Testing Hypotheses about Language Learning Using Structural Equation Modeling

In this chapter, I review a statistical method for hypothesis or theory testing called structural equation modeling (SEM). First, I describe what a model of second language acquisition (SLA) is. I do this so anyone, even those new to the field of applied linguistics, can understand the basic concepts underlying SEM; that is, SEM researchers first articulate a model of SLA, then get empirical data from the real world that operationalize the variables in the model. Researchers use an SEM program to test the model on the data (to see if the model fits the data; if the model is plausible in relation to the learning context of the people from whom the data were collected). After explaining the basics of SEM, I provide a review of 39 applied linguistics studies that have been published in the last five years (between 2008 and 2013) and that present at least one SEM analysis as part of the results. I discuss four problematic areas related to the use of SEM that I believe these 39 studies highlighted: (a) sample size, (b) model presentation, (c) reliability, and (d) the number of Likert-scale points. I conclude with possible solutions for the four problem areas and outline future directions.