who are primarily unstable or inert, but with passable intellects, reasoning from the statistics on abnormal groups merely repeats a common fallacy. The fact that some inmates of institutions test XII does not let us know how many outside the institutions who test XII actually survive in society.

The randomly selected groups of children on which Binet tried out his tests were so ridiculously small that he continually cautioned against adopting his suggestions as to borderlines as anything but tentative. For judging the borderline for the mature there were no test results which had not been seriously affected by the methods of selecting the groups, so we collected the data on this random group of Minneapolis 15-year-olds. I trust that this will make any examiner more careful about assuming that adults testing XI are clearly unable to survive socially, unless he is ready to claim that 10% of the general population are unfit socially.

It is to be noted that, taken literally, the description of the American Association is not in terms of the Binet scale, but of the mental development of a normal child of twelve years, although the framers of the resolution undoubtedly had the Binet scale of mental ages in mind. It was soon found that the tests for the older ages in the Binet 1908 scale were too difficult for the places assigned them. This is certainly true with the tests for twelve years and probably with those for eleven. This evidence is assembled in Table IV. The combined results should be used only with great caution since the methods of the investigators differed in detail and the groups were differently chosen. In the groups of children which Bobertag and Bloch and Preiss tested, there had been eliminated some of those who were backward in school, while Goddard's group did not include the best 12-year-olds.

TABLE IV.

RESULTS WITH THE BINET TESTS FOR MENTAL AGES XI AND XII
(_1908 Series_)

───────────────┬─────────────┬─────────────┬─────────────────────────── │No. of Cases │ Pass tests │ Pass tests XI or better │ │XII or better│ ───────────────┼─────────────┼─────────────┼─────────────────────────── │ Life-Age │ Life-Age │ Life-Ages ───────────────┼─────────────┼─────────────┼─────────────┬───────────── Investigators │ 12 11 │ 12 │ 11 │ 12 │ No. No. │ No. % │ No. % │ No. % ───────────────┼─────────────┼─────────────┼─────────────┼───────────── Binet and Simon│ │ │ │ (School in poor│ │ │ │ quarter) │ │ │ │ 1908 study │ 11 │ 2 18 │ │ 7 64 │ 20 │ │ 13 65 │ 1911 study │ 23 │ │ │15[13] 65 ───────────────┼─────────────┼─────────────┼─────────────┼───────────── Bloch and │ 21 │ 21 100 │ │ 21 100 Preiss │ │ │ │ (Only pupils up│ 15 │ │ 13 87 │ to grade) │ │ │ │ ───────────────┼─────────────┼─────────────┼─────────────┼───────────── Bobertag │ 33 │ 19 57 │ │ 29 88 (Pupils │ 34 │ │ 18 53 │ averaged │ │ │ │ satisfactory) │ │ │ │ ───────────────┼─────────────┼─────────────┼─────────────┼───────────── Dougherty │ 46 │ 9 20 │ │ 36 78 (Includes 8th │ 44 │ │ 22 50 │ grade) │ │ │ │ ───────────────┼─────────────┼─────────────┼─────────────┼───────────── Goddard │ 144 │ 39 27 │ │ 75 52 (Includes none │ 166 │ │ 73 44 │ above 6th │ │ │ │ grade) │ │ │ │ ───────────────┼─────────────┼─────────────┼─────────────┼───────────── Johnston │ 24 │ 6 25 │ │ ? (Includes some │ 29 │ │ 7 24 │ high school │ │ │ │ pupils) │ │ │ │ ───────────────┼─────────────┼─────────────┼─────────────┼───────────── Terman and │ 35 │ 3 9 │ │ 29 83 Childs │ │ │ │ (Includes a few│ 44 │ │ 14 32 │ in 8th grade) │ │ │ │ ───────────────┼─────────────┼─────────────┼─────────────┼───────────── Rogers and │ 20 │ 1 5 │ │ 5 25 McIntyre │ │ │ │ │ 27 │ │ 6 22 │ ───────────────┼─────────────┼─────────────┼─────────────┼───────────── Totals │ 357 379 │ 100 │ 166 │ 217? ───────────────┴─────────────┴─────────────┴─────────────┴─────────────

Binet and Simon. L'Annee Psychol., 1908, _14_: 1911, _17_: 145-200.
Bloch and Preiss. Zeits. f. angew. Psychol., 1912, _6_: 539-547.
Bobertag. Zeits. f. angew. Psychol., 1912, _6_: 495-538.
Dougherty. J. of Educ. Psychol., 1913, _4_: 338-352.
Goddard. Ped. Sem., 1911, _18_: 232-259.
Johnston. J. of Exper. Ped., 1911, _1_: 24-31.
Terman and Childs. J. of Educ. Psychol., 1912, _3_: (Feb.-May).
Rogers and McIntyre. Brit. J. of Psychol., 1914, _7_: 265-299.

