"There are three kinds of lies: lies, damned lies, and
statistics"

declared Mark Twain, or Benjamin Disraeli, or somebody.

A common error made by people doing statistical tests is to forget
about their underlying assumptions.

Some of the most commonly used statistical tests are based upon sample
values taken from populations. These tests make assumptions about the
distributions of those populations. The efficacy of those tests
have been proven using parametric equations that describe the assumed underlying
distributions, and so they are called parametric tests.

A test performed on samples that do not meet the test's underlying assumptions
is meaningless, so much numerical masturbation.

Although different tests make different assumptions, the most common
assumption is for a normal distribution of the population values.
Unfortunately, populations that are not normally distributed (especially
in the social sciences) appear with alarming frequency.

What happens then when your sample values don't match the assumptions
of the test you wanted? Use a test that doesn't make those assumptions.

One test that does not assume anything about a population's distribution
is the chi square^{1} test; another is the Kolmogorov - Smirnov test, which can be used to determine if a population sample follows a given distribution (such as a normal distribution).

Many parametric tests have counterparts that are based upon the *order*
of the values, rather than the actual values:

These tests are not as powerful as their parametric counterparts when the
assumptions are met, but at least you're not generating gibberish when
they're not met.

(If you use the SPSS statistical package, a whole hierarchy of commands
beginning with NPAR TESTS is available for use).

So, in the future, you're going to test your samples for a normal distribution
before performing a parametric test, right?

^{1}If that link doesn't work, try

chi-square