Page 32 - Statistics II for Dummies

16 Part I: Tackling Data Analysis and Model-Building Basics

Then, to test for differences in average lifetime for the four brands of tires,
you basically compare the variability between the four data sets to the
variability within the entire data set, using a ratio. This ratio is called the
F-statistic. If this ratio is large, the variability between the brands is more than
the variability within the brands, giving evidence that not all the means are
the same for the different tire brands. If the F-statistic is small, not enough
difference exists between the treatment means compared to the general vari-
ability within the treatments themselves. In this case, you can’t say that the
means are different for the groups. (I give you the full scoop on ANOVA plus
all the jargon, formulas, and computer output in Chapters 9 and 10.)

Multiple comparisons

Suppose you conduct ANOVA, and you find a difference in the average life-
times of the four brands of tire (see the preceding section). Your next ques-
tions would probably be, “Which brands are different?” and “How different
are they?” To answer these questions, 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. With this information, you’re 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 are placed together
in a group.

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. 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.

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. Computer
software will never stop you from doing a follow-up analysis, even if it’s wrong
to do so.

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 were to take the two
individual medications separately.

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