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Statistical tests are used to test the fit between a hypothesis and the data. [1] [2] Choosing the right statistical test is not a trivial task. [1]The choice of the test depends on many properties of the research question.
The wider applicability and increased robustness of non-parametric tests comes at a cost: in cases where a parametric test's assumptions are met, non-parametric tests have less statistical power. In other words, a larger sample size can be required to draw conclusions with the same degree of confidence.
The Wilcoxon signed-rank test is a non-parametric rank test for statistical hypothesis testing used either to test the location of a population based on a sample of data, or to compare the locations of two populations using two matched samples. [1] The one-sample version serves a purpose similar to that of the one-sample Student's t-test. [2]
Nonparametric models are therefore also called distribution free. Nonparametric (or distribution-free) inferential statistical methods are mathematical procedures for statistical hypothesis testing which, unlike parametric statistics, make no assumptions about the frequency distributions of the variables being assessed.
Not all statistical packages support post-hoc analysis for Friedman's test, but user-contributed code exists that provides these facilities (for example in SPSS, [10] and in R. [11]). Also, there is a specialized package available in R containing numerous non-parametric methods for post-hoc analysis after Friedman. [12]
Illustration of the Kolmogorov–Smirnov statistic. The red line is a model CDF, the blue line is an empirical CDF, and the black arrow is the KS statistic.. Kolmogorov–Smirnov test (K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section 2.2), one-dimensional probability distributions that can be used to test whether a sample came from a ...
Median test (also Mood’s median-test, Westenberg-Mood median test or Brown-Mood median test) is a special case of Pearson's chi-squared test. It is a nonparametric test that tests the null hypothesis that the medians of the populations from which two or more samples are drawn are identical. The data in each sample are assigned to two groups ...
In statistics, the Brunner Munzel test [1] [2] [3] (also called the generalized Wilcoxon test) is a nonparametric test of the null hypothesis that, for randomly selected values X and Y from two populations, the probability of X being greater than Y is equal to the probability of Y being greater than X.