A researcher using a factorial design for his study ends up

A researcher using a factorial design for his study ends up comparing twelve independent samples to one another. Using the ANOVA technique, she discovers that there is a significant difference between at least two of the samples. She begins to compare the samples to each other, taken two at a time. For each comparison, she decides to use an a-level of 0.05.

How many comparisons will she make altogether?

What is her overall experiment-wise error rate?

Which multiple-comparison correction would be best suited for this analysis? Why?

Solution

Number of comparisons = 12C2 = 66

Overall error = 1-(1-0.05)^12 =0.4596

I would suggest the Tukey Kramer procedure for comparison of means.