146 PART 4 Comparing Groups
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» The values come from two or more different participants who have been
paired, or matched, in some way as part of the study design. For example,
in a study of participants who have Alzheimer’s disease compared to healthy
participants, investigators may choose to age-match each Alzheimer’s patient
to a healthy control when they recruit so both groups have the same age
distribution.
Comparing means of matched pairs
If you have paired data, you must use a paired comparison. Paired comparisons are
usually handled by the paired student t test that we describe later in this chapter
under “Surveying Student t tests.” If your data aren’t normally distributed, you
can use the nonparametric Wilcoxon Signed-Ranks test instead.
The paired Student t test and the one-group Student t test are actually the same
test. When you run a paired t test, the statistical software first calculates the dif-
ference between each pair of numbers. If comparing a post-treatment value to a
pretreatment value, the software would start by subtracting one value from the
other for each participant. Finally, the software would run a test to see if those
mean differences were statistically significantly different from the hypothesized
value of 0 using a one-group test.
Using Statistical Tests for
Comparing Averages
Now that you have reviewed the different types of comparisons, you can continue
to consider the basic concepts behind them as you dig more deeply. In this section,
we discuss executing these tests in statistical software and interpreting the out-
put. We do that with several tests, including Student t tests, the ANOVA, and non-
parametric tests.
We opted not to clutter this chapter with pages of mathematical formulas for the
following tests because based on our own experience, we believe you’ll probably
never have to do one of these tests by hand. If you really want to see the formulas,
we recommend putting the name of the test in quotes in a search engine and look-
ing on the Internet.