We
are going to compare multiple groups (beyond two) on the basis of sample means.
Suppose we want to compare the effects of more than 2 different food
supplements on children height. So in this case we ran an experiment to compare
the effects of 3 supplements. This can be translated in testing the null
hypothesis that the mean heights of children is equal whatever they received
(supplement 1, supplement 2 or supplement 3) against the alternative that at
least one of three supplement’s treatment is different from others i.e.; three
supplements do not create the same effects on children height.

Ha:
At least one of the three is different from the others.

Based
upon this test we can get know whether we could reject the null hypothesis or
accept the alternative hypothesis and vice versa. This test tells us that small
differences between sample means are usually present but it is not confirmed
that they are significant. It is further noticed that the general alternative
does not clearly specify which sample means are different from one another but
only there exist some differences.