Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Parametric and Non-Parametric Tests

Statistical tests can be divided into two groups (depending on their prerequisites):

  • parametric tests which are sometimes called non-distribution-free tests, and
  • distribution-free or nonparametric tests.

The expression parametric tests comes from the fact that these tests are based on the parameters of a particular distribution (e.g. a normal distribution).

In contrast to these stand the distribution-free or nonparametric tests: such tests do not make any assumptions about an underlying distribution of the data.

Given a particular level of significance the associated type II error is always higher with nonparametric tests than with parametric tests. Parametric tests show a greater power than nonparametric ones. This fact is the reason why one should always prefer a parametric test if the specific assumptions of this test are met.

Another important point for the decision which test to apply is the level of measurement of the data. Parametric tests always require metric scales, ordinal or nominal data must not be tested by parametric tests. Although there are reports that (Baker et al. ) that parametric tests of the t-family are relatively insensitive against violations of the level of measurement requirement.