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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, one consisting of data whose values are higher than the median value in the two groups combined, and the other consisting of data whose values are at the median or below. A Pearson's chi-squared test is then used to determine whether the observed frequencies in each sample differ from expected frequencies derived from a distribution combining the two groups.
Relation to other testsedit
The test has low power (efficiency) for moderate to large sample sizes. The Wilcoxon–Mann–Whitney U two-sample test or its generalisation for more samples, the Kruskal–Wallis test, can often be considered instead. The relevant aspect of the median test is that it only considers the position of each observation relative to the overall median, whereas the Wilcoxon–Mann–Whitney test takes the ranks of each observation into account. Thus the other mentioned tests are usually more powerful than the median test. Moreover, the median test can only be used for quantitative data.[1]
It is crucial to note, however, that the null hypothesis verified by the Wilcoxon–Mann–Whitney U (and so the Kruskal–Wallis test) is not about medians. The test is sensitive also to differences in scale parameters and symmetry. As a consequence, if the Wilcoxon–Mann–Whitney U test rejects the null hypothesis, one cannot say that the rejection was caused only by the shift in medians. It is easy to prove by simulations, where samples with equal medians, yet different scales and shapes, lead the Wilcoxon–Mann–Whitney U test to fail completely.[2]
However, although the alternative Kruskal-Wallis test does not assume normal distributions, it does assume that the variance is approximately equal across samples. Hence, in situations where that assumption does not hold, the median test is an appropriate test. Moreover, Siegel & Castellan (1988, p. 124) suggest that there is no alternative to the median test when one or more observations are "off the scale."
See alsoedit
Sign test – a paired alternative to the median test.
^Divine, George W.; Norton, H. James; Barón, Anna E.; Juarez-Colunga, Elizabeth (2018-07-03). "The Wilcoxon–Mann–Whitney Procedure Fails as a Test of Medians". The American Statistician. 72 (3): 278–286. doi:10.1080/00031305.2017.1305291. ISSN 0003-1305.
Siegel, S., & Castellan, N. J. Jr. (1988, 2nd ed.). Nonparametric statistics for the behavioral sciences. New York: McGraw–Hill.
Friedlin, B. & Gastwirth, J. L. (2000). Should the median test be retired from general use? The American Statistician, 54, 161–164.
January 01, 1970
median, test, help, expand, this, article, with, text, translated, from, corresponding, article, german, june, 2013, click, show, important, translation, instructions, machine, translation, like, deepl, google, translate, useful, starting, point, translations,. You can help expand this article with text translated from the corresponding article in German June 2013 Click show for important translation instructions Machine translation like DeepL or Google Translate is a useful starting point for translations but translators must revise errors as necessary and confirm that the translation is accurate rather than simply copy pasting machine translated text into the English Wikipedia Consider adding a topic to this template there are already 9 118 articles in the main category and specifying topic will aid in categorization Do not translate text that appears unreliable or low quality If possible verify the text with references provided in the foreign language article You must provide copyright attribution in the edit summary accompanying your translation by providing an interlanguage link to the source of your translation A model attribution edit summary is Content in this edit is translated from the existing German Wikipedia article at de Median Test see its history for attribution You may also add the template Translated de Median Test to the talk page For more guidance see Wikipedia Translation 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 one consisting of data whose values are higher than the median value in the two groups combined and the other consisting of data whose values are at the median or below A Pearson s chi squared test is then used to determine whether the observed frequencies in each sample differ from expected frequencies derived from a distribution combining the two groups Relation to other tests editThe test has low power efficiency for moderate to large sample sizes The Wilcoxon Mann Whitney U two sample test or its generalisation for more samples the Kruskal Wallis test can often be considered instead The relevant aspect of the median test is that it only considers the position of each observation relative to the overall median whereas the Wilcoxon Mann Whitney test takes the ranks of each observation into account Thus the other mentioned tests are usually more powerful than the median test Moreover the median test can only be used for quantitative data 1 It is crucial to note however that the null hypothesis verified by the Wilcoxon Mann Whitney U and so the Kruskal Wallis test is not about medians The test is sensitive also to differences in scale parameters and symmetry As a consequence if the Wilcoxon Mann Whitney U test rejects the null hypothesis one cannot say that the rejection was caused only by the shift in medians It is easy to prove by simulations where samples with equal medians yet different scales and shapes lead the Wilcoxon Mann Whitney U test to fail completely 2 However although the alternative Kruskal Wallis test does not assume normal distributions it does assume that the variance is approximately equal across samples Hence in situations where that assumption does not hold the median test is an appropriate test Moreover Siegel amp Castellan 1988 p 124 suggest that there is no alternative to the median test when one or more observations are off the scale See also editSign test a paired alternative to the median test References edit http psych unl edu psycrs handcomp hcmedian PDF bare URL PDF Divine George W Norton H James Baron Anna E Juarez Colunga Elizabeth 2018 07 03 The Wilcoxon Mann Whitney Procedure Fails as a Test of Medians The American Statistician 72 3 278 286 doi 10 1080 00031305 2017 1305291 ISSN 0003 1305 Corder G W amp Foreman D I 2014 Nonparametric Statistics A Step by Step Approach Wiley ISBN 978 1118840313 Siegel S amp Castellan N J Jr 1988 2nd ed Nonparametric statistics for the behavioral sciences New York McGraw Hill Friedlin B amp Gastwirth J L 2000 Should the median test be retired from general use The American Statistician 54 161 164 Retrieved from https en wikipedia org w index php title Median test amp oldid 1205847746, wikipedia, wiki, book, books, library,
