Reasons to express I.Q. with a standard deviation of 15

© 2003-2013 Paul Cooijmans

Scores on high-range I.Q. tests have in the past often been reported on a scale with a standard deviation (S.D.) of 16. This was inspired by the Stanford-Binet, a childhood test. There are, however, a number of reasons to prefer a scale with an S.D. of 15, similar to the Wechsler Adult Intelligence Scale (WAIS):

To further explain the last point: Originally the Stanford-Binet I.Q.'s were obtained by dividing the subject's mental age by the subject's chronological age and multiplying by 100. These ratio I.Q.'s had a standard deviation of about 12 in the first version of the test, and in later versions went up to about 16. The distribution however was not "normal"; in the "gifted" range scores were way over-represented, the very highest scores even behaving more in accordance with a standard deviation of 24 or thereabout, had the distribution been "normal". Studies of the distribution of these scores have shown that for instance a ratio I.Q. of 160 only corresponds to about 150 in a normal distribution with S.D. = 16, and I.Q. 170 corresponds to about 156 in a true normal distribution. A later version of the Stanford-Binet, Revision IV of 1986, has dropped the concept of mental age, and expresses the I.Q.'s directly on a scale with S.D. = 16 (such I.Q.'s are called "deviation I.Q.'s"). As a result, I.Q.'s in the "gifted" range are markedly lower than in the past. An again later version of the Stanford-Binet has even adopted an S.D. of 15, as recommended in the present article.

As the general public is mostly not well informed in these matters, there is much confusion of ratio I.Q.'s and deviation I.Q.'s in popular talk about I.Q. Astronomic ratio I.Q.'s are often quoted in relation to famous persons, without realization that these can not be compared to adult deviation I.Q.'s. There are in fact even quite a few "high-I.Q." societies who accept Stanford-Binet scores by the same norm as deviation scores, apparently not realizing they are thus selecting far below their intended level.

The WAIS has from the start on used deviation I.Q.'s, so there is never confusion with ratio I.Q.'s and over-representation of high scores. If high-range tests are supposed to extend the range of regular tests upward, the 15-scale is the most appropriate.