48 PART 1 Getting Started with Biostatistics
Chapter 24). Because the classic distribution functions are all written as mathe-
matical expressions involving parameters (like means and standard deviation),
they’re called parametric distribution functions.
Parametric tests assume that your data conforms to a parametric distribution func-
tion. Because the normal distribution is the most common statistical distribution,
the term parametric test is often used to mean a test that assumes normally dis-
tributed data. But sometimes your data don’t follow a parametric distribution. For
example, it may be very noticeably skewed, as shown in Figure 3-5a.
Sometimes, you may be able to perform a mathematical transformation of your
data to make it more normally distributed. For example, many variables that have
a skewed distribution can be turned into normally distributed numbers by taking
logarithms, as shown in Figure 3-5b. If, by trial and error, you can find some kind
of transformation that normalizes your data, you can run the classical tests on the
transformed data, as described in Chapter 9.
If you transform your data to get it to assume a normal distribution, any analyses
done on it will need to be “untransformed” to be interpreted. For example, if you
have a data set of patients with different lengths of stay in a hospital, you will
likely have skewed data. If you log-transform these data so that they are normally
distributed, then generate statistics (like calculate a mean), you will need to do an
inverse log transformation on the result before you interpret it.
But sometimes your data are not normally distributed, and for whatever reason,
you give up on trying to do a parametric test. Maybe you can’t find a good trans-
formation for your data, or maybe you don’t want to have to undo the transfor-
mation in order to do your interpretation, or maybe you simply have too small of
FIGURE 3-5:
Skewed data (a)
can sometimes
be turned into
normally
distributed data
(b) by taking
logarithms.
© John Wiley & Sons, Inc.