Most statistical procedures in CoStat (including Statistics : Correlation, Statistics : Descriptive, and parts of Statistics : Frequency Analysis and Statistics : Miscellaneous) assume that the data is normally distributed. Sometimes there are other assumptions; for example, standard ANOVAs assume that the variances of the subgroups are homogeneous. These assumptions allow the tests to make powerful inferences about the data.
For some datafiles, the assumptions are not valid. Several other tests have been devised ("nonparametric" tests) which do not make assumptions about the distribution of the data. Most of these tests rank the data and then do statistical tests with the ranked values. These tests are generally not as powerful (that is, not as good at rejecting the null hypothesis) as the traditional tests, but they are very useful when you can't use the traditional tests.
Unfortunately, there aren't replacement nonparametric tests for all of the traditional tests. CoStat has these options (on the Statistics : Nonparametric menu):