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Distribution-Free Tests

Most statistical tests assume normal distributions. Any deviation from normality can distort the results. Usually the type I error-rate decreases when normality assumptions are violated. While this seems to be good at first sight, it also substantially decreases the power of the test.

In order to cope with these situations, tests have been developed which do not assume any special distribution (thus the name "distribution-free tests"). Distribution-free tests are also called non-parametric tests. These tests are always weaker than parametric tests (typically, the efficiency of non-parametric tests falls into the range of 90 to 95 %).

Note: The efficiency of a test is specified by the ratio of the number of observations required for a parametric test (to achieve a predefined level of significance) to the number of observations required by the non-parametric test.

Last Update: 2005-Jšn-25