Karl J. Holzinger

The Bi-factor method

The Bi-factor Method of factor analysis is described and illustrated with a small group of fourteen tests. A detailed illustration is given of how the method may be modified to the case of overlapping group factors. It is advocated that the Bi-factor pattern in unmodified form be used to determine the adequacy of tests for the measurement of unitary traits.

A simple method of factor analysis

A simple method for extracting correlated factors simultaneously is described. The method is based on the idea that the centroid pattern coefficients for the sections of unit rank of the complete matrix may be interpreted as structure values for the entire matrix. Only the routine centroid average process is required.

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.

Factoring test scores and implications for the method of averages

The general procedure and detailed steps for attaining complete factor analyses of scores are presented. Both orthogonal and oblique factors are considered. It is shown that a single average by conventional procedure gives an incomplete summarization of the data when the rank exceeds one. There should be as many averages as there are common factors.

Selected References on Statistics, the Theory of Test Construction, and Factor Analysis

THE following bibliography, with a few exceptions, has been selected from issues of educational and psychological journals from March, 1943, to January, 1944, inclusive. Sharp distinctions do not exist between the fields covered in this list, but, as an assistance to the student with special interests in one or more of the fields, the references have been classified under the following categories: theory and use of statistical methods, problems of test construction, and factor analysis. No articles dealing primarily with the use of tests have been included because these items are distributed functionally in other lists in the cycle, such as those dealing with secondary-school instruction, guidance, etc.

Why do people factor

This is a very simple explanation of factor analysis primarily for the “factorial layman.” The interpretation of factors and the comparisons of various factor solutions are illustrated with a hypothetical example so designed that the reader can visualize all the relationships in a two-dimensional graph.

Selected References on Statistics and the Theory of Test Construction

The following bibliography has been selected from issues of educational and psychological journals for March, 1934, to February, 193 5, inclusive. The first part contains items dealing with the theory and use of statistical methods, while the second part includes studies and discussions of problems of test construction. No articles on the use of tests have been included in the present list, since these items are distributed functionally to other lists in the cycle, for example, the lists concerned with secondary-school instruction, educational psychology, and guidance published in other issues of the School Review and the lists concerned with elementary-school instruction and exceptional children published in the Elementary School Journal.

Interpretation of second-order factors

It is shown that a “second-order” factor pattern is equivalent to the transformation employed in rotating an orthogonal factor pattern to an oblique form. The correlation among the second-order factors may then be interpreted as due to the original first-order factors.

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.