Items have been studied heretofore for their value as elements of particular tests to the neglect of more fundamental research into the multiple potentiality of items. This article proposes a method of grouping items into “synonymies” comprising all of the items which correlate with a given key item. These synonymies can be used for interpretation of the total meaning of the key item: (1) by inspection of the constituent items and (2) by correlational study of obtained single scores of individual persons. The method is illustrated by four items with inter- and intra-correlations, and characteristics of an ideal background reservoir of items are pointed out.

This paper discusses the influence of test difficulty on the correlation between test items and between tests. The greater the difference in difficulty between two test items or between two tests the smaller the maximum correlation between them. In general, the greater the number of degrees of difficulty among the items in a test or among the tests in a battery, the higher the rank of the matrix of intercorrelations; that is, differences in difficulty are represented in the factorial configuration as additional factors. The suggestion is made that if all tests included in a battery are roughly homogeneous with respect to difficulty existing hierarchies will be more clearly defined and meaningful psychological interpretation of factors more readily attained.

The numerical evaluation of determinants with a modern computing machine is discussed. Various methods are presented and their relations to each other are indicated. The methods presented parallel those developed in the previous paper on “The Solution of Simultaneous Equations.” Especially emphasized are the Abbreviated Doolittle and the Compact methods. Additional topics include the evaluation of partially symmetric determinants by means of symmetric methods and the evaluation of determinantal ratios.

It is pointed out that the scoring weights for test items should be approximations to regression-equation weights. For this reason any estimate of reliability of the weight should not be permitted to influence the size of the weight but should be used in determining the limit of acceptability of an item. A simple approximation weight is recommended for general use, and an abac is provided for the estimation of it when the correlation between item and criterion is the phi coefficient. A formula for the standard error of this weight is derived and tables of significant and very significant weights are presented in terms of deviations from the median weight.

Bi-factor and multiple-factor analyses of the same data are compared in two respects. First, two criteria are suggested for determining when the factorization is adequate. This problem being more acute for the centroid method than for the bi-factor method, the latter is used primarily for comparison only. It is shown also that the omission from the simple structure of entries smaller than .10 yields a pattern which is a poorer fit to the original correlations than is the bi-factor pattern. Second, the second-order general factor obtained from the intercorrelations of the primaries is found to be highly correlated with the general factor of the bi-factor pattern.

Mental test data of Chrysostomm and of Garrett, Bryan, and Perl are reinvestigated in order to determine the shifts in test clusters with chronological age. It is found that the factors under survey tend to become more independent with increasing age.

Up to the present only empirical methods have been available for determining the number of factors to be extracted from a matrix of correlations. The problem has been confused by the implicit attitude that a matrix of intercorrelations between psychological variables has a rank which is determinable. A table of residuals always contains error variance and common factor variance. The extraction of successive factors increases the proportion of error variance remaining to common factor variance remaining, and a point is reached where the extraction of more dimensions would contain so much error variance that the common factor variance would be overshadowed. The critical value for this point is determined by probability theory and does not take into account the size of the residuals. Interpretation of the criterion is discussed.

A fictitious factor matrix including 16 tests and 3 factors, one of which was ag factor, was prescribed. From it two typical factor problems, including errors of sampling, were derived. Students in training, without awareness of the factor patterns, arrived at essentially correct solutions by the use of Thurstone's centroid method with rotation of axes. Errors in the calculated factor matrix were very close in size to the sampling errors in the correlation coefficients. It is concluded that a g factor need not escape detection by Thurstone's procedures if the criteria of complete simple structure are not demanded.

On viewing Thurstone's psychophysical scale from the point of view of the mathematical theory of one-parameter continuous groups, it is seen that a variety of different psychological or statistical assumptions can all be made to lead to a scale possessing similar properties, though requiring different computational techniques for their determination. The natural extension to multi-dimensional scaling is indicated.

In continuation of previous studies, the interreaction of two social classes is investigated from a somewhat different point of view. An exchange of results of activities of the two classes is considered, and a mathematical approach is outlined based on the use of such psychological concepts as the satisfaction function.

A case studied in a previous paper, concerning the changes of the relative number of individuals of different types in a social group, is treated under more general assumptions. It is shown that under those more general conditions periodical fluctuations in the structure of the social group may occur.

The IBM card counting sorter may be readily used for a number of statistical operations independent of the tabulating unit. In this article, use of the counting sorter in computing the mean and standard deviation with 2-digit variables and the coefficient of correlation with scores coded in a single column will be described. Both processes involve machine work which is essentially the same. A method for finding the correlation between 2-digit variables will also be given.

Fisher's method of maximum likelihood is applied to the problem of estimation in factor analysis, as initiated by Lawley, and found to lead to a generalization of the Eckart matrix approximation problem. The solution of this in a special case is applied to show how test fallability enters into factor determination, it being noted that the method of communalities underestimates the number of factors.

This paper questions the oft-repeated statement that clinical psychology is an art by examining the main functions of clinical psychologists, i.e., diagnosis and treatment. In examining the concept of diagnosis, evidence is presented which supports the notion that a diagnostic statement has meaning only when it has a referent in the future—when it provides a prediction. A prediction (probability-statement) is determined empirically and may be stated in terms of a regression equation or in terms of a crude generalization from clinical experience. Treatment likewise is determined by tacit or expressed predictions of behavior under alternative conditions. The various conceptions of art as applied to clinical psychology are examined and the conclusion is drawn that clinical psychology is a scientific as opposed to an artistic or intuitive enterprise.

The instrument to be described was developed from apparatus the original design of which, by Landahl and Bechtoldt, was unpublished. Its function is to measure the times of simple reaction, choice, perception of projected patterns, and perception of dim patterns after light adaptation. It may also be used to time verbal response to multiple-choice material when combined with the response relay described by Libby elsewhere in the present journal.

The complete instrument, including chronoscope, subject keys, and experimenter keys, may be carried in a case ll"x6.5"x6.5". The chronoscope, M, occupies the left half of the case. The upper half of the right-hand section serves for carrying the subject key (H) or, as shown in the accompanying cut, the microfilm container and projector slides. All remaining apparatus is in the lower half of this compartment.

A method for computing the biserial correlation coefficients with the aid of punch card equipment is oultined. A numerical example and a work sheet layout is included in the presentation.

Two batteries of music tests were factored by the centroid method. From each battery three oblique factors were extracted and in each case were tentatively identified as tonal sensitivity, retentivity (memory for elements), and memory for form. The correlations of the music tests of one battery with subtests of Cattell's intelligence test and with tests of a literary nature are also reported.