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Chapter 10: Sorting Out the Means with Multiple Comparisons 177

✓ Purpose: When you know that a group of means aren’t all equal, you
zoom in to explore the relationships between them, depending on the
purpose of your research. Maybe you just want to figure out which
means are equivalent and which are not. Maybe you want to sort them
into statistically equivalent groups from smallest to largest. Or it may be
important to compare the average of one group of means to the average
of another group of means. Different multiple comparison procedures
were built for different purposes; for the most part, if you use them for
their designed purposes, you have a better chance of finding specific dif-
ferences you’re looking for, if those differences are actually there.
✓ Price: Any statistical procedure you use comes with a price: the prob-
ability of making a Type I error in your conclusions somewhere during
the procedure, due to chance. (A Type I error is committed when Ho is
rejected when it shouldn’t be; in other words, you think two means are
different but they really aren’t. See your Stats I textbook or my book
Statistics For Dummies (Wiley) for more info.) This probability of making
at least one Type I error during a multiple comparisons procedure is
called the overall error rate (also known as the experimentwise error
rate (EER), or the familywise error rate). Small overall error rates are
of course desirable. Each multiple comparison procedure has its own
overall error rate; generally the more specific the relationships are that
you’re trying to find, the smaller your overall error rate is, assuming
you’re using a procedure that was designed for your purpose.
In the next section, I describe two all-purpose multiple comparison pro-
cedures: Fisher’s LSD and Tukey’s test.
Don’t attempt to explore the data with a multiple comparison procedure if the
test for equality of the populations isn’t rejected. In this case, you must con-
clude that you don’t have enough evidence to say the population means aren’t
all equal, so you must stop there. Always look at the p-value of the F-test on
the ANOVA output before moving on to conduct any multiple comparisons.

Pinpointing Differing Means

with Fisher and Tukey

You’ve conducted ANOVA to see whether a group of k populations has the
same mean, and you rejected Ho. You conclude that at least two of those
populations have different means. But you don’t have to stop there; you can
go on to find out how many and which means are different by conducting
multiple comparison tests.

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