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Question

There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they? State the null hypothesis for a one-way ANOVA test if there are four groups.

Solution

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The null hypothesis is simply that all the group population means are the same. The null hypothesis for the four groups is given below:

$H_{0} : \mu_{1}=\mu_{2}=\mu_{3}=\ldots=\mu_{k}$

Where, $\mu_{1}$ is the mean of the first group, $\mu_{2}$ is the mean of the second group, $\mu_{3}$ is the mean of the third group and $\mu_{k}$ is the mean of the k-th group.

In our case k=4, so, our null hypothesis will be:

$H_{0} : \mu_{1}=\mu_{2}=\mu_{3}=\mu_{4}$

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