(b) The Year Unit Of The Binet Scale.

A sharp disagreement of opinion as to whether the Binet year units can be regarded equivalent has arisen between Karl Pearson, Director of the Galton Laboratory in London, and certain psychologists who have used the Binet scale. Cyril Burt, for example, says, as quoted by Pearson:

“Except for rough and popular purposes, any measurement of mental capacity in terms of age is unsatisfactory.... The unit fluctuates in its significance all along the scale. When the child is just beginning to walk and talk, when he is 7 or 8, when he is 10 to 11, when he is on the verge of puberty—at these different periods a retardation of a single year means very different things” (164, p. 36).

A number of good psychologists including Yerkes, Terman, and Kuhlmann, agree with Burt in maintaining that a year of retardation at different ages has very different significance.

With this statement of Burt, Pearson takes issue, saying:

“Can the psychologist to the London County Council ever have seen the growth curves of children, or would he write thus?... There is no valid reason to suppose that a year's growth in mental power may not be taken for all practical purposes to mean the same unit for ages of 6 to 15, the period for which Binet and Jaederholm have used the tests” (164, p. 44).

Like many other apparently opposite statements both contain truth. The conflict arises apparently, first from a disagreement between the data obtained with the Jaederholm form of the scale, on which Pearson bases his statement, and data obtained with other forms of the scale; second, from a discrepancy in the points of view. Pearson stresses the fact that the mental year-marks equal average growth increment with the Jaederholm scale ([167]). He shows that the regression of years of mental excess (or deficiency) on increase of life-age is a straight line, just as he found it with physical measurements. Moreover, the standard deviation of the mental measurements for the entire group of normal school children, 6-14 years of age, was found to be about one year of mental age (.96 year for the corrected data) ([167]). To which Pearson's opponents might reply, these facts are of comparatively little significance unless the deviations for the separate ages are alike in terms of these year units on the scale. Neither linear regression nor the balancing of years of excess by years of deficiency at each age indicates that the deviations of the separate ages are alike in terms of the year units. The new Stanford scale, for example, shows both of these conditions and yet the range of months of life-ages which sets off the middle 50% of the children of the different tested ages increased decidedly from 6 to 14 years of age. The middle half of the tested ages, for example, at age VI on the scale include a randomly selected group of six-year-old children whose range of life-age is ten months, at age VIII on the scale this range is 13.4 months, at X it is 16 months, at XII, 20 months, and at XIV, 26 months. “The number of 6-year-old children testing 'at age' is approximately twice as great as the number of 12-year-olds testing at age, and 50% greater than in the case of the 9-year-olds” (196, p. 557).

To this argument Pearson might reply that he had not overlooked the question of variation in the deviations from one age to the next for he has a footnote in which he states regarding the Jaederholm data: “There are, however, relatively little differences in these mental age standard-deviations of the normal children beyond what we may attribute to the effect of random sampling” (164, p. 46). In this respect, then, the Jaederholm data differ notably from Terman's data obtained with random groups with the Stanford scale and, as I shall show, from data obtained by Goddard with the 1908 Binet scale, the two largest groups of Binet test data which have been collected. Even with the Jaederholm data on efficient school children, although the largest difference between the standard deviations of different age groups is only about twice its probable error, it is notable that 24 of his 39 7-year-olds are included within an interval of the middle year of tested age, while only 9 of his 35 11-year-olds are included within the same middle year interval.

Taking Goddard's data for the 1908 scale for the separate ages from 5-11 at which probably the factor of selection for his groups may be neglected, I have calculated the standard deviations from his Table I and find them as follows:

Life-Ages
567891011
Standard deviations in Mental Excess or Deficiency1.10.98.93.991.041.231.19