Question

The null hypothesis for an Analysis of Variance (ANOVA) problem usually states that all treatment means are equal (at the population level, not the sample level). In order to reject such a null hypothesis, how many treatment means must be different from the other treatment means?

Answer 1

Answer:

To reject such a null hypothesis, at least one of the treatment mean must be different from the other treatment means.

Explanation:

In the ANOVA, there are two possible hypotheses:

• The null hypothesis, H₀: μ₁=μ₂=μ₃=μₙ. It states that all treatment means are equal to each other.

• The alternative hypothesis, H₁ states that at least one of the treatments means is different.

When the p-value of the ANOVA test is inferior to the alfa-level of signification chosen for the analysis, then we can reject the null hypothesis. This means that there is at least one mean of the groups under study that is different from the rest.

We can get all the means values different from each other, or just some of them. But having only one different mean value is enough to reject the null hypothesis.