The null hypothesis for an ANOVA states that the group means are not different. In terms of the population means, van Rossum, van de Schoot, and Hoijtink (2013) stated the following null hypothesis for an ANOVA with four group means:
H0: μ1 = μ2 = μ3 = μ4.
(a) If a researcher was computing a two-way ANOVA, then how many levels of each factor must have been observed in this example with four group means?
(b) According to this text, and B. H. Cohen (2002), "the denominator of all three F ratios [for the two-way ANOVA] is the same" (p. 196). What is the denominator of the test statistic for each test with the two-way between-subjects ANOVA?