Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
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See also: randomization tests, hypothesis testing  
DistributionFree Tests
Most statistical tests require to know the distribution of the statistic (i.e. a normal distribution, or an F distribution. Any deviation from normality can distort the results. Usually the type I errorrate 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 "distributionfree tests"). Distributionfree tests are also called nonparametric tests. These tests are always weaker than parametric tests (typically, the efficiency^{1} of nonparametric tests falls into the range of 90 to 95 %).
Typical examples of nonparametric tests are the KolmogorowSmirnow test for normality, the MannWhitney U test for comparing means, the Wilcoxon test for comparing medians of two samples, or the runs test to check the randomness of a series of random numbers.


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Last Update: 20121008