What is mean separation?
Sometimes called "multiple comparisons", mean separations are comparisons of every pair of means. Since the ANOVA test for treatments will only show if at least one mean differs from the others, the objective is to identify where and how many differences exist.
For example, suppose you have 4 treatments, and the ANOVA test gives P=.0238. We conclude that at least one of the treatments is different. But we have no information about how they differ. Possibly Treat1 differs from Treat2 and Treat3, but not from Treat4.
Mean separation works by comparing 1 to 2, 1 to 3, 1 to 4, 2 to 3, 2 to 4, and 3 to 4. By making all these comparisons, you can see that we will surely find where the differences occur.
Note that the number of tests is: t*(t-1)/2
where t is the number of treatments. This is a large number, and one difficulty is how to report the results.
A common convention is to use letters. For the example above, results might look like:
Again by convention, the highest mean is assigned the letter A. Since treatments 2, 3 and 4 all have A, they are not different. Treatment 1 does differ from treatments 2 and 3, since they have no letter in common. But treatment 1 does not differ from treatment 4. In fact, treatment 4 does not differ from any other mean, as it has a letter in common with all other treatments.