Page 201 - Intermediate Statistics for Dummies

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Part III: Comparing Many Means with ANOVA
Pinpointing Differing Means
with Fisher and Tukey
You’ve conducted ANOVA to see whether a group of k populations have the
same mean, and you rejected Ho. You conclude that at least two of those pop-
ulations 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 multi-
ple comparison tests.
In this section, you see two of the most well-known multiple comparison pro-
cedures: Fisher’s paired differences (also known as Fisher’s test or Fisher’s LSD)
and Tukey’s simultaneous confidence intervals (also known as Tukey’s test).
Although I only discuss two procedures in this section, tons of other multiple
comparison procedures are out there. Although the other procedures’
methods differ a great deal, their overall goal is the same: to figure out
which population means differ by comparing their sample means.
Fishing for differences with Fisher’s LSD
In this section, I outline Fisher’s LSD and apply it to the cell-phone example.
Examining Fisher’s LSD procedure
Suppose you’re comparing k population means. Fisher’s LSD (short for least
^
kk - 1h
significant difference) conducts a t-test on each of the pairs of popu-
2
lations in the study, each one at level α = 0.05. For example, if you have four
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44 - 1h
populations labeled A, B, C, D, you would have = 6 t-tests to perform:
2
A versus B; A versus C; A versus D; B versus C; B versus D; and C versus D.
The number of tests is calculated by knowing that you have k possible means
for the first one in the pair, then k – 1 left for the second one in the pair.
Because the order of the means doesn’t matter, you can divide by 2 to avoid
overcounting.
Fisher’s LSD is very straightforward, easy to conduct, and easy to understand.
However, Fisher’s LSD has some issues. Because each t-test is conducted at α
level 0.05, each test done has a 5 percent chance of making a Type I error
(rejecting Ho when you shouldn’t have — see Chapter 3). Although a 5-percent
error rate for each test doesn’t seem too bad, the errors have a multiplicative
effect as the number of tests increases. For example, the chance of making at
least one Type I error with six t-tests, each at level α = 0.05, is 26.50 percent,
which would be your overall error rate for the procedure.