# Factor Analysis and Related Methods

## Synopsis

Factor Analysis is a genetic term for a somewhat vaguely delimited set of techniques for data processing, mainly applicable to the social and biological sciences. These techniques have been developed for the analysis of mutual relationships among a number of measurements made on a number of measurable entities. In the broad sense, factor analysis comprises a number of statistical models which yield testable hypotheses -- hypotheses that may confirm or disconfirm in terms of the usual statistical procedures for making tests of significance. It also comprises a number of simplifying procedures for the approximate description of data, which do not in any sense constitute disconfirmable hypotheses, except in the loose sense that they supply approximations to the data. In literature, the two types of analysis have often been confused.

This book clarifies the concepts of factor analysis for students or professionals in the social sciences who wish to know the technique, rather than the mathematics, of factor theory. Mathematical concepts are described to have an intuitive meaning for the non-mathematical reader. An account of the elements of matrix algebra, in the appendix, and the (mathematical) notes following each chapter will help the reader who wishes to receive a more advanced treatment of the subject. Factor Analysis and Related Methods should prove a useful text for graduate and advanced undergraduate students in economics, the behavioral sciences, and education. Researchers and practitioners in those fields will also find this book a handy reference.

## Excerpt

This book is a revision and expansion of a set of chapters on factor analysis written in 1975 while I was on study leave in the Department of Psychology, University College, London. These chapters have been used as course notes for postgraduate classes in factor analysis at the Ontario Institute for Studies in Education over a number of years, and the reactions of my students have helped to guide the process of revising and completing the text.

It is hoped that the book will serve both as a textbook for postgraduate and advanced undergraduate students in the social sciences and as a reference book.

In writing the book, I have tried to imagine, as the reader, a student or worker in one of the social sciences who wishes to be able to read studies using factor analysis and perhaps to do research using factor-analytic methods, with technical advice, but who does not wish to learn the mathematics of factor theory. (The term social science is here interpreted widely to include economics, behavioral science, and education.) Specifically, I disciplined myself not to use any matrix algebra or multivariate statistical theory in the body of the text. An account of the elements of matrix algebra (in the appendix and in the mathematical notes at the ends of the chapters) can be skipped without any sense of discontinuity or loss, but they would be helpful to the reader who wishes to make a transition to more advanced treatments of these topics and could also deepen understanding of the account in the main text. An attempt has been made to use verbal expressions to describe what are basically mathematical concepts in such a way that they will have an intuitive meaning for the nonmathematical reader, while not appearing to be shamefully lacking in rigor from the point of view of a mathematician. Others may judge the success of this attempt.

It has to be admitted frankly that in contrast to some other areas of research method (e.g., the main body of univariate statistical methods) factor analysis, in . . .

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