Multiple Comparisons
After a one-way ANOVA rejects $H_0$, the next question is usually which treatment means differ from each other.
If there are $k$ treatments, then the number of pairwise comparisons is
$$ c = \binom{k}{2}. $$Performing many pairwise tests creates a multiple comparison problem because the chance of making at least one false rejection increases with the number of comparisons.