Each of the studies indicated in the table, except that of Bloch and Preiss, gives evidence that the XII-year tests are too difficult for 12-year-old children. Moreover, we find that in the 1911 revision of their scale Binet and Simon advanced their 1908 XII-year tests to test-age XV and four out of the five XI-year tests to test-age XII. Passing the XII-year (1908) tests would, therefore, seem to bring a child above the upper limit of feeble-mindedness as defined even by the American Association for the Study of Feeble-mindedness, since it means more than the intelligence of a child of 12.

Goddard still adhered to this borderline of the American Association in 1914 in his work on Feeble-Mindedness. He says: “We have practically agreed to call all persons feeble-minded who do not arrive at an intelligence higher than that of the twelve year old normal child” (p. 573). In the same year Schwegler's “Teachers' Manual” for the use of the Binet scale says that a person who tests XII is a moron if mature (_180_). Since the evidence of Table IV indicates that 75% of the twelve-year-olds do not test above XI, even those who adhere to the high limit of the intelligence of a 12-year-old should have required an adult to test XI on the Binet scale in order to show deficiency.

In 1911 we find Wallin writing, regarding the 1908 tests, “it is a question whether the line of feeble-mindedness should not be drawn between eleven and twelve instead of between twelve and thirteen.... A number of our twelve-year-olds are certainly very slightly, if at all, feeble-minded” (_210_). Jennings and Hallock (_31_) and Morrow and Bridgman (_39_) in testing delinquents reported in 1911 and 1912 that they regarded those passing the tests for twelve years as socially fit. Chotzen (_31_) thinks that the two children in his group of pupils from a _Hilfsschule_ who test ten and are three years or more retarded are not feeble-minded. Davis thinks that those “showing mentality from ten to twelve years” may possibly not be called mentally defective (_133_, p. 187).

In 1915 the editors of the magazine “Ungraded” in their recommendations regarding the use of the Binet scale say “a mental age of 10 or above is not necessarily indicative of feeble-mindedness, regardless of how old the examinee may be” (_66_, p. 7). In the same year Kohs, in reporting the examinations of 335 consecutive cases at the Chicago House of Correction, says: “We find normality to range within the limits 12^2 and 10^4 and feeble-mindedness not to extend above the limit 11^2. In other words, none of our cases testing 11^3 or over was found, with the aid of other confirmatory data, to be mentally defective. None of our cases testing 10^3 or below was found to be normal. Of those testing between 10^4 and 11^2, our borderline cases, a little less than half were found normal, and somewhat more than half were found feeble-minded” (_33_). His exponents here refer to number of tests and not to tenths of a test-year. Hinckley (_182_) reports examinations with the Binet 1911 scale on 200 consecutive cases at the New York Clearing House for Mental Defectives which show that with these suspected cases, which were from 13 to 43 years of age, seven-eighths tested X or below. Referring to adults, Wallin states that he has “provisionally placed the limen somewhere between the ages of IX and X” (_215_). Dr. Mabel Fernald at the Bedford Reformatory laboratory said in 1917, “many of us for some time have been using a standard that only those who rank below ten years mentally can be called feeble-minded with certainty” (_16_). The reader should also see the admirable review and discussion of the borderlines on the Binet scale in Chap. II of Wallin's _Problems of Subnormality_. Two descriptions of the scale borderlines in books on mental testing which appeared in 1917 are of interest. In his _Clinical Studies in Feeble-Mindedness_ (p. 76), E. A. Doll says:

“By the Binet-Simon method feeble-mindedness is almost always
(probably more than 95 times in a hundred) an accurately safe
diagnosis when the person examined exhibits a mental age under 12
years with an absolute retardation of more than three years, or a
relative retardation of more than 25 per cent.”

