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Non-parametric (or distribution-free) inferential statistical methods are mathematical procedures for statistical hypothesis testing which, unlike parametric statistics, make no assumptions about the probability distributions of the variables being assessed. The most frequently used tests include
Siegel–Tukey test, named after Sidney Siegel and John Tukey, is a non-parametric test which may be applied to data measured at least on an ordinal scale. It tests for differences in scale between two groups. The test is used to determine if one of two groups of data tends to have more widely dispersed values than the other.
Durbin test is a non-parametric statistical test for balanced incomplete designs that reduces to the Friedman test in the case of a complete block design. In the analysis of designed experiments , the Friedman test is the most common non-parametric test for complete block designs.
The Wilcoxon signed-rank test is a nonparametric test of nonindependent data from only two groups. The Skillings–Mack test is a general Friedman-type statistic that can be used in almost any block design with an arbitrary missing-data structure. The Wittkowski test is a general Friedman-Type statistics similar to Skillings-Mack test. When the ...
Nonparametric models differ from parametric models in that the model structure is not specified a priori but is instead determined from data. The term nonparametric is not meant to imply that such models completely lack parameters but that the number and nature of the parameters are flexible and not fixed in advance.
The logrank test statistic compares estimates of the hazard functions of the two groups at each observed event time. It is constructed by computing the observed and expected number of events in one of the groups at each observed event time and then adding these to obtain an overall summary across all-time points where there is an event.
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.
It is an extension of the Kruskal–Wallis test, the non-parametric equivalent for one-way analysis of variance , to the application for more than one factor. It is thus a non-parameter alternative to multi-factorial ANOVA analyses. The test is named after James Scheirer, William Ray and Nathan Hare, who published it in 1976. [1]