One Size Doesn't Fit All: Using Factor Analysis to Gather Validity Evidence When Using Surveys in Your Research

Abstract

Across all sciences, the quality of measurements is important. Survey measurements are only appropriate for use when researchers have validity evidence within their particular context. Yet, this step is frequently skipped or is not reported in educational research. This article briefly reviews the aspects of validity that researchers should consider when using surveys. It then focuses on factor analysis, a statistical method that can be used to collect an important type of validity evidence. Factor analysis helps researchers explore or confirm the relationships between survey items and identify the total number of dimensions represented on the survey. The essential steps to conduct and interpret a factor analysis are described. This use of factor analysis is illustrated throughout by a validation of Diekman and colleagues' goal endorsement instrument for use with first-year undergraduate science, technology, engineering, and mathematics students. We provide example data, annotated code, and output for analyses in R, an open-source programming language and software environment for statistical computing. For education researchers using surveys, understanding the theoretical and statistical underpinnings of survey validity is fundamental for implementing rigorous education research.

FIGURE 1.

Conceptual illustration of EFA and CFA. Observed variables (items 1–8) by squares, and constructs (factors F1 and F2) are represented by ovals. Factor loading/pattern coefficients representing the effect of the factor on the item (i.e., the unique correlation between the factor and the item) are represented by arrows. σ_j, variance for factor j; E_i, unique error variance for item i. The factor loading for one item on each factor is set to 1 to give the factors an interpretable scale.

FIGURE 2.

Results from the final five-factor CFA model. Survey items (for items descriptions see Table 3) are represented by squares and factors are represented by ovals. The numbers below the double-headed arrows represent correlations between the factors; the numbers by the one-directional arrows between the factors and the items represent standardized factor loadings. Small arrows indicate error terms. *, p < 0.01; p < 0.001 for all other estimates.