Page 203 - Statistics II for Dummies

Chapter 10: Sorting Out the Means with Multiple Comparisons 187

Compared to other multiple comparison procedures, Dunnett’s test is better
able to find real differences in this situation because it focuses only on the
differences between each treatment and the control — not on the differences
between every single pair of treatments in the entire study.

Staying cool with Student Newman-Keuls

Student Newman-Keuls test is a different approach from Tukey and Fisher
in comparing pairs of means in a multiple comparison procedure. This test
comes from the work of three people: “Student,” Newman, and Keuls.

The Student Newman-Keuls procedure is based on a stepwise or layer
approach. You order sample means from the smallest to the largest and then
examine the differences between the ordered means.

You first test the largest minus smallest difference, and if that turns out to be
statistically significant, you conclude that their two respective populations
are different in terms of their means. Of the remaining means, the ones that
are farthest apart in the order are tested for a significant difference, and so
on. You stop when you don’t find any more differences.

Duncan’s multiple range test

David B. Duncan designed the Duncan’s multiple range test (MRT) in 1955.
The test is based on the Student Newman-Keuls test but has increased power
in its ability to detect when the null hypothesis is not true (see Chapter 3)
because it increases the value of α at each step of the Student Newman-Keul’s
test. Duncan’s test is used especially in agronomy (crop and farm land man-
agement) and other types of agricultural research. One of the neatest things
about being a statistician is you never know what kinds of problems you’ll be
working on or who will use your methods and results.

Although Duncan won the favor of many researchers who used his test (and
still do), he wasn’t without his critics. Both John Tukey (who developed
Tukey’s test) and Henry Scheffe (who developed Scheffe’s test) accused
Duncan’s test of being too liberal by not controlling the rate of an overall
error (called a familywise error rate in the big leagues). But Duncan stood his
ground. He said that means are usually never equal anyway, so he wanted to
err on the side of making a false alarm (Type I error) rather than missing an
opportunity (Type II error) to find out when means are different.
Every procedure in statistics has some chance of making the wrong conclu-
sion, not because of an error in the process but because results vary from
data set to data set. You just have to know your situation and choose the
procedure that works best for that situation. When in doubt, consult a
statistician for help in sorting it all out.

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