Wilcoxon Test: An Introduction
The Wilcoxon test, also known as the Wilcoxon-Mann-Whitney test, is a statistical procedure used for non-parametric tests of differences between two independent groups of scores. It is a type of rank-sum test, widely used to compare two samples of continuous data. In particular, the Wilcoxon test is used to test for the uniformity of a sample set or to test for differences between two sample sets. It is a non-parametric version of the two-sample t-test and is also closely related to the Mann-Whitney U test.
The Wilcoxon test is based on the sample medians of the two datasets. It is a test of the null hypothesis that the medians of the two datasets are equal. The test statistic is the sum of the ranks of one dataset. The p-value is calculated from the Wilcoxon test statistic. If the p-value is less than the predetermined significance level, then the null hypothesis of identical medians is rejected.
The Wilcoxon test is commonly used in a wide range of fields including psychology, biology, medicine, finance, and engineering. It is particularly useful in situations where the assumptions of the parametric two-sample t-test are not met. It is also useful for comparing paired data when the data are not normally distributed.
In conclusion, the Wilcoxon test is a valuable statistical procedure for non-parametric tests of differences between two independent groups of scores. It is easy to calculate, requires fewer assumptions than parametric tests, and is widely used in many disciplines.
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Kruschke, J. K. (2013). Doing Bayesian data analysis: A tutorial with R and BUGS. Elsevier.
Kulinskaya, E. (2008). Nonparametric Statistics for the Behavioural Sciences. Taylor & Francis.
Wilcox, R. R. (2012). Introduction to robust estimation and hypothesis testing. Academic Press.