Suppose we are trying to find the effects of 3 categorical variables on the response (numerical) variable. Factor A with a levels, Factor B with b levels, and Factor C with c levels. Therefore, there are a.b.c treatments and (as a result) a.b.c population means (Let g=a.b.c). Our goal is to test the hypothesis:
Ho: μ1 = μ2 = ... = μg = μ vs.
Ha: At least one of μi ≠ μ.
Use the same method we developed for TWO-WAY ANOVA in class to test the hypothesis of equality of all population means (hypothesis stated above). State all null and alternative hypotheses we need firstly to test in order to test the final hypothesis and explain your procedure. Hint: Your procedure must contain 7 hypotheses. At each step we test a hypothesis, if we fail to reject the null hypothesis we will continue, and if we reject the null hypothesis we will stop.