The paired t-test as a simple latent change score model

Abstract

The t-test is a common statistical test of differences in means. Despite the fact that its extension, the paired t-test (t-testP), appears in most introductory statistics textbooks, it is less known that for repeated variables the t-testP is in fact a model of change that can be replicated within the Structural Equation Modeling (SEM) framework. We show how to perform the t-testP with latent change scores (LCS) models, which allow for direct testing of significance of mean changes, and moreover can explain inter-individual (and group) differences in changes over time.