Shiken: JALT Testing & Evaluation SIG Newsletter - Statistics Corner - Choosing the Right Type of Rotation in PCA and EFA

Aug 30, 2026

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A newsletter column addresses key questions in language testing statistics through the lens of principal components analysis and exploratory factor analysis. It defines rotation and explains why rotation is used to achieve clearer, more interpretable factor-loading patterns. The column contrasts orthogonal and oblique rotation, surveys common methods (e.g., varimax, quartimax, equamax, direct oblimin, promax), and provides decision guidance based on factor-correlation thresholds. An applied example reports factor correlations to justify nearly orthogonal solutions, supporting informed method selection in questionnaire development contexts.

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Statistics Corner

Choosing the Right Type of Rotation in PCA and EFA

What Is Rotation?

What Are the Different Types of Rotation?

Shiken: JALT Testing & Evaluation SIG Newsletter. 13 (3) November 2009 (p. 20-25) Statistics Corner Questions and answers about language testing statistics: Choosing the Right Type of Rotation in PCA and EFA James Dean Brown (University of Hawai‘i at Manoa) Question: In Chapter 7 of the 2008 book on heritage language learning that you co-edited with Kimi Kondo-Brown, there is a study (Lee & Kim, 2008) comparing the attitudes of 111 Korean heritage language learners. On page 167 of that book, a principal components analysis (with varimax rotation) describes the relation of examining 16 purported reasons for studying Korean with four broader factors. Several questions come to mind. What is a principal components analysis? How does principal components analysis differ from factor analysis? What guidelines do researchers need to bear in mind when selecting “factors”? And finally, what is a varimax rotation and why is it applied? Answer: This is an interesting question, but a big one, made up of at least four sets of sub-questions:(a) What are principal components analysis (PCA) and exploratory factor analysis (EFA), how are they different, and how do researchers decide which to use? (b) How do investigators determine the number of components or factors to include in the analysis? (c) What is rotation, what are the different types, and how do researchers decide which particular type of rotation to use? And,(d) how are PCA and EFA used in language test and questionnaire development? I addressed the first two questions in previous columns (Brown, 2009a & b) . I’ll attend to the third one here, and address the last one in the next column. What Is Rotation? In the PCA/EFA literature, definitions of rotation abound. For example, McDonald (1985, p. 40) defines rotation as “performing arithmetic to obtain a new set of factor loadings (v-ƒ regression weights) from a given set,” and Bryant and Yarnold (1995, p. 132) define it as “a procedure in which the eigenvectors (factors) are rotated in an attempt to achieve simple structure.” Perhaps a bit more helpful is the definition supplied in Vogt (1993, p. 91): “Any of several methods in factor analysis by which the researcher attempts to relate the calculated factors to theoretical entities. This is done differently depending upon whether the factors are believed to be correlated (oblique) or uncorrelated (orthogonal) .”And even more helpful is Yaremko, Harari, Harrison, and Lynn (1986), who define factor rotation as follows: “In factor or principal-components analysis, rotation of the factor axes (dimensions) identified in the initial extraction of factors, in order to obtain simple and interpretable factors.” They then go on to explain and list some of the types of orthogonal and oblique procedures. How can a concept with a goal of simplification be so complicated? Let me try defining rotation from the perspective of a language researcher, while trying to keep it simple. I think of rotation as any of a variety of methods (explained below) used to further analyze initial PCA or EFA results with the goal of making the pattern of loadings clearer, or more pronounced. This process is designed to reveal the simple structure. The choices that researchers make among the orthogonal and oblique varieties of these rotation methods and the notion of simple structure will be the main topics in the rest ofthis column. 21 What Are the Different Types of Rotation? As mentioned earlier, rotation methods are either orthogonal or oblique. Simply put, orthogonal rotation methods assume that the factors in the analysis are uncorrelated. Gorsuch (1983, pp. 203-204) lists four different orthogonal methods: equamax, orthomax, quartimax, and varimax. In contrast, oblique rotation methods assume that the factors are correlated. Gorsuch (1983, pp. 203-204) lists 15 different oblique methods.1 Version 16 of SPSS offers five rotation methods: varimax, direct oblimin, quartimax, equamax, an

FAQs

What are principal components analysis (PCA) and exploratory factor analysis (EFA), and how do researchers decide which to use?

PCA and EFA are distinct approaches used to analyze structure in data, and the column notes that researchers need criteria to decide between them. The piece references prior columns for how that choice is determined.

What is “rotation” in PCA/EFA, and what goal does it serve?

Rotation refers to methods that further analyze initial PCA or EFA results to make the loading pattern clearer. The intended outcome is a simpler, more interpretable structure.

How do researchers choose between orthogonal and oblique rotation?

Orthogonal rotation assumes factors are uncorrelated, while oblique rotation assumes they are correlated. The column provides guidance using factor-correlation inspection with thresholds (e.g., correlations around .32 or above indicate enough overlap to consider oblique rotation).

Aug 30, 2026

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