Psycholinguistic data are often analyzed with repeated-measures analyses of variance (ANOVA), but this paper argues that mixed-effects (multilevel) models provide a better alternative method. First, models are discussed in which the two random factors of participants and items are crossed, and not nested. Traditional ANOVAs are compared against these crossed mixed-effects models, for simulated and real data. Results indicate that the mixed-effects method has a lower risk of capitalization on chance (Type I error). Second, mixed-effects models of logistic regression (generalized linear mixed models, GLMM) are discussed and demonstrated with simulated binomial data. Mixed-effects models effectively solve the "language-as-fixed-effect-fallacy", and have several other advantages. In conclusion, mixed-effects models provide a superior method for analyzing psycholinguistic data. (Contains 4 tables and 1 figure.)