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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 Wald–Wolfowitz runs test (or simply runs test), named after statisticians Abraham Wald and Jacob Wolfowitz is a non-parametric statistical test that checks a randomness hypothesis for a two-valued data sequence. More precisely, it can be used to test the hypothesis that the elements of the sequence are mutually independent.
Parametric tests assume that the data follow a particular distribution, typically a normal distribution, while non-parametric tests make no assumptions about the distribution. [7] Non-parametric tests have the advantage of being more resistant to misbehaviour of the data, such as outliers . [ 7 ]
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]
Cochran's test is a non-parametric statistical test to verify whether k treatments have identical effects in the analysis of two-way randomized block designs where the response variable is binary. [ 1 ] [ 2 ] [ 3 ] It is named after William Gemmell Cochran .
That is, no parametric equation is assumed for the relationship between predictors and dependent variable. Nonparametric regression requires larger sample sizes than regression based on parametric models because the data must supply the model structure as well as the parameter estimates.
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.. In statistics, the Kolmogorov–Smirnov test (also 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.