The personnel classification problem arises in its pure form when all job applicants must be used, being divided among a number of job categories. The use of tests for classification involves problems of two types: (1) problems concerning the design, choice, and weighting of tests into a battery, and (2) problems of establishing the optimum administrative procedure of using test results for assignment. A consideration of the first problem emphasizes the desirability of using simple, factorially pure tests which may be expected to have a wide range of validities for different job categories. In the use of test results for assignment, an initial problem is that of expressing predictions of success in different jobs in comparable score units. These units should take account of predictor validity and of job importance. Procedures are described for handling assignment either in terms of daily quotas or in terms of a stable predicted yield.

Formulas are derived by which, given the factor loadings and the internal reliability of a test of unit length, the following estimates can be made: (1) the common-factor loadings for a similar (homogeneous) test of length n; (2) the number of times (n) that a test needs to be lengthened homogeneously to achieve a factor loading of a desired magnitude; and (3) the correlation between two tests, either or both of which have been altered in length, as a function of (a) the new factor loadings in the altered tests or (b) the original loadings in the unit-length tests. The appropriate use of the derived formulas depends upon the fulfillment of four assumptions enumerated.

A procedure is proposed for testing the significance of group differences in the standard error of measurement of a psychological test. Wilks' criterion is used to assure that the tests used in ascertaining reliability and hence variance of errors of measurement may be assumed parallel for each group. Votaw's criterion may be used to check whether the test scores of all the groups have the same mean, variance, and covariance. It is possible, however, for the variance and reliability of the test to differ widely from group to group, so that Votaw's criterion is not satisfied even though the variance of errors of measurement stays relatively constant. For this case a modification of Neyman and Pearson's criterion is developed to test agreement among standard errors of measurement despite group differences in mean, variance, and reliability of the test.

Some methods are presented for estimating the reliability of a partially speeded test without the use of a parallel form. The effect of these formulas on some test data is illustrated. Whenever an odd-even reliability is computed it is probably desirable to use one of the formulas noted in Section 2 of this paper in addition to the usual Spearman-Brown correction. Since the formulas given here involve the mean and the standard deviation of the “number unattempted score,” a method is given in Section 4 for computing this mean and standard deviation from item analysis data. If the item analysis data are available, this method will save considerable time as compared with rescoring answer sheets.

Nineteen different anthropometric measures were obtained on all members of each of two racial groups. A procedure was developed and applied to the data to give maximum differentiation between the groups. The method is applicable wherever we have a large number of independent variables and a dependent variable. In such cases, the conventional methods for determining multiple regression constants are very laborious. An iteration method is presented which is more rapid than any with which the writers are familiar. The method selects in sequence those variables which together yield the largest multiple correlation with the criterion. At each step in the procedure, rapid estimates of the regression weights and the multiple correlation at that point are available.

Item-analysis data are usually obtained from a single test administration, with a given item sequence and time limit. Questions can be raised as to the effects upon item data resulting from changes in item-position and test-timing. In this study, two forms of a verbal test and two forms of a mathematics test were used. In each case, both forms of each test contained the same items, but items coming early in one form were placed late in the other. Each of these forms was administered once with a short time limit and once with generous timing to comparable groups of high school students. The relationships of various speed and power scores were determined, and the changes which occurred during the added time were studied. Values of the item indices p (proportion right), Δ† (another difficulty index), and the item-test biserial correlation coefficient were obtained for both the speed and the power conditions and were systematically compared. The proportion right of those attempting the item, the Δ index, and the biserial r were all found to have undesirable characteristics for items appearing late in a speeded test.

A method of ratio scaling is described for treating comparative judgments of paired stimuli. A method of comparative judgment developed by Metfessel is employed. Formulas for scale values and the solution of a sample problem are provided. The method is designed to provide internal-consistency checks on the scale values. Experimental interpretations of equal-unit and ratio properties of measurement scales are inherent in the procedure.