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The puzzles which this average child among a hundred Californian children of the same age about the year 1913 could answer are the yardstick by which "mental age" is measured in what is known as the Stanford Revision of the Binet-Simon Scale. Each correct answer gives a credit of two months' mental age. So if a child of seven can answer all tests up to the seven-year-old tests perfectly, and cannot answer any of the eight-year-old tests, his total score is seven years. He is said to test "at age," and his "intelligence quotient" or "I. Q." is unity or 100 percent. Anybody's I. Q. can be figured, therefore, by dividing his mental age by his actual age. A child of five who tests at four years' mental age has an I. Q. of 80 (4/5 = .80). A child of five who tests at six years' mental age has an I. Q, of 120 (6/5 = 120).

The aspect of all this which matters is that "mental age" is simply the average performance with certain rather arbitrary problems. The thing to keep in mind is that all the talk about "a mental age of fourteen" goes back to the performance of eighty-two California school children in 1913-14. Their success and failures on the days they happened to be tested have become embalmed and consecrated as the measure of human intelligence. By means of that measure writers like Mr. Stoddard fix the relative values of all the peoples of the earth and of all social classes within the nations. They don't know they are doing this, however, because Mr. Stoddard at least is quite plainly taking everything at second hand.

However, I am willing for just a moment: to grant that Mr. Terman in California has worked out a test for the different ages of a growing child. But I insist that anyone who uses the words "mental age" should remember that Mr. Terman reached his test by seeing what the average child of an age group could do. If his group is too small or is untypical his test is in the same measure inaccurate.

Remembering this, we come to the army tests. Here we are dealing at once with men all of whom are over the age of the mental scale. For the Stanford-Binet scale ends at "sixteen years." It assumes that intelligence stops developing at sixteen and everybody sixteen and over is therefore treated as "adult" or as "superior adult." Now the adult Stanford-Binet tests were "standardized chiefly on the basis of results from 400 adults" (Terman p. 13) "of moderate success and of very limited educational advantages" and also thirty-two high school pupils from sixteen to twenty years of age. Among these adults those who tested close together have the honor of being considered the standard of average adult intelligence.

Before the army tests came along, when anyone talked about the average adult he was talking about a few hundred Californians. The army tested about 1,700,000 adult men. But it did not use the Binet system of scoring by mental ages. It scored by a system of points which we need not stop to describe. Naturally enough everyone interested in mental testing wanted to know whether the army tests agreed in any way with the Stanford-Binet mental age standard. So by another process, which need also not be described, the results of the army tests were translated into Binet terms. The result of this translation is the table which has so badly misled poor Mr. Stoddard. This table showed that the average of the army did not agree at all with the average of Mr. Terman's Californians. There were then two things to do. One was to say that the average intelligence of 1,700,000 men was a more representative average than that of four hundred men. The other was to pin your faith to the four hundred men and insist they gave the true average.

Mr. Stoddard chose the average of four hundred rather than the average of 1,700,000 because he was in such haste to write his own book that he never reached page 785 of Psychological Examining in the United States Army, the volume of the data edited by Major Yerkes. (1) He would have found there a clear warning against the blunder he was about to commit, the blunder of treating the average of a small number of instances as more valid than the average of a large number.