N. J. Melville, in his _Standard Method of Testing Juvenile Mentality_ (p. 10), says:

“Conservative estimates today place the upper limit of
feeble-mindedness at least in a legal sense at Binet age ten; others
place it at Binet age eleven.... A Binet age score below eleven when
accompanied by a sub-age (retardation) of more than three years is
usually indicative of serious mental deficiency. Even when
accompanied by a slight sub-age score, a Binet age score below
eleven may be indicative of potential mental deficiency when the
test record reveals a Binet base that is six or more years below the
life age.”

In 1916 the new Stanford scale appeared and its tests are arranged so that approximately 50% of each age instead of 75%, test at age or above. Even with this lowering of the scale units, Dr. Terman describes his borderline for “definite feeble-mindedness” as below an intelligence quotient of 70. This would mean for his 16-year-old mature borderline a mental age on this scale of XI.2. We have no means of determining to what positions these points on the Stanford scale would correspond on the 1908 or 1911 Binet scales. Dr. Terman says “the adult moron would range from about 7-year to 11-year intelligence” (_57_). Apparently also referring to the Stanford scale, the physicians at the Pediatric Clinic of that university agree with this borderline and say: “morons are such high grade feeble-minded as never at any age acquire a mental age greater than 10 years” (_169_). That there is still need for more caution is evidenced by the statement of a prominent clinician in 1916 that “cases prove ultimately to be feeble-minded since they never develop beyond 12 years intelligence” (_135_).

Most interesting perhaps is the fact that Binet and Simon themselves, the collaborators who first formulated the scale for measuring intelligence by mental ages, after their years of experience with the tests came, by rule of thumb, to regard IX as the highest level reached by those testing deficient. Dr. Simon stated the borderline for the mature in this way in a paper read in England in 1914 and published the next year. He said:

“Provisionally it might be proposed to fix at 9 years the upper
level of mental debility.... We have reason to think that a
development equivalent to the normal average at 9 years of age is
the minimum below which the individual is incapable of getting along
without tutelage in the conditions of modern life. A certain number
of facts suggest this view and are mutually confirmatory. Nine years
is the intellectual level found in the lowest class of domestic
servants, in those who are just on the border of a possible
existence in economic independence; it is, on the other hand, the
highest level met with in general paralytics who come under asylum
care on account of their dementia; so long as a general paralytic,
setting aside any question of active delirious symptoms, has not
fallen below the intellectual level of 9 years, he can keep at
liberty; once he has reached that level, he ceases to be able to
live in society. And lastly, when we examine in our asylums cases of
congenital defect, brought under care for the sole reason that their
intelligence would not admit of their adapting themselves
sufficiently to the complex conditions of life, we find that amongst
the most highly developed the level of intelligence does not exceed
that of a normal child of 9 years of age” (_182_).

In connection with their 1911 revision of the scale Binet and Simon had stated that among 20 adults in a hospital where custodial care was provided for the deficient “we found that the best endowed did not surpass the normal level of nine or ten years, and in consequence our measuring scale furnished us something by which to raise before them a barrier that they could not pass” (_79_, p. 267). They, however, then expressed complete reserve as to the application of this criterion to subjects in different environments on their presumption that deficiency for the laboring class is different from that for other classes in the population.

The Germans seem to have early recognized a lower borderline for the mature than we did in this country for we find Chotzen saying in 1912 that he agreed with Binet's finding that “idiots do not rise above a mental age of three, imbeciles not over seven, and debile not over ten” (_89_, p. 494). Stern also quotes Binet as declaring that the moron does not progress beyond the mental age of nine (_188_, p. 70).

The tendency of interpretation indicated by these studies is plainly to lower the borderline for passable mature intellects until it approaches the limits which the percentage definition suggests as reasonable from our available evidence. The percentage plan thus confirms the borderline that has been approached gradually by hit or miss methods. An adult testing IX is presumed deficient, while one testing X is in an uncertain zone. The numerous studies of delinquents which have regarded adults who tested XI and even XII as deficient have seriously overestimated the problem of the deficient delinquent, as we shall see in our later chapter on tested delinquents.

B. THE BORDER REGION FOR THE IMMATURE.

(a) FOR THE BINET 1908 SCALE.

