MORE ANOVAs

1. MORE ANOVAs • ANOVA can be done with any number of factors, between and within • Dividing the variance changes • The F-tests are interpreted in the same way

2. Error Terms • The denominator of the F-test in any ANOVA is also called the error term. • The error term always contains only non-systematic variance. • One-Way and Two-Way BS ANOVA: error term is MS Within Groups.

3. Higher Order ANOVA • Factorials may have more than two i.v.’s • ANOVA on these factorials is called higher order: • three way ANOVA for three i.v.’s • four way ANOVA for four i.v.’s

4. 1 A 2 1 B 1 2 C 1 A 2 1 B 2 2

5. Effects Tested in Three-Way ANOVA: • A • B • C • AxB • AxC • BxC • AxBxC

6. three-way interaction: two-way interaction changes depending on the level of a third i.v. Example: Therapy, Drug, and Setting are manipulated in a 2x2x2 factorial. For inpatients, the effect of the drug is greater for people getting cognitive than behavior therapy. For outpatients, the effect of the drug is greater for people getting behavior therapy.

7. Drug Drug Placebo Prozac Placebo Prozac Beh Beh 20 60 40 20 Therapy Therapy 20 60 20 40 Cog Cog Inpatient Outpatient Setting

8. “Never Eat Anything Bigger Than Your Head” • Results of higher-order ANOVAs become difficult to interpret • Don’t do the analysis if you won’t know how to interpret it • You must always interpret the most complex effect that is significant