When the null hypothesis for an ANOVA analysis comparing four treatment means is rejected,________.
A)two comparisons of treatment means can be made
B)four comparisons of treatment means can be made
C)six comparisons of treatment means can be made
D)eight comparisons of treatment means can be made

Question

Quizplus · Accepted Answer

The number of possible pairwise comparisons between four treatment means is (n*(n-1))/2, where n is the number of treatment means. Therefore, for four treatment means, the number of possible pairwise comparisons is (4*(4-1))/2 = 6. When the null hypothesis is rejected in an ANOVA analysis, it means that at least one of the treatment means differs significantly from the others, but it does not indicate which specific means are different. Therefore, to further explore the differences between the means, post-hoc tests (such as Tukey's HSD or Bonferroni) can be conducted to make pairwise comparisons between the means. Since there are six possible pairwise comparisons for four treatment means, a post-hoc test can make up to six comparisons.

When the Null Hypothesis for an ANOVA Analysis Comparing Four