Chapter V: Adapting the Percentage Definition to the Binet Scale (2)

When we turn to data from randomly selected groups for judging the borderlines with other developmental scales than the 1908 Binet, we find that a group of children in the rural schools of Porter County, Indiana, have been examined with the Goddard adaptation of the Binet 1911 scale (_92_) and a group of school children in a Minnesota city, with the Kuhlmann adaptation of the 1911 scale (_138_). The important results with each study are given in Table VI. In the Indiana study the children were examined through the eighth grade. The elimination of older children from school would certainly affect the groups over 13 years of age and probably disturb the results even for the 13-year olds. For this group the results are published only for nearest mental and nearest life-ages. The results are, therefore, not strictly comparable with those of Table V. for the 1908 scale. It is doubtful whether tests on children in the rural schools should be used for indicating borderlines. The table suggests, however, that the borderlines we have indicated for the 1908 scale are not too conservative for the immature tested with the 1911 scale. It is possible, however, that with Goddard's adaptation the break comes at 9 years of age instead of 10.

TABLE VI.

TABLE VI.—MENTAL RETARDATION OF CHILDREN AS TESTED WITH THE 1911 BINET
SCALE

_Children in the Rural Schools of Porter County, Indiana, tested with
the Goddard 1911 scale. (From Table XIII, U. S. Public Health Bulletin,
No. 77)_

───────────┬───────────┬───────────────────────────────────────────────
Nearest │ Total │Percentages showing the following years of
Life-Ages │ Pupils │tested retardation according to the nearest
│ │mental ages:
───────────┼───────────┼───────────┬───────────┬───────────┬───────────
│ │Two or more│ Three or │ Four or │ Five or
│ │ │ more │ more │ more
───────────┼───────────┼───────────┼───────────┼───────────┼───────────
6│ 107│ 2.8│ │ │
7│ 232│ 6.03│ .43│ │
8│ 234│ 8.12│ 2.12│ .42│
9│ 216│ 12.04│ 5.54│ 1.84│ .92
10│ 278│ 19.88│ 3.58│ 1.08│ .36
11│ 212│ 18.3│ 8.4│ 1.8│
12│ 243│ 33.9│ 12.9│ 2.6│
13│ 249│ 63.7│ 27.9│ 8.4│ 2.8
───────────┴───────────┴───────────┴───────────┴───────────┴───────────

_Number of Pupils Testing retarded according to Kuhlmann's revision of
the Binet 1911 scale. (From Kuhlmann's Table VIII.)_

──────────────┬──────────────┬─────────────────────────────────────────
│ │ Exact years of retardation.
──────────────┼──────────────┼─────────────┬─────────────┬─────────────
Nearest │ Total Pupils │ 1 or more │ 2 or more │ 3 or more
Life-Age │ │ │ │
──────────────┼──────────────┼─────────────┼─────────────┼─────────────
6│ 38│ 0│ 0│ 0
7│ 82│ 4│ 0│ 0
8│ 95│ 9│ 0│ 0
9│ 91│ 12│ 2│ 0
10│ 84│ 16│ 9│ 1
11│ 88│ 18│ 4│ 0
12│ 75│ 32│ 8│ 1
──────────────┴──────────────┴─────────────┴─────────────┴─────────────

Kuhlmann, with the assistance of twenty teachers whom he started in the work and whom he regards as “untrained examiners,” measured “the public school children from the first to the seventh grade, inclusive, in a Minnesota city.” The essential figures from his results are given in Table VI. These results are not directly comparable with those of Goddard using the 1908 scale, since Kuhlmann tabulates the nearest ages instead of the actual ages. His age groups would therefore average a half year younger chronologically than Goddard's. Moreover, the exact amount of retardation to tenths of a year was then calculated from the exact age, and it is to be remembered that the method of calculating the mental age was changed in 1911 so as to start with a basal age in which all tests were passed. The effect of these changes would be that some of those recorded in Kuhlmann's table as two years retarded might easily be a year more retarded under the same methods of calculation that were previously used. Using his method of computation, it is clear that the general borderline for the immature with this scale would not be as low as we have indicated for the 1908 Binet scale. It would apparently be about a year less, _i. e._, two years of retardation for those six to nine years of age, and three years retardation for those 10 or above in order to fall within our doubtful group. The 13 year old group are not included here. They would not be even approximately random since those who had reached the eighth grade or above were not examined. It is interesting to note that the break in frequency of serious retardation again occurs in the change from those chronologically 9 years of age to those 10 years of age.

