When you have repeated measures data in psychology, the decision between using a repeated measures ANOVA or a mixed model is not trivial. For years, repeated measures ANOVA was the default option in the majority of published studies, and you still find it in a very high proportion of articles. However, mixed models (also called linear mixed-effects models or multilevel models) have been increasingly gaining ground as a more flexible alternative and, in many scenarios, a more appropriate one.
The fundamental difference between the two approaches has to do with how they handle the structure of the data. Repeated measures ANOVA assumes sphericity -- that is, that the variances of the differences between all pairs of conditions are equal. When this assumption is violated (and it is violated frequently), corrections such as Greenhouse-Geisser or Huynh-Feldt are applied, which essentially adjust the degrees of freedom to compensate. The problem is that these corrections are a patch: they do not solve the underlying problem but rather attempt to minimize its impact on the p-value.
Mixed models, on the other hand, do not require the sphericity assumption. Instead, they explicitly model the covariance structure of the data, which allows them to be much more flexible. You can specify different covariance structures (unstructured, autoregressive, compound symmetry) and let the data tell you which fits best. This is not a minor detail, because the covariance structure you choose can substantially affect the results and the conclusions you draw.
The problem of missing data
Perhaps the most practical advantage of mixed models is how they handle missing data. In a classical repeated measures ANOVA, if a participant does not have data for one of the conditions, that participant is entirely removed from the analysis. This can result in a considerable loss of information, especially in longitudinal studies where dropout is frequent. Moreover, if the data are not missing completely at random (what in statistics is called MCAR), listwise deletion can introduce important biases in the estimates.
Mixed models use maximum likelihood estimation, which allows them to leverage all available information from each participant, even when data are incomplete. If a participant completed three out of five assessment sessions, their three observations contribute to the model. The required assumption is less restrictive: it is sufficient that the data are missing at random conditional on the variables in the model (what is known as MAR). This makes mixed models considerably more robust in clinical and longitudinal contexts, where missing data are the norm rather than the exception.
Random effects and individual variability
Another aspect that differentiates the two approaches is the treatment of individual differences. Repeated measures ANOVA estimates an average effect of the within-subjects factor but treats all participants as if they responded in the same way to the experimental manipulation. Mixed models allow the inclusion of random effects, such as random intercepts (each participant can have a different baseline level) and random slopes (each participant can show a different effect of the factor). This flexibility is especially relevant in psychology, where we know that between-person variability is enormous and where assuming that everyone responds the same way is, in many cases, simply unrealistic.
The inclusion of random slopes has important implications for inference. Barr et al. (2013) demonstrated that failing to include the appropriate random effects structure can inflate Type I error rates. That is, you can find significant effects that do not actually exist, simply because your model is not adequately capturing the variability between participants. This article generated considerable debate, because models with a full random effects structure sometimes fail to converge or produce unstable estimates, but the underlying message is clear: ignoring individual variability has a real statistical cost.
Years later, Matuschek, Kliegl, Vasishth, Baayen and Bates (2017) qualified this recommendation. They showed that a model with the maximal random-effects structure protects against Type I error but sacrifices statistical power when some of those random effects are actually close to zero. Their proposal -- a parsimonious model that keeps only the random effects the data support -- is now the pragmatic consensus: start from the maximal structure your design justifies and simplify it when convergence problems or a singular fit appear. With missing data, it is also worth checking the missingness mechanism (MCAR, MAR, MNAR) before trusting maximum likelihood estimation.
When to use each approach
Having said all this, repeated measures ANOVA is not a bad tool. In simple designs with few levels of the factor, complete samples, and reasonable sphericity, it produces results that are practically identical to those of a mixed model. It is easier to implement, easier to explain to reviewers who are not familiar with mixed models, and most statistical software offers it in an accessible manner. If your design is a 2x2 with repeated measures on one factor and you have no missing data, an ANOVA will probably suffice.
However, when your design is more complex (multiple factors, nested designs, unbalanced data), when you have missing data, or when you suspect that individual variability in the effects is considerable, mixed models are clearly superior. In longitudinal studies with more than three or four time points, the advantage is especially notable. They are also preferable when working with data that do not fit the normal distribution well, since generalized mixed models can accommodate binomial, Poisson, and other distributions.
In practice, my recommendation is that you learn to use both approaches. Many reviewers still expect to see a repeated measures ANOVA and may ask for explicit justification if you use mixed models. Having a clear understanding of why you choose one over the other will allow you to argue your decision with confidence. If you are getting started with mixed models, packages like lme4 in R or the MIXED function in SPSS are good starting points. The important thing is to understand what each model is doing with your data, not simply to follow a recipe.
Before you submit: this exact decision, mixed model or repeated measures ANOVA, is one of the first things a methodological reviewer asks you to justify, and a random-effects structure that is never explained is an easy target. If your manuscript is already written, run it through the AI Paper Reviewer, a free Reviewer 2 style pre-review that tells you which part of your analysis would be questioned before the journal questions it.
If your dissertation involves longitudinal data or repeated measures and you are torn between ANOVA and mixed models, my statistical support for doctoral theses fits the model in R or SPSS and prepares the methodological justification your committee will read.