Quade test

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The Quade test , also known as Quade's range of rank test, is a statistical test for examining three or more paired samples for equality of the location parameter . Since it does not require a specific distribution of the data in the samples, it is one of the non-parametric methods . It is an extension of the Wilcoxon signed rank test to be used for more than two samples and a parameter-free alternative to ANOVA with repeated measurements . The test was named after the American biostatistician Dana Quade, who published it in 1979 in the Journal of the American Statistical Association .

Test description

The Quade test assumes that the values ​​are paired between samples and are independent of one another within the samples. In addition, the data must be available on cardinal scale, since the range of the measured values ​​is taken into account in the Quade test .

The analysis is based on a sorting of the values ​​in each unit of investigation, that is to say each paired set of data, from the smallest to the largest value, with each value set being sorted separately. In addition, the range from the smallest to the largest measured value is determined for each examination unit. All examination units are then sorted according to the range in a ranking order, so that each examination unit is assigned a range ranking with the value 1 for the smallest and the number of examination units N for the largest ranking. For each individual rank of a measured value, its deviation from the rank average is then weighted by multiplication with the range rank of the corresponding investigation unit. In this way, span differences between the individual examination units are taken into account, in that examination units with larger spans are given greater weight. Then the individual ranks weighted with the range rank are added in each sample.

The p-value as a measure of statistical significance is lower, the greater the differences between the sums of ranks of the individual samples. Assuming that the samples examined have a comparable frequency distribution, the test's null hypothesis is the assumption that there is no difference in position between the samples . A p-value less than 0.05 is therefore generally interpreted in such a way that the median value of at least one of the examined samples differs significantly from that of the other samples.

Alternative procedures

The Quade test is a parameter-free alternative to parametric ANOVA with repeated measurements , which requires a normal distribution of the data. Instead of the Quade test, the likewise non-parametric Friedman test can be used. In direct comparison, the Quade test is generally considered to be stronger for comparing up to five samples, while the Friedman test is generally considered to be stronger for more than five samples. In addition, the Quade test is much more suitable than the Friedman test for data with different ranges in the individual samples. On the other hand , in contrast to the Friedman test, it is not possible to use the Quade test for ordinally scaled data that were collected, for example, as rank data or are based on the rank transformation of cardinally scaled measured values.

In contrast to the Quade test , the likewise non-parametric Kruskal-Wallis test is used to analyze the variance of three or more unpaired samples. One parameter-free method for comparing two paired samples is the Wilcoxon signed rank test , on which the Quade test is based. However, the application of the Wilcoxon signed rank test to carry out multiple two-group comparisons between several samples should either be limited to a few comparisons planned in advance or supplemented by a correction of the alpha error accumulation , which, for example, with the Bonferroni Method can be carried out.

literature

  • Dana Quade: Using Weighted Rankings in the Analysis of Complete Blocks with Additive Block Effects. In: Journal of the American Statistical Association. 74 (367) / 1979, pp. 680-682, doi : 10.1080 / 01621459.1979.10481670 JSTOR 2286991
  • Quade's Span Rank Test. In: Jürgen Bortz, Gustav Lienert, Klaus Boehnke: Distribution-free methods in biostatistics. 3rd, corrected edition. Springer, Heidelberg 2008, pp. 272-274, ISBN 978-3-540-74706-2 .