The Stanford Revision and Extension of the Binet-Simon Scale (_57_) has included a percentage designation of the degrees of ability by a classification of intelligence quotients (I Q's). It is interesting to find the percentage method of setting forth the borderlines is utilized to supplement the intelligence quotients in this important revision of the Binet-Simon Scale. It shows how the method may be adapted to testing of intelligence quotients. For fixing the borderline for the immature the Stanford scale affords the best means provided by any of the revisions or adaptations of the Binet scale. The amount of data on randomly selected groups of school children, by which these borderlines were determined, is, however, less than with the 1908 Binet Scale as given by Goddard and summarized in our Table V. The Stanford Scale was standardized for the immature by testing 80 to 120 native born school children at each age from 5 to 14 inclusive, a total of 905. While the 1908 scale gives corresponding distributions for 114 to 222 children at each age from 5 to 11 inclusive, a total of 1269. Using the I Q's adopted by Dr. Terman for the Stanford Scale, the lowest 1% of the children were found to reach only an I Q of 70 or below, 2% to reach 73 or below, 5% to reach 78 or below. The author designates below 70 as “definite feeble-mindedness,” 70-80 as “borderline deficiency, sometimes classified as dullness, often as feeble-mindedness.” His “definite feeble-mindedness” thus includes somewhat fewer than our “presumably deficient” and “uncertain groups” combined. The distribution of the intelligence quotients was “found fairly symmetrical at each age from 5 to 14.” The range including the middle 50% of the I Q's, was found practically constant (_57_, p. 66). The data for the extreme cases have not been published except for ages 6, 9 and 13. For these ages 1% were 75 or below at 6 years, 2% at nine years, and 7% at 13 (_197_). The results with the extreme cases at each age are the most important factor in fixing the borderline. The combined per cent. results with I Q of 905 children at different ages, which show 0.33% testing 65 or below and 2.3% 75 or below, may be deceptive for separate ages.

It seems clear that the criterion for tested deficiency suggested by our study is more conservative than that of the Stanford scale which says:

“All who test below 70 I Q by the Stanford revision of the
Binet-Simon Scale should be considered feeble-minded, and it is an
open question whether it would not be justifiable to consider 75 I Q
as the lower limit of “normal” intelligence. Certainly a large
proportion falling between 70 and 75 can hardly be classed as other
than feeble-minded, even according to the social criterion.” (_57_,
p. 81)

In regard to the borderline for the mature with the Stanford scale it is especially important to note that at present no randomly selected mature group has been tested with this scale so that we are at a loss to know what would be a safe borderline for adults with it. It is peculiarly unsafe, it seems to me, to carry over an intelligence quotient which may shut out the lowest 1% of children who distribute normally, to the uncertain borderline of an adult group composed of thirty business men, 150 migrating unemployed, 150 adolescent delinquents and 50 high school students. By these data it would be impossible to tell what per cent. of a random group of adults would be shut out by this borderline of 70.

TABLE VII.—BORDERLINE RESULTS WITH THE POINT SCALE

The lower range of “intelligence coefficients” for the normal group of
school children and adults (226, Table III).

───────────────┬───────┬───────┬───────┬───────┬───────┬───────┬─────── Nearest Ages │ 4-5 │ 6-7 │ 8-9 │ 10-11 │ 12-13 │ 14-15 │ 18-on ───────────────┼───────┼───────┼───────┼───────┼───────┼───────┼─────── No. of Cases │ 84 │ 357 │ 196 │ 161 │ 120 │ 77 │ 284 ───────────────┼───────┼───────┼───────┼───────┼───────┼───────┼─────── Presumably │ │ Under │ │ Under │ │ │ Under deficient │ │ .61 │ │ .61 │ │ │ .61 │ │ 0.4% │ │ 0.6% │ │ │ 0.7% ───────────────┼───────┼───────┼───────┼───────┼───────┼───────┼─────── Doubtful │ Under │.61 to │ Under │.61 to │ Under │ Under │.61 to │ .51 │ .81 │ .51 │ .71 │ .51 │ .61 │ .71 ───────────────┼───────┼───────┼───────┼───────┼───────┼───────┼─────── Both │(4.8%) │ 1.5% │ 1.5% │(5.0%) │ 1.7% │ 1.3% │(6.3%) ───────────────┴───────┴───────┴───────┴───────┴───────┴───────┴───────

Pupils of Grammar School B, Cambridge, Mass. (225, Table III)

───────────────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬────── Ages │ 6 │ 7 │ 8 │ 9 │ 10 │ 11 │ 12 │ 13 ───────────────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼────── No. of Pupils │ 71 │ 73 │ 61 │ 71 │ 76 │ 79 │ 60 │ 52 ───────────────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼────── Per Cent of │ 1.4 │ 1.4 │ 1.5 │ 2.7 │ 1.3 │ 1.3 │ 1.7 │ 2.0 Pupils at │ │ │ │ │ │ │ │ and Below │ 11 │ 14 │ 15 │ 21 │ 35 │ 40 │ 33 │ 38 Points │ │ │ │ │ │ │ │ ───────────────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────

