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 12² and 10⁴ and feeble-mindedness not to extend above the limit 11². In other words, none of our cases testing 11³ or over was found, with the aid of other confirmatory data, to be mentally defective. None of our cases testing 10³ or below was found to be normal. Of those testing between 10⁴ and 11², 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.

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.

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.

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.

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.