Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 8 population means (from equal sized samples) are not all equal. We
Should expect that
A) at least 4 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Tukey test.
B) at least 8 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X }$, would be significant using the Tukey test.
C) at least 1 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X }$, would be significant using the Tukey test.
D) all 28 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Tukey test.

Question

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 8 population means (from equal sized samples) are not all equal. We
Should expect that 
A) at least 4 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Tukey test.
B) at least 8 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X }$, would be significant using the Tukey test.
C) at least 1 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X }$, would be significant using the Tukey test.
D) all 28 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Tukey 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 comparisons are significantly different. Therefore, we can only be certain that at least one comparison among the means will be significant, not the exact number or which ones.

Assume That the Conclusion from an ANOVA Is That the Null