In attempting to adapt the percentage method of description to the border region for the immature, it is essential that the tests shall have been tried out on randomly selected groups. Neither teachers nor the examiner should pick out children to be tested, if we are to know much about the region of lowest intellects. While Bobertag's method of choosing typical groups by balancing those backward in school by those advanced, is serviceable for his purpose of determining norms, the personal element of choice involved makes the results thus obtained almost useless in determining the lower limit of ability.

In regard to the diagnosis of intellectual deficiency by the Binet 1908 or 1911 scales, we know much more about the interpretation of results obtained with the 1908 scale than with the 1911 scale. The 1908 scale was therefore used for our examinations of juvenile delinquents. The best available data on which to base a description of the borderline for the immature is that collected by Goddard (_119_). He says that he “arranged to test the entire school population of one complete school system. This system includes about five thousand population within a small city and as many more outside, so that we have, city and country, a school population of about two thousand children.... In the seventh and eighth grammar grades and the high school, the children were tested in groups.” Since only the first six grades were tested individually and only these results are published in sufficient detail to be available, we shall confine this account to the school children below the seventh grade. It must be remembered that any children of the idiot class and possibly some of the low imbeciles would not be included in his figures for they would probably have been excused from school attendance. In a small rural community it is not likely that these would be numerous enough to change the rough borderline materially. We thus have a fairly random group for a small town and its environs.

Since we cannot use Goddard's results for our purpose above the sixth grade, it is plain that we would not sufficiently approach a random distribution for any age above 11 years. In Minneapolis, for example, a recent census showed 28% of the public school children 12 years of age are in the seventh grade or above, while 6% of the better eleven-year-olds would be excluded by including only those below the seventh grade. We have therefore omitted from our calculations all of Goddard's results for children above eleven years of age as too unreliable for purposes of percentage estimations. Even his eleven-year-olds may be affected.

Although it is not clear in the published reports whether the nearest or last birthday was used, Dr. Goddard has informed me that his table shows the results for ages at the last birthday. A child is regarded as six until he has reached his seventh birthday, as is customary. Throughout this book I have followed this method of using age to mean age at last birthday, or _avowed age_. This is in conformity with the common use of age and with general anthropometric practise. It is less confusing and less subject to mistake or errors of record. On the whole, I believe that in statistical work avowed age is preferable to nearest age.

TABLE V.

PERCENTAGES OF MENTALLY RETARDED CHILDREN TESTED WITH THE 1908 BINET
SCALE. (_From Goddard's Table._)

───────────┬───────────┬───────────────────────────────────────────────
│ │ Years Retarded
───────────┼───────────┼───────────╥───────────┬───────────┬───────────
Life-Age │ No. of │Two or more║ Three or │ Four or │ Five or
│ cases │ ║ more │ more │ more
───────────┼───────────┼───────────╫───────────┼───────────┼───────────
5│ 114│ 5.3║ 1.8│ ...│ ...
6│ 160│ 2.5║ 0.6│ 0.6│ ...
7│ 197│ 5.6║ 1.5│ 0.5│ 0.0
8│ 209│ 2.4║ 1.9│ 1.0│ 0.0
9│ 201│ 1.3║ 0.0│ 0.0│ 0.0
│ │ ╟═══════════╢ │
10│ 222│ 18.9│ 8.1║ 1.4│ 0.0
11│ 166│ 25.9│ 10.8║ 3.0│ 0.6
│ ————│ │ ║ │
│ 1269│ │ ║ │
───────────┴───────────┴───────────┴───────────╨───────────┴───────────

In the accompanying Table V Goddard's results are arranged so as to show the percentages at each life-age retarded two or more, three or more, four or more, and five or more years according to the Binet 1908 scale. The heavy black line indicates the upper borderline of the doubtful group according to our interpretation. In spite of irregularities, due mainly to insufficient numbers, the trend of the table is fairly plain. The column of percentages two or more years retarded and to the left of the heavy line suggests that the break comes at ten years of age. Using our tentative criterion of 0.5% presumably deficient and the next 1.0% uncertain intellectually, the outcome of this analysis is a rather striking demonstration of the feasibility of the percentage procedure even when the groups examined at each age are only composed of about 200 cases. I have preferred to take the empirical data at the lower extreme of each age distribution instead of projecting the tail of a smoothed distribution curve for each age.

