When does it make sense to use repeated measures two-way ANOVA?
It seems to me that biologists tend to overuse repeated measures two-way ANOVA.
"Two way" means there are two factors in the experiment, say different treatments, and different conditions. Repeated-measures means that the same subject received more than one treatment and or more than one condition. When one of the factors is repeated-measures and the other is not, the analysis is sometimes called a mixed-model ANOVA (but watch out for that word mixed, which can have a variety of meanings in statistics). This is the only kind of repeated measures two-way ANOVA offered by Prism 5. Prism 6 can also handle repeated-measures in both factors.
Let's consider an example. You want to compare the effects of two drugs on the plasma concentration of a hormone, and want to do so while the subject is resting, while the subject is exercising, and while the subject is sleeping. So one factor is the condition (rest, exercise, asleep) and the other factor is drug (one of two alternatives). You give one set of subjects drug A, and another set drug B. You collect blood, and measure plasma levels of the hormone, for each subject in all three conditions (rest, exercise, and sleep).
These data would be appropriately analyzed by two-way ANOVA with repeated measures in one factor (also called mixed model ANOVA). Measuring the plasma level of hormone in each subject in all three conditions means that the subject is serving as his or her own control. The repeated-measures analysis controls for this. If the subjects vary a lot from one another, the repeated-measures analysis will have more power than ordinary two-way ANOVA.
Two-way ANOVA is often applied to comparing time courses or dose response curves. In these situations one of the factors is dose or time. The ANOVA analysis treats different time points (or different concentrations) exactly as it would treat different drugs or different species. The concept of trend is entirely ignored (except in some special post tests). So the entire point of the experiment is usually ignored when you perform two-way ANOVA.
What is the alternative to two-way ANOVA? It would be much better to quantify the data for each subject in some biologically meaningful way. Perhaps this would be area under the curve. Perhaps the peak level. Perhaps the time to peak. Perhaps you can fit a curve and determine a rate constant. Now take these values (the areas or rate constants...) and compare between groups of subjects. This kind of analysis follows the scientific logic of the experiment, unlike two-way ANOVA which essentially ignores the entire logic of the experiment.