How Good are Our Measures? Investigating the Appropriate Use of Factor Analysis for Survey Instruments

Abstract

Background: Evaluation work frequently utilizes factor analysis to establish the dimensionality, reliability, and stability of surveys. However, survey data is typically ordinal, violating the assumptions of most statistical methods, and thus is often factor-analyzed inappropriately. Purpose: This study illustrates the salient analytical decisions for factor-analyzing ordinal survey data appropriately and demonstrates the repercussions of inappropriate analyses. Setting: The data used for this study are drawn from an evaluation of the efficacy of a drama-based approach to teaching Shakespeare in elementary and middle school. Intervention: Not applicable. Research Design: Survey research. Data Collection and Analysis: Four factor analytic methods were compared: a traditional exploratory factor analysis (EFA), a full-information EFA, and two EFAs within the confirmatory factor analysis framework (E/CFA) conducted according to the Jöreskog method and the Gugiu method. Findings: Methods appropriate for ordinal data produce better models, the E/CFAs outperform the EFAs, and the Gugiu method demonstrates greater model interpretability and stability than the Jöreskog method. These results suggest that the Gugiu E/CFA may be the preferable factor analytic method for use with ordinal data. Practical applications of these findings are discussed. Keywords: factor analysis; ordinal data; E/CFA; survey research.