Repeated measures ANOVA or mixed ANOVA: which do you have?

This is decided by your design, not by preference. Answer one question: does every participant experience every condition?

The distinction

Repeated-measures ANOVA: every factor is within-subjects. Everyone gets every condition. Measuring the same people at weeks 1, 2 and 4.

Mixed ANOVA: at least one within-subjects factor and at least one between-subjects factor. Measuring the same people at weeks 1, 2 and 4, where each person was randomised to drug or placebo. Time is within, group is between.

Between-subjects ANOVA: every factor is between-subjects. Each person appears once.

Why it matters

Repeated measurements on the same person are correlated. Treating them as independent observations badly understates your error and inflates significance. The within-subjects structure exists to account for that.

Assumptions

Both need sphericity for any within-subjects factor with three or more levels. See Mauchly's test.

Mixed ANOVA additionally needs homogeneity of variance across the between-subjects groups.

Both use listwise deletion: a participant missing any time point is dropped entirely. With substantial dropout this can remove a large part of your sample.

When to use a linear mixed model instead

Missing data, unbalanced designs, unequally spaced time points, or more than one grouping level such as participants nested within sites. A mixed model handles all of these and does not discard incomplete cases.

In Plotara

One-way and two-way repeated-measures ANOVA, mixed ANOVA, and linear, logistic and Poisson mixed models, with listwise deletion stated explicitly in the output.