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Experimental designs that sample both subjects and stimuli from a larger population need to account for random effects of both subjects and stimuli using mixed-effects models. However, much of this research is analyzed using analysis of variance on aggregated responses because researchers are not confident specifying and interpreting mixed-effects models. I will explain how to simulate data with random-effects structure (using the faux R package) and analyze the data using linear mixed-effects regression (with the lme4 R package), with a focus on interpreting the output in light of the simulated parameters.