For the Point Scale for Measuring Mental Ability, prepared by Yerkes, Bridges and Hardwick, we have two sets of data which give the only empirical basis for estimating the percentage borderlines for the various ages (_225_, _226_). These data are restated in terms of percents in Table VII. The first part of the table shows the borderline results with the normal group composed of 829 pupils of the Cambridge schools, 166 pupils of Iowa schools, 237 in the group of Cincinnati 18-year-old working girls and an adult Massachusetts group of 50. The table illustrates how difficult it is to find a common borderline in terms of a ratio, in this case the “coefficient of intelligence,” for a series of life-ages. It certainly seems hazardous to attempt to smooth these empirical borderlines for the different ages by accepting, on the present evidence, the suggestion of the authors that a coefficient of .50 or less at any of these ages indicates the individual is “dependent” and coefficients from .51-70 that he is “inferior,” since the data show the lowest group would include only the lowest 0.04% of 18 years of age and over, while it includes 4.8% of those in their table four and five years of age. Indeed, the authors note that “a few months' difference in age will alter the coefficient of a five or six year old child by ten to thirty per cent.” Under such circumstances it would be better for the present to use the empirical basis suggested from the data of Table VII rather than to attempt to use a uniform borderline coefficient for the various ages. For calculating the coefficient of a particular individual, his point scale record should presumably be divided by the revised norms published by the authors, which are as follows for the nearest life-ages, reading the dots on their graph: 4 yrs. 15 points, 5 yrs. 22, 6 yrs. 28, 7 yrs. 35, 8 yrs. 41, 9 yrs. 50, 10 yrs. 58, 11 yrs. 64, 12 yrs. 70, 13 yrs. 74, 14 yrs. 79, 15 yrs. 81, 16 yrs. 84, 17 yrs. 86, 18 yrs. 88.

Since all the pupils in Grammar School B, who were not absent during the periods of examination, were examined, the distribution of these 675 pupils may be serviceable for obtaining a rough idea of the borderlines in terms of points at the different ages from 6-13 inclusive. These individuals “constituted the population of a city grammar school in a medium to poor region and including grades from the kindergarten to the eighth, inclusive.” On account of the small number of individuals at each age the errors are large and the limits should be used only with much caution as an indication of the general trend of the table.

All the scales, it should be noted, have been tried out on immature groups composed only of school children. These would not include those children who are so deficient as not to be sent to school. The borderlines determined with school children, therefore, tend to shut out a slightly larger percentage of all children than of school children. They would, therefore, tend to class slightly too many as deficient. Moreover, the groups tested were probably in communities which are somewhat above the average in ability so that we should be doubly cautious in using the borderlines for the immature.

(c) THE CHANGE IN INTERPRETING THE BORDERLINE FOR THE IMMATURE.

The confusion over the amount of allowable retardation in evaluating the results of Binet tests is illustrated by the variations in practise. In 1908 Binet and Simon said: “On the contrary, a retardation of two years is rare enough; ... Let us admit that every time it occurs, the question may be raised as to whether the child is subnormal, and in what category he should be placed” (_79_, p. 269). In 1911 they had become much more conservative. With their new scale they stated: “We would add that a child should not be considered defective in intelligence no matter how little he knows unless his retardation of intelligence amounts to more than two years” (_78_). This cautious statement seems to have been converted by the various translators into a rule that every child retarded three years was to be regarded deficient. Drummond, for example, in his translation says: “Should a child's mental age show a retardation of three years as compared with his chronological age, and should there be no evident explanation of this, such as ill health, neglect of school attendance, etc., he is reckoned as deficient mentally” (_77_, p. 163). Wallin, however, in 1911 kept to the original conservative statement, “children retarded less than three years should probably not be rated as feeble-minded” (_211_, p. 16).

In his book on Mentally Defective Children, before the 1908 scale had appeared, Binet had adopted the Belgian practise of making a distinction between younger and older children as to the amounts of allowable _school_ retardation before the question of mental deficiency should be raised. As a method of preliminary selection for examination he used a retardation in school position of two years when the child was under 9 years of age and three years when he had passed his ninth birthday (_77_, p. 42). This practise was carried over into the field of mental tests, and Huey then qualified these limits by the safer allowance of four and three years of tested retardation with the change still at nine years (_129_).

The German standard, formulated by Bobertag and accepted by Chotzen (_89_, p. 494), is to place the lower limit for the normal as less than three years retardation at ten years of age or less than two years retardation under that age. The change in the amount of retardation allowed came at the same position we advocated instead of at 9 as was earlier suggested.

