Median test

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The median test , also known as Mood's median test , Westenberg mood median test or Brown Mood median test , is a statistical test that can be used to examine whether two or more independent samples from populations with the same thing Median originate. Since the test does not make any assumptions about the frequency distribution of the data, it is a non-parametric method . The median test is very easy to carry out, but is considered obsolete for most applications due to its low test strength compared to alternative methods . Generally attributed to Alexander McFarlane Mood.

Test description

The median test assumes independence of the values ​​both between the samples and within the samples. In addition, the values ​​must have been determined by random selection from the population . The test is not tied to a specific frequency distribution of the data, but the density function near the median value and thus the shape of the distribution should be similar between the samples.

To carry out the median test, the common median of all values ​​is first determined after combining the samples. The values ​​are then assigned to two groups within each sample, depending on whether they are larger or smaller than the common median. There are various options for treating values ​​that are exactly the same as the common median. If their number is small compared to the total number of values, they can either be ignored or they are distributed among the groups in such a way that the result of the test is influenced as little as possible. The determined distributions in the two groups of each sample are then compared in the form of a contingency table using a chi-square test .

The null hypothesis of the median test is the assumption that the medians of the samples do not differ. A p-value less than 0.05 should therefore be interpreted in such a way that at least one sample differs significantly from the other samples with regard to its median value . However, the p-value says nothing about the number of significantly different samples or the direction of the difference.

Alternative procedures

Compared to other methods, the median test has a low test strength for both small and medium to large samples .

The non-parametric methods of choice instead of the median test are the Mann-Whitney U test for two unpaired samples and the Kruskal-Wallis test for three or more unpaired samples , both of which are aimed at determining ranks of values ​​in the Samples and the calculation of rank sums are based. These two tests are not based on the assumption of a normal distribution, but they not only test the deviation from the median, but also take into account differences in the variance (across their ranks). If both the assumption of normal distribution and the assumption of homogeneity are violated, the median test can be a preferable alternative (see, for example, Vorberg & Blankenberger, 1999). For paired data which is also based on ranks are two-sample Wilcoxon signed-rank test or sign test and for three or more samples of the rank-based Friedman test to use. The Tukey rapid test is an easy-to-use, non-parametric method for rapid estimation .

If there are large differences in the spread of the individual samples, the median test should be used instead of the alternatives mentioned. Compared to this method, the median test also offers advantages when considering data outside the measurement range and other data whose value or rank is not exactly known, provided that at least a decision is possible as to whether they are above or below the common median value.

literature

  • Alexander McFarlane Mood: Introduction to the Theory of Statistics. McGraw-Hill Book Co., New York 1950, pp. 394-398
  • The median test for independent samples. In: David Sheskin: Handbook of Parametric and Nonparametric Statistical Procedures. Fourth edition. CRC Press, Boca Raton 2007, ISBN 1-58-488814-8 , pp. 645/646
  • JD Gibbons: Median Test, Brown – Mood. In: Encyclopedia of Statistical Sciences. John Wiley & Sons, 2006, doi : 10.1002 / 0471667196.ess0181.pub2
  • Boris Friedlin, Joseph L. Gastwirth: Should the Median Test Be Retired From General Use? In: The American Statistician. 54/2000. American Statistical Association, pp. 161-164, doi : 10.1080 / 00031305.2000.10474539 , JSTOR 2685584
  • Dirk Vorberg, Sven Blankenberger: The selection of statistical tests and measurements. In: Psychological Rundschau. 50 (3 )/1999. Hogrefe Verlag, pp. 157-164, doi : 10.1026 // 0033-3042.50.3.157