Return to Chicago
It was in the summer of 1924 that Thelma Gwinn and I were married and we returned to Chicago where I had been appointed an associate professor of psychology. (At that time, and several years later, we had the opportunity to go to Berkeley, California.) Both Thelma and I had been graduate students at Chicago and we were thrilled to return there. Since I had been teaching statistics at Carnegie, I volunteered to give such a course at Chicago. Professor Carr was willing for students in psychology to take a one-quarter course in descriptive statistics if they wanted it. Although this course was a novelty in the department at Chicago, it was not important
(304) work. My main attention went to the teaching of mental test theory. In all of the American colleges this subject was taught mainly from the various authors' manuals, and practically all such courses were confined to detail of the Stanford-Binet test. Neither instructors nor students seemed to have any interest in the theory of this subject, and this circumstance was probably responsible for the low prestige of mental test work. I decided to make some contribution toward improving this situation, and I now had the definite objective to start work on fundamental problems in psychological measurement. Most of my previous work had been concerned with descriptive and applied aspects of psychological measurement.
There was general discussion about the normality of the distribution of intelligence at point age and I investigated the application of this assumption to various educational scales that had been constructed. In the early educational scales it was assumed, in effect, that the distribution of any educational test was the same for young children as for educated adults and that they differed only in the mean. Turning to the description of general intelligence, I assumed two parameters for each age-group, namely, the mean and a measure of dispersion. Applying this idea, a scaling method for psychological tests was developed and this was my first paper on the theory of psychological measurement.[5]I regard that paper as one of my best.
The next problem was to examine the mental-age concept which had previously been criticized by Otis and others. In another paper[6]I described the logical difficulties of the mental-age concept. In scoring the test performance of a child there is always some uncertainty as to whether the child is failing in a test item or whether he is merely distracted. In an attempt to minimize this source of error in the total score, I wrote a paper proposing that the score should be a scale value which is exceeded by as many successes as there are failures below it.[7]Interesting things are often discovered accidentally. At one time I asked my research assistant, Annette McBroom (Wiley), to plot two curves for some psychological test data, namely, the relations between mean-test performance against age and the dispersion against age. Both of these were determined first by scaling. Although I had not asked for it, she also plotted the relation between the mean-test performance and the standard deviation for each age after these values had been obtained by scaling. I then noticed that the relation was linear for the successive ages. Capitalizing on this simple relation, I located a rational origin for the scale of intelligence. This was done by extrapolating the linear relation until it reached a base line of zero dispersion. I reasoned that if we locate a point on a scale at which variability of test performance vanishes,
(305) then such a point ought to represent a rational origin because the dispersion cannot be negative. This idea is perhaps remotely analogous to some ideas in the kinetic theory of gases. I tried this procedure on a number of psychological tests that had been scaled, and I found that the age at which the rational origin is located turns out to be several months before birth. My neurological friends assured me that such a finding could be justified and a paper on this subject was published in 1928.[8]Next we turned attention to the problem of the mental growth curve. The special difficulty with this problem, in contrast with similar curves for physical growth, is that in psychology we had no metric for appraising intelligence. Since the scaling method provides such a metric and a test for its internal consistency, we decided to construct a mental growth curve by a scaling method and with a method of locating a rational origin. That material was published in 1929.[9]