An ANOVA is when we want to run a means test on more than 2 groups. However, the same basic structure of the hypothesis testing that we have done remains.
Using the hockey data, test if there is a difference between the true average number of goals scored by the different divisions. Second, test if there is a difference between the actual mean number of goals allowed by teams of different quality (where teams with at least 100 points are the top tier, those with 90-99 are the middle tier, and those with less than 90 make up the bottom tier).
If either of these tests shows significance, run a multiple comparison test among the groups. (Note that this is essentially the two-sample testing we just did but with an adjustment to ensure that we don’t have inflated error probabilities.) Use a 0.05 significance level for all tests.
As you do this for your own data set, ensure that at least one of the two problems shows the significance and requires pairwise comparisons. My suggestion is to not test more than 3 or 4 groups, but there’s nothing that says you can’t have more groups than that.
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