Analyzing randomized controlled interventions: Three notes for applied linguists

I discuss three common practices that obfuscate or invalidate the statistical analysis of randomized controlled interventions in applied linguistics. These are (a) checking whether randomization produced groups that are balanced on a number of possibly relevant covariates, (b) using repeated measures ANOVA to analyze pretest-posttest designs, and (c) using traditional significance tests to analyze interventions in which whole groups were assigned to the conditions (cluster randomization). The first practice is labeled superfluous, and taking full advantage of important covariates regardless of balance is recommended. The second is needlessly complicated, and analysis of covariance is recommended as a more powerful alternative. The third produces dramatic inferential errors, which are largely, though not entirely, avoided when mixed-effects modeling is used. This discussion is geared towards applied linguists who need to design, analyze, or assess intervention studies or other randomized controlled trials. Statistical formalism is kept to a minimum throughout.