Scheirer-Ray-Hare test

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The Scheirer Ray Hare test or SRH test is a statistical test that can be used to examine whether a measured variable is influenced by two or more factors. Since it does not make any assumptions about the distribution of the model errors, it is a nonparametric method . It is an extension of the Kruskal-Wallis test , the nonparametric equivalent for the way analysis of variance ( English analysis of variance , shortly ANOVA ), the application for more than one factor. It thus represents a non-parametric alternative to multi- factor analysis of variance . The test is named after James Scheirer, William Ray and Nathan Hare, who published it in 1976.

Test description

The Scheirer-Ray-Hare test is used analogously to the parametric multi-factorial analysis of variance to examine the influence of two different factors on a measured variable for which different samples are available with regard to the factors . As with parametric analysis of variance, the test can be used to examine the null hypotheses that the two examined factors have no influence on the location parameters of the samples and thus on the measured variable, and that there are no interactions between the two factors. A p-value of less than 0.05 for one or more of these three hypotheses leads to their rejection. As with many other non-parametric methods, the analysis in this method relies on evaluating the ranks of the values ​​in the samples rather than the actual observation values. Modifications allow the test to be expanded to include more than two factors.

The test strength of the Scheirer-Ray-Hare test, i.e. the probability of actually finding a statistically significant result, is significantly lower than that of the parametric multi-factorial analysis of variance, so that it is considered more conservative in a comparison of the two methods. For this reason, and because the method was described later than most other parametric and non-parametric tests for analysis of variance, it has so far not found much use in textbooks and software for statistical data analysis . With computer programs that contain a function for parametric multi-factorial variance analysis, it is also possible to calculate the Scheirer-Ray-Hare test with additional manual effort.

Since the Scheirer-Ray-Hare test only makes a statement about the differences in all samples considered, it makes sense to carry out a post-hoc test that compares the individual samples in pairs.

Alternative procedures

The parametric alternative to the Scheirer-Ray-Hare test is the multi-factor analysis of variance, in which, however, a normal distribution of the data within the samples is a prerequisite. In contrast to this, the Kruskal-Wallis test , from which the Scheirer-Ray-Hare test is derived, is used to examine the influence of exactly one factor on the measured variable. A non-parametric test for comparing exactly two unpaired samples is the Wilcoxon-Mann-Whitney test .

Individual evidence

  1. ↑ James Scheirer, William S. Ray, Nathan Hare: The Analysis of Ranked Data Derived from Completely Randomized Factorial Designs. In: Biometrics. 32 (2 )/1976. International Biometric Society, pp. 429-434, doi : 10.2307 / 2529511
  2. ↑ a b c Scheirer-Ray-Hare test. In: Calvin Dytham: Choosing And Using Statistics: A Biologist's Guide. Wiley-Blackwell, 2003, ISBN 1-40-510243-8 , pp. 145-150

literature