In industrial acceptance sampling one frequently makes use of operating characteristic curves to describe the discriminating power of a particular sampling plan. Similarly, it is possible to demonstrate the selective efficiency of a test battery in terms of (a) the Applicant's Operating Characteristic (A.O.C.); (b) the Selector's Operating Characteristic (S.O.C.). The A.O.C. determines the chance of selection by means of a test for any given level of true ability. The S.O.C. connects functionally probability of success on the criterion with the predictor scores of a battery. For the case of a normal bivariate distribution the exact mathematical expressions of the OC curves are derived in terms of the correlation coefficient ρ, the cut-off points α and β, and the predictor and criterion scores X and Y (in standard measures). The Efficiency Index H is defined as the percentage of successful subjects gained by the use of a test battery, taking chance selection as a yardstick for comparison. Its optimum, for fixed ρ and α, is derived. The distribution law of the criterion scores of selectees is deduced and its first four moments are shown to depart little from normality for cases usually encountered in practice. A “Quality-Gainae” diagram graphically illustrates the improvements secured. Another simple device, the “Cost-Utility” diagram, explains to management the full implications of selecting personnel by means of a test battery. Neither of the diagrams requires an understanding of the correlation coefficient. The confidence belt of the OC curves, the standard error of the mean criterion score of selectees and the standard error of the predicted number of successful applicants are determined. Finally, the full theory is applied in detail to a real test battery.

A rapid method is described for machine computation of biserial correlations in item analysis with several criteria. This method has been found to yield biserial correlations from punched IBM cards at the rate of about 41 per hour.

A factor analysis was made of 39 experimental printed aptitude tests and seven reference tests selected from the Army Air Forces Aircrew Classification Battery. Thirteen factors were extracted and two independent orthogonal rotational solutions were completed. Twelve factors were interpreted. Of these, seven were clearly identifiable with previously known factors: numerical, perceptual-speed, spatial-relations, visualization, visual-memory, paired-associates-memory, and length-estimation factors. A planning factor was not as clearly identifiable. A reasoning factor was probably a composite of two or more factors that failed to separate. A new factor possibly has to do with orientation with respect to the points of the compass. Two factors were doublets, each apparently specific to one kind of test. Better conceptions were gained of the spatial-relations and visualization factors and of the kinds of tests that measure them best. Efforts to improve measures of unique factors were not uniformly successful. The attempt to duplicate a psychomotor test rather directly by analogy in printed form failed almost completely.

An equation is derived for predicting the effect of chance success, relative to item difficulty, on item-test correlation. The values predicted by this equation and by equations derived by Guilford and Carroll for predicting the effect of chance success on item difficulty and test reliability are compared with empirical values in an experiment which used identical test items in multiple-choice and answer-only form.

In order to facilitate garment and pattern construction, a research which involved taking a minimum of fifty-five measurements on several thousand women was conducted by the Bureau of Home Economics. Partial correlations with age held constant were computed for a representative group of 4,128 of the women. The correlations among twenty-nine of these variables served as the basis of the present study. By a combination of the multiple-group and the centroid method of factoring, five factors were extracted. After twenty-nine rotations, simple structure was evident, and the factors were interpreted as bone length, size of joints, circumference below the waist, circumference of extremities, and circumference above the waist. The intercorrelations of the primaries were computed, and two second-order factors were extracted. One of these seems to be primarily related to the growth of fatty tissue and the other to the development of the bones.

For multiple-choice tests where no a priori key exists, the initial selection of a key for maximum validity may be made on the basis of the number of persons choosing each alternative and their mean criterion score. The keying formula is derived. Once the initial keying has been done, further precision in keying and item selection may use, in addition, the mean total test score for persons choosing each alternative. Item-selection formulas suggested by Horst and by Gulliksen for maximizing test validity are both in the form of a ratio, an “item-validity index” divided by an “item-reliability index.” The formula derived here is shown to be equivalent to the numerators of these formulas. The expression in the denominators uses the total test score. Although a radical appears in the denominator of Horst's formula and not in the denominator of Gulliksen's formula, both of them select the same items in practice.

The theory is advanced that personality factors obtained in the first order may often represent combinations of temperament traits that occur in the experimental population. Under these circumstances an investigation of the second order represents a purification process and yields factors which represent the more basic or pervasive characteristics of the original behavior items included in the factorial study. These second-order factors can be obtained directly in the first order by a careful selection of the variables which enter into the analysis. A second-order analysis was undertaken of the nine factors inherent in three of J. P. Guilford's inventories, and four clearly interpretable second-order factors were obtained. Three of these factors were obtained directly in the first order in a new factorial study of twenty-two behavior items. Attention is drawn to the similarities between these factors and traits of temperament postulated by an independent investigator.