Analysis checklist: Repeated measures two-way ANOVA

Are the data matched?        

If the matching is effective in controlling for experimental variability, repeated-measures ANOVA will be more powerful than regular ANOVA.

Are there two factors?

One-way ANOVA compares three or more groups defined by one factor. For example, you might compare a control group with a drug treatment group and a group treated with drug plus antagonist. Or you might compare a control group with five different drug treatments. Prism has a separate analysis for one-way ANOVA.

Some experiments involve more than two factors. For example, you might compare three different drugs in men and women at four time points. There are three factors in that experiment: drug treatment, gender and time. These data need to be analyzed by three-way ANOVA, also called three-factor ANOVA. Prism does not perform three-way ANOVA.

Are both factors “fixed” rather than “random”?

Prism performs Type I ANOVA, also known as fixed-effect ANOVA. This tests for differences among the means of the particular groups you have collected data from. Different calculations are needed if you randomly selected groups from an infinite (or at least large) number of possible groups, and want to reach conclusions about differences among ALL the groups, even the ones you didn't include in this experiment.

Can you accept the assumption of 'circularity'

A random factor that causes a measurement in one subject to be a bit high (or low) should have no affect on the next measurement in the same subject. This assumption is called circularity or sphericity. It is closely related to another term you may encounter in advanced texts, compound symmetry.

You only have to worry about the assumption of circularity when your experiment truly is a repeated-measures experiment, with measurements from a single subject. You don't have to worry about circularity with randomized block experiments where you used a matched set of subjects (or a matched set of experiments)

Repeated-measures ANOVA is quite sensitive to violations of the assumption of circularity. If the assumption is violated, the P value will be too low. You'll violate this assumption when the repeated measurements are made too close together so that random factors that cause a particular value to be high (or low) don't wash away or dissipate before the next measurement. To avoid violating the assumption, wait long enough between treatments so the subject is essentially the same as before the treatment. Also randomize the order of treatments, when possible.

Some advanced programs do special calculations to detect, and correct for, violations of the circularity or sphericity assumption. Prism does not.

Consider alternatives to repeated measures two-way ANOVA.

Two-way ANOVA may not answer the questions your experiment was designed to address. Consider alternatives.