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Answer :
Final answer:
In a 2x2 ANOVA test, we are comparing three effects against the null hypothesis: the main effects of the two factors and their interaction effect. In a 2x2x2 ANOVA, we compare seven effects: the main effects of the three factors, their three two-way interaction effects, and the one three-way interaction effect.
Explanation:
The student is asking about the number of effects being compared against their null hypothesis in both a 2x2 and a 2x2x2 ANOVA test. In a 2x2 ANOVA, we compare the main effects of two factors (A and B), as well as their interaction effect (AxB), thus totaling three effects.
In contrast, a 2x2x2 ANOVA involves three factors (A, B, and C), each with two levels, and we compare their main effects, all possible two-way interaction effects (AxB, AxC, and BxC), and the three-way interaction effect (AxBxC), amounting to seven different hypothesis tests. Hence, we have a total of three effects for 2x2 ANOVA and six effects for 2x2x2 ANOVA.
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