CHAPTER 2. 



A GENERAL METHOD OF STATISTICAL INTERPRETATION OF THE PRINCIPAL SAMPLE. 



Section 1. — Statistical interpretation. 



The plan to tabulate on a large scale the data of intelligence examinations obtained in the 

 Army required as its complement an adequate method of interpretation. An ideal method 

 would eliminate irrelevant factors, such as differences in the technique of examination, and 

 permit direct comparison of the subgroups of the tabulated sample with respect to the intel- 

 lectual ability that is measurable by the Army tests. The problem of interpretation stated in 

 its simplest terms is to combine the results of the several different methods of testing intelli- 

 gence (i. e., different kinds of examinations) in such a way as to permit the calculation of the 

 more important statistical constants by means of which the quantitative aspects of groups are 

 ordinarily described. Otherwise stated, we require for a given group, part of which has been 

 examined by alpha, part by beta, and part by individual examination, measures of central 

 tendency and variability, which shall be independent of the proportions of the group tested 

 by each of these examinations, for only thus can we directly compare the given group with 

 another group which (for reasons wholly irrelevant to the distribution of intelligence within 

 itself) may be composed of alpha, beta, and individual cases in very different proportions. 1 



At the outset we must set up a certain limitation and we must establish some terms. We 

 are not concerned with the question of the relation of illiteracy to intelligence when we deal 

 with scores in the two group examinations, alpha and beta; for, if the final statistical constants 

 can be freed from the effect of differences in the examination technique they will also be freed 

 from the literacy factors to the extent that these are independent of intelligence. The terms 

 "illiteracy" and " intelligence " are in this connection used in the sense in which they are defined 

 by alpha and beta. "Illiteracy" is to be understood in this chapter as meaning nothing but 

 the inability to read well enough to earn a score in alpha consistent with whatever score in beta 

 the illiterate individual may be capable of earning. What is meant by "consistent with" will 

 appear later hi this chapter. By "intelligence" we mean the ability that manifests itself 

 quantitatively in a set of consistent scores in all of the types of examination upon which our 

 data are based. 



The problem of combining the data obtained from the different examinations demands 

 the discovery of some sort of "common denominator." Our definition of intelligence • immedi- 

 ately suggests the nature of the most probably valid "common denominator," viz, a composite 

 scale formed by pooling the alpha, beta, and individual examinations. Thus, if an individual 

 has actually taken all the different examinations we consider his best rating to be given by the 

 sum of all his scores. Lacking an "outside criterion" of intelligence we are unable to determine 

 the relative weights to be assigned to scores in the different types of tests and we therefore 

 adopt the simplest policy, that of adding them together unweighted. 



As a matter of fact, however, almost no individual was given all forms of examination, 

 except in the case of a small special group (Group X) described in this volume, Chap. I, sec. 2. 

 Therefore in order to rate all individuals on a scale which is based upon all examinations, it will 

 be necessary in most cases to calculate from the earned score hi some one examination probable 

 scores in the remaining examinations and add these calculated scores to the earned scores. 

 Such procedure would require all the possible regression equations connecting the different 

 variables (scores in different examinations) and would be a simple treatment of the data, or 

 not, according to the degree of difficulty experienced in obtaining satisfactory regression equa- 



1 Prof. Raymond Pearl kindly advised the Section of Psychology concerning the treatment of results. 



! No attempt is made here to give a novel definition of intelligence; but clearly a definition of intelligence in terms other than those in which 

 our data are given would be useless. We therefore propose to avoid circumlocution by using the word "intelligence" to refer to the ability that 

 has actually been measured, without concerning ourselves about the theoretical problem of what types of potentiality for reaction may be properly 

 included under the term "intelligence" in its technical sense. 



573 



