Assume that the conclusion from an ANOVA is that the null hypothesis is rejected; in other words, the 4 population means are not all equal. We should expect that:
A) all 6 of the comparisons of means $\bar { X } _ { i \text { versus } } \bar { X } _ { j \text { would be significant using the Scheffé test. } }$
B) at least 4 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j \text { would be significant using the Scheffé test. } }$
C) at least 2 of the comparisons of means $\bar { X } _ { i \text { versus } } \overline { \mathrm { X } } _ { \text {jwould be significant using the Scheffé test. } }$
D) at least 1 of the comparisons of means $\bar { X } _ { i v e r s u s } \bar { X } _ { \text {jwould be significant using the Scheffé test. } }$

Question

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected; in other words, the 4 population means are not all equal. We should expect that: 
A) all 6 of the comparisons of means $\bar { X } _ { i \text { versus } } \bar { X } _ { j \text { would be significant using the Scheffé test. } }$
B) at least 4 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j \text { would be significant using the Scheffé test. } }$
C) at least 2 of the comparisons of means $\bar { X } _ { i \text { versus } } \overline { \mathrm { X } } _ { \text {jwould be significant using the Scheffé test. } }$
D) at least 1 of the comparisons of means $\bar { X } _ { i v e r s u s } \bar { X } _ { \text {jwould be significant using the Scheffé test. } }$

Quizplus · Accepted Answer

Since the null hypothesis is rejected, we know that at least one of the means is significantly different from the others. The Scheffé test is a conservative post-hoc test that controls for Type I error rate, so it is expected to have a lower power than other post-hoc tests. Therefore, we should expect at least one significant comparison out of the six possible comparisons, but not necessarily all of them. Thus, the best choice is D, which corresponds to at least one significant comparison.

Assume That the Conclusion from an ANOVA Is That the Null