Overview of Distribution-Free Tests (1 of 2)
Most
inferential statistics assume
normal distributions. Although these statistical tests work well
even if the assumption of normality is violated, extreme deviations from
normality can distort the results. Usually the effect of violating the
assumption of normality is to decrease the
Type
I error rate.
although this may sound like a good thing, it often is accompanied by
a substantial decrease in
power. Moreover,
in some situations the Type I error rate is increased.
There is
a collection of tests called distribution-free tests that do not make
any assumptions about the distribution from which the numbers were
sampled. Thus the name, "distribution-free." The main advantage
of distribution-free tests is that they provide more power than traditional
tests when the samples are from highly-
skewed distributions.
Since alternative means of dealing with skewed distributions such as
taking logarithms or square roots of the data are available, distribution-free
tests have not achieved a high level of popularity. Distribution-free
tests are nonetheless a worthwhile alternative. Moreover, computer
analysis has made possible new and promising variations of these tests.