Harry H. Harman

Comparison of two factorial analyses

A Bi-factor analysis is made of Professor Thurstones battery of fifty-seven tests employing his tetrachoric correlations. Although this analysis is made entirely independent of his multiple factor analysis, a very close agreement is found between the group factors obtained here and Thurstones verbal descriptions previously published.

Resolution of the heywood case in the minres solution

In the course of developing the minres method of factor analysis the troublesome situation of communalities greater than one arose. This problem—referred to as the generalized Heywood case—is resolved in this paper by means of a process of minimizing the sum of squares of off-diagonal residuals. The resulting solution is superior to the otherwise very efficient original minres method without requiring additional computing time.

The square root method and multiple group methods of factor analysis

The square root method for the solution of a set of simultaneous linear equations or the reduction of a matrix has been known for some time under a variety of names. Because of its usefulness in statistical work, especially in factor analysis, the square root method is presented in general terms and an example given. Several independently developed “multiple group methods” for factor analysis are compared and synthesized. Their fundamental concepts are set forth and an appropriate system of notation developed. Detailed computational procedures are outlined, and the square root method is emphasized as a computing aid in multiple group analysis.

On the rectilinear prediction of oblique factors

The general problem of estimating correlated or uncorrelated factors is treated. It is specifically indicated wherein the prediction of oblique factors differs from that of orthogonal factors. A shortened method of estimation of correlated factors is developed.

Extensions of factorial solutions

A method is developed for extending any type of factor solution to new tests. The theoretical basis for this approximating scheme is thoroughly investigated, and then a simplification in the technique is introduced for practical purposes. An example is presented which illustrates the procedure of extending a factor solution to three new tests simultaneously.

Chapter XIII: Factor Analysis

S I N C E FACTOR ANALYSIS is a relatively new subject and only a very brief review of its literature (705) has appeared in previous issues of the Review of Educational Research, it seems desirable to start at the beginning. Only the most significant articles can be considered in the alloted space. Many of the early papers which contributed to methodology, but whose proposals have since been replaced by simpler and more efficient procedures, have been omitted here. Greatest emphasis has been placed on the research of the last four years, but even for this period about half of the published articles had to be omitted.