Assume that the conclusion from an ANOVA is that the null hypothesis is rejected

Question

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 6 population means (from equal sized samples) are not all equal. We should expect that

A. at least 3 of the comparisons of means Xi versus Xj would be significant using the Tukey test.

b. all 15 of the comparisons of means Xi versus Xj would be  significant using the Tukey test.

c. at least 1 of the comparisons of means Xi versus Xj would be significant using the Tukey test.

d. at least 6 of the comparisons of means Xi versus Xj would be significant using the Tukey test.

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 6 population means (from equal sized samples) are not all equal. We should expect that

A. at least 3 of the comparisons of means Xi versus Xj would be significant using the Tukey test.

b. all 15 of the comparisons of means Xi versus Xj would be  significant using the Tukey test.

c. at least 1 of the comparisons of means Xi versus Xj would be significant using the Tukey test.

d. at least 6 of the comparisons of means Xi versus Xj would be significant using the Tukey test.

Explanation / Answer

When we use ANNOVA the null hypothesis is "all means are equal" and alternate hypothesis is "atleast one of the mean is not equal. Rejection of null hypothesis is equivalent to accepting alternate hypothesis and hence our conclusion should be

c. at least 1 of the comparisons of means Xi versus Xj would be significant using the Tukey test.

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