When the null hypothesis for an ANOVA analysis comparing four treatment means,is rejected,
A)4 comparisons of treatment means can be made.
B)8 comparisons of treatment means can be made.
C)12 comparisons of treatment means can be made.
D)16 comparisons of treatment means can be made.

Question

Quizplus · Accepted Answer

If the null hypothesis is rejected in an ANOVA analysis comparing four treatment means, we conclude that at least one of the treatment means is different from the others. To determine which specific means are different, post-hoc tests are conducted. There are several options for post-hoc tests, including Tukey's HSD, Bonferroni correction, and Scheffe's method. Regardless of the specific test used, the number of comparisons between treatment means is equal to the number of pairwise comparisons between the treatment groups, which is (4 choose 2) = 6. Since each pairwise comparison can be made in both directions (e.g. comparison 1-2 and 2-1), the total number of comparisons is 6 x 2 = 12. Therefore, choice C is correct.

When the Null Hypothesis for an ANOVA Analysis Comparing Four