Analysis of variance with repeated measures (repeated measures ANOVA) is one of the most misused techniques.
Many researchers, as soon as they see the group of patients measured several times, use Repeated Measures ANOVA in their statistical software without reservation.
However, they are mistaken often, because Repeated Measures ANOVA is an approach that requires a series of very strong assumptions that are almost never met.
Since Repeated Measures ANOVA uses listwise deletion, if there is a lack of at least one measurement it will be equivalent to losing information about entire the case (for example, all measurements of a patient, if you’re analyzing clinical data). This loss of information is not tolerable, especially when you have small sample size.
Time has to be measured as a continuous variable
Repeated measures ANOVA uses time as a categorical variable. If you have 3 times, say t1, t2 and t3, in repeated measures ANOVA, the distances t1-t2 and t2-t3 are considered identical. In other words, the effect of time on your dependent variable is modelled poorly.
Different number of repeated measurements per subject
If your subjects have been measured a different number of times, the Repeated Measures ANOVA fails. You understand very well how difficult it is, especially in an observational study, to meet this assumption.
Moreover, Repeated Measures ANOVA is unable to handle more complex data structures, such as data organized on more than two levels. For example, it is useless when more repeated measurements have been done in inpatients from different hospitals.
At the same time, this technique cannot be used in analyses when covariates determine your dependent variable in a not homogenous manner; for example, the repeated measures ANOVA does not enable the analysis of time-dependent variables.
What do you do instead of Repeated measures ANOVA?
In the majority of cases, mixed (multilevel) models are used.
Repeated measures ANOVA is fine, but only when the experiment is designed ad hoc (the cases that are not described in this post).
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