Analyzing individual differences in second language research

Second language (L2) learners differ on myriad attributes, ranging from cognitive abilities (e.g. auditory perceptual acuity, working memory) to linguistic abilities like L2 proficiency to personality or motivational factors. For decades, scholars have been interested in understanding the impact of these individual differences on L2 outcomes as well as on the learner’s responsiveness to instructional treatments. In contrast to categorical factors like gender, when the attribute of interest varies along a continuum, there are various approaches for analyzing the individual difference variable. Simpler approaches involve reducing the complexity of the analysis by binning or splitting a sample into categorical groups (e.g. by performing a median split) then conducting traditional analyses such as t-tests and ANOVAs. But the concomitant loss of information in the individual difference measure can greatly reduce statistical power, thereby rendering it much more difficult to detect true effects — particularly when the effects are small, as they typically are in L2 research. Moreover, the resulting inferences may no longer map cleanly onto the research questions that originally motivated the research. Mixed effects models — a variant of regression — provide flexibility in the analysis of individual differences that can maintain the observed variability in the data so that scholars can directly test the hypotheses motivating their research. In this chapter, through a series of example models worked out in the R statistical software, I demonstrate the feasibility and ease of using mixed effects models to examine individual differences in L2 research. The examples focus on a scenario requiring the analysis of individual differences while also modeling the main and interactive effects of multiple factors (i.e. experimental design manipulations).