Random effects vs. fixed effects ANOVA.

Prism only performs Type I ANOVA, also known as fixed-effect ANOVA.

This kind of ANOVA tests for differences among the means of the particular groups you have collected data from. Type II ANOVA, also known as random-effect ANOVA, assumes that you have randomly selected groups from an infinite (or at least large) number of possible groups, and that you want to reach conclusions about differences among ALL the groups, even the ones you didn't include in this experiment. Type II random-effects ANOVA is rarely used in biological sciences, and Prism does not perform it.

Example 1: You do one-way ANOVA comparing four different species. You enter the data into four columns, and use one-way ANOVA to test the null hypothesis that the populations means are equal. Type I ANOVA (fixed-effect, what Prism and InStat compute) asks only about those four species. Type II ANOVA (random-effects, not performed by any GraphPad software), asks about the effects of difference among species in general. It assumes the four species included in this experiment were simply randomly chosen from a huge number of possible species.

Example 2: Each column is a different drug, then Type I ANOVA asks if those particular drugs have an impact on the result. Type II ANOVA would assume that you picked drugs randomly from the universe of all possible drugs, and are asking about the effect of drugs in general. That would not be useful.

Example 3: Each column represents a different interviewer, and you are asking if different interviewers rate job candidates differently.  Type I ANOVA would ask about the differences among these particular interviewers. Type II ANOVA asks about the effects of interviewers in general, and assumes the interviewers used in this study were randomly selected from (or at least are representative of) a larger population of possible interviewers. This example came from Nancy Zhang, who has good lecture notes on this topic.