Until better data are available we have adopted in practise, as a result of the study of this table, the procedure of considering any child who is ten years of age or over as testing of doubtful capacity if he is four or more years retarded below his chronological age, three or more years retarded if he is under ten years of age. If he shows one additional year of retardation we consider, in the absence of some other explanation of his retardation, that he is presumably intellectually deficient enough to justify a recommendation of isolation. Of course no such recommendation should be made without a complete medical examination, a full knowledge of the history of the case and a checking of the record by further tests at different times when there is any suspicion that the child has not done as well as he might under other conditions.

The fact that we have no data on random groups 12, 13 and 14 years of age leaves a gap which may mean that our criterion of 5 years retardation for presumable deficiency at these ages is too small. It is possible that the shift to 6 years retardation should be made before 15 years, which is the position where our criterion for the borderline for the mature automatically makes the shift. We say a 15-year-old testing X is above the group presumably deficient as he has entered the “doubtful” adult class.

It is also to be remembered that the standard error expected from the results of samples as small as these is 0.5% when the sample is 200 and 0.7% when it is 100. The limits thus might easily shift a year. The suggested borderlines for the immature can at best be regarded only as the most likely under the meager evidence available.

Whether the borderlines for deficiency on the Binet scale should be described in terms of years of retardation is doubtful except, as in this case, for practical convenience. It is certainly only a rough indication of the borderlines. When this method has not been followed the most common practise is to use some form of Stern's “intelligence quotient.” An extended discussion of this question is reserved for Part II of this book, to which the reader is referred. It need only be said here that the percentage procedure adapts itself to either method of description. Since the designation of the limits must be very rough until we have much further information from tests upon unselected groups, we have adopted the common method of description in terms of years of retardation, since it seems to afford for the 1908 scale the simplest expression of the borderline until the tests have been much improved. It happens that the empirical results for 5 years of age and over lend themselves to designating the lowest percentages in terms of years of retardation with only a single shift at 9 years of age. An equally accurate designation by the intelligence quotient would be quite complicated if it were adapted equally well to the different life-ages.

The fact that the Binet mental ages do not signify corresponding norms at each age has been frequently pointed out (_200_). Moreover it is probable that one year of retardation on the scale means a different thing at different chronological ages. With the new Stanford form of the scale, for example, “a year of deviation at age 6 is exactly equivalent to a deviation of 18 months at age 9, and to 2 years at age 12, etc.” (_197_) when measured in terms of the deviation in ability at these ages. This variation does not interfere, however, with our use of the “years of retardation” merely as a short method for describing empirically the positions on the scale which roughly and conservatively designate the same percentages of children of low ability at various ages. Besides its convenience in this respect, there is no question but that such a description does help better than a quotient to convince the public of the seriousness of the deficiency.

A more serious theoretical objection to describing the borderline for the immature in terms of years of retardation is that, when one changes from three to four years of retardation, it is clear that a moron who tests VI at 9 years of age would be supposed to be still only VI at 10 years in order to remain below the borderline, while it is known that there is some, albeit a small, amount of progress made by the higher class deficients at these ages. In the crude state in which the Binet scale still remains, however, we have preferred to waive these theoretical objections in favor of the prevalent custom which has the advantages of simplicity, practical convenience, popular significance and, in this case, equal accuracy.

It is, of course, very desirable that the results obtained by Goddard as well as our Minneapolis results should be checked by data on unselected groups elsewhere. With the 1908 scale the only other data which seems fairly to represent a random selection are those of Terman and Child's (_195_, p. 69). Since they examined less than 50 at any age, however, their table helps only to check roughly the borderline suggested. The percentages retarded two years or more changed to the basis of calculation we used, indicate that the break comes at 10 years. The percentages from six up to ten years run 0, 3, 7, 6, when they change to 12% or more for the following ages. While the groups are too small to indicate the borderlines for each age, yet, when we group the children from 6-9 years inclusive, under our interpretation we find that a year less than our upper borderline for the uncertain group would give 4.8% of 147 cases. With 142 cases in the group 10, 11, and 12 years old, 5.6% would be caught by placing the borderline for the doubtful a year less than we have indicated. Our scale borderlines are thus in harmony with these data.

(b) DATA FOR OTHER DEVELOPMENTAL SCALES.