Question

Which of the following is NOT​ true?

A. The F test statistic is very sensitive to sample​ means, even though it is obtained through two different estimates of the common population variance.
B. If the decision from ANOVA is to reject the equality of the three population​ means, the particular mean that differs from the others is known.
C. When testing for equality of three population​ means, do not use multiple hypothesis tests with two samples at a time.
D. As the number of tests of significance​ increase, the risk of finding a difference by chance alone increases.

Answer 1

Explanation:

The statement that is NOT true is option B. If the decision from ANOVA is to reject the equality of the three population means, the particular mean that differs from the others is known.

In ANOVA (Analysis of Variance), when we reject the equality of the three population means, it indicates that there is at least one mean that differs from the others. However, ANOVA does not provide information about which specific mean is different. To determine which mean(s) is different, additional tests, such as post-hoc tests or pairwise comparisons, need to be conducted.

Therefore, option B is not true.