In case I have three categorical variables with more than two groups and I want to study their effect on a variable that is measured on a continuous scale. Is it enough to run three-way ANOVA or one-way then two-way then three-way? Why? Doesn’t three-way ANOVA include one-way and two-way in its outputs?
Similarly, does one-way ANOVA combined with post hoc suffice for multiple two samples t-tests?
Thanks in advance,
Hello Mohammad,
you should go for a single three-way ANOVA. Calculating multiple ANOVA will only cause alpha-inflation, so it is not even justified, let alone helpful.
In general, the ANOVA is an omnibus test, because it combines the variance components of all factors for testing. Defining specific posthoc-tests is certainly more difficult when running a three-way ANOVA, just because you have many more combinations you could test (also consider interactions). Keep in mind that these posthoc-tests are mostly more conservative than a t-test to account for the data-driven comparisons and to avoid alpha-inflation. That is way the have less statistical power than a t-test.
Does that answer your questions?
Best,
Steffen
Hello Mohammed, I strongly support Jens-Steffen Scherer advise. Left to me I would rather go for single 3-way ANOVA to avoid complexity.
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