The early practise in the United States was merely to regard three years retardation as the sign of feeble-mindedness. This custom was even followed in 1914 for all under 16 years of age by Mrs. Streeter in the investigation by the New Hampshire Children's Commission of Institutions in that state. She did not call any feeble-minded who tested over XII (_40_, p. 79). In both the 1908 and 1911 editions of the Binet scale issued by Goddard, he stated that if a child “is more than three years backward he is mentally defective,” giving no caution about a borderline for the mature. This is a practise which has been followed so far as the immature are concerned, by Goddard's students generally. Kuhlmann carefully avoids the statement of a borderline with both his 1908 and 1911 adaptations of the Binet scale, but he has since advocated using an intelligence quotient of less than .75 with his 1911 scale to indicate feeble-mindedness and leaving a doubtful area from .75 to .80 (_140_). Stern suggested a borderline of .80 with the intelligence quotient (_188_). Even a quotient of .75 would call a child feeble-minded by Kuhlmann's 1911 scale if he tested two years retarded at eight and three years retarded at twelve. Haines suggests using, with caution, a borderline with a modified Point Scale which should be at 75% of the average performance measured in points at each age for individuals over thirteen years, and four years retardation for 13 years and younger (_26_).

Pintner and Paterson collected in one table the test results with the Binet scale published by thirteen different investigators and covering 4,429 children tested (_44_, p. 49). They do not attempt to readjust these results so as to allow for the very great differences in the methods by which the different groups were chosen to be tested or the different uses of actual life-age and nearest life-age. Such a table is, as they recognize, too hazardous to use for determining the borderlines of deficiency. There might be an average difference of at least a year in the mental ages obtained by different investigators when no allowance is made for their different procedures. Nevertheless, it is interesting to note that a mental quotient of .75 is less conservative than the lowest 3% which is the borderline of feeble-mindedness that they suggest. The lowest 3% they find would include, for example, those who were 1.5 years or more retarded at age 5, 2.1 years retarded at 9 and 2.8 years at age 10.

The most important confirmation of the claim that a borderline for the immature should require at least 4 years retardation comes from the Galton biometric laboratory in London. Karl Pearson has furnished a careful statistical treatment of Jaederholm's results in testing all the 301 children in special classes in Stockholm compared with 261 normal children in the same schools. Pearson found that the modified 1911 Binet scale which Jaederholm used could be corrected so that the normal children at each age averaged very closely to their age norms from 7 to 14 years of age. Under these conditions of the scale he generalized on the basis of the children in the Stockholm special classes who were from 7 to 15 years of age, as follows:

“The reader may rest assured that until the mental age of a child is
something like four years in arrear of its physical age it is not
possible to dogmatically assert, on the basis of the most scientific
test yet proposed as a measure of intelligence, that it is
feeble-minded. Even then all we can say is that such a child would
be unlikely to occur once in 261 normal children, or occurs under ½%
in the normal child population.” (_167_, p. 18).

In a later paper he says that those children “from 4 to 4.5 years and beyond of mental defect could not be matched at all from 27,000 children,” on the assumption of a normal distribution fitted to the normal Stockholm school children (_164_, p. 51). He says further:

“It is a matter of purely practical convenience where the
division—if there must be an arbitrary one—between the normal and
defective child is placed; we suggest that it be placed at either 3
or 4 years of mental defect. But as mental defect increases with the
age of the mentally defective the division will be really a function
of the child's age” (_167_, p. 37).

Since he finds the children in the special classes fall further behind the normal children on the average 4 months each year of life, this means that 3 years retardation at 7 years of age would be equivalent to 4 years at 10.

In spite of uncertainty introduced by the use of quotients, the general tendency in interpretation of results with Binet scales has thus been to make a distinction in the amount of retardation signifying deficiency among younger and older children and to require four years retardation, at least for the older ages. Our criterion for the borderline of three years retardation for children under 10 years and four years for 10 years and over, with an extra year to be quite sure that the deficiency is sufficient to justify isolation, seems to be in line with the best practise at present among those who have had much experience with the Binet scale. Fortunately, little harm has been done to the individuals themselves by this uncertainty in the interpretation of the scores with the scale, since only questionable cases have been affected. These have generally been diagnosed, before disposing of the child, by some expert who understands the sources of error in mental tests. On the other hand, shifting the limit of allowable retardation by one year makes a great difference in the estimation of the frequency of feeble-mindedness in particular groups, as will be shown in our discussion of deficient delinquents.

-----

Footnote 11:

Throughout this study I shall use the literal translation of the
German term “lebensalter,” life-age, instead of the awkward
“chronological age.”

Footnote 12:

_S. E._ = √(_p._ _q._/_n_)

Footnote 13:

Tests XI were recorded as XII in the 1911 series.