Page 44 - Intermediate Statistics for Dummies

05_045206 ch01.qxd 2/1/07 9:41 AM Page 23
Chapter 1: Beyond Number Crunching: The Art and Science of Data Analysis
Multiple comparisons
Suppose you conduct ANOVA, and you find a difference in the average life-
times of the four brands of tire (see preceding section). Your next questions
would probably be, which brands are different, and how different are they?
To answer these questions, you use multiple-comparison procedures.
A multiple-comparison procedure is a statistical technique that compares
means to each other and finds out which ones are different and which ones
aren’t. You’re then able to put the groups in order, from those with the largest
mean to those with the smallest mean, realizing that sometimes two or more
groups were too close to tell and so you put them in the same group.
Suppose you compare the exam scores of four different classes (call them
class one, class two, class three, and class four), and your ANOVA procedure
finds out that not all the means were the same. That means the F-statistic is
large. Next, you use multiple-comparison procedures in order to make sepa-
rate comparisons and figure out which classes were about the same and 23
which ones were different, and come up with an ordering of the classes. It
may be, for example, that class four was statistically higher than all the
others; classes one and two were statistically equivalent, but both were lower
than class four. And class one was in a group all by itself at the bottom. The
ordering is: class four (highest average), classes two and three (tied for
second highest), and class one (the lowest average).
Never take that second step to compare the means of the groups if the ANOVA
procedure doesn’t find any significant results during the first step. (See Chap-
ter 11 for more information.)
Many different multiple-comparison procedures exist to compare individual
means and come up with an ordering in the event that your F-statistic does
find that some difference exists. Some of the multiple-comparison procedures
include Tukey’s test, LSD, and pairwise t-tests. (While these tests’ names may
cause you to raise an eyebrow, don’t worry. They’re legitimate statistical
tests.) Some procedures are better than others, depending on the conditions
and your goal as a data analyst. I discuss multiple-comparison procedures in
detail in Chapter 11.
Interaction effects
An interaction effect in statistics operates the same way that it does in the
world of medicine. Sometimes if you take two different medicines at the same
time, the combined effect is much different than if you take the two individual
medications separately.