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 9 population means (from equal sized samples) are not all equal. We should expect that all 36 of the comparisons of means versus would be significant using the Tukey test.

at least 9 of the comparisons of means versus would be significant using the Tukey test.

at least 5 of the comparisons of means versus would be significant using the Tukey test.

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

Explanation / Answer

If ANOVA is rejected, it means that at least one of the comparisons of means would be significant. Only one such difference can result in the rejected the ANOVA null hypothesis.

So the correct answer is :

at least 1 of the comparisons of means versus would be significant using the Tukey test

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