Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 5 population means are not all equal. We should expect that
A) at least 3 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Scheffe test.
B) at least 5 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X }$, would be significant using the Scheffe test.
C) all 10 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Scheffe test.
D) at least 1 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Scheffe test.

Question

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 5 population means are not all equal. We should expect that 
A) at least 3 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Scheffe test.
B) at least 5 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X }$, would be significant using the Scheffe test.
C) all 10 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Scheffe test.
D) at least 1 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Scheffe test.

Quizplus · Accepted Answer

Rejecting the null hypothesis in ANOVA only indicates that not all population means are equal; it does not specify how many or which specific comparisons are significantly different. The Scheffe test, a post-hoc analysis, is used to investigate specific differences between means. Therefore, at a minimum, we should expect at least one comparison to be significant, but there's no guarantee on the exact number of significant comparisons beyond that.

Assume That the Conclusion from an ANOVA Is That the Null