Wilcoxon test

Information

• The Wilcoxon test, also known as the Wilcoxon rank-sum test or Mann-Whitney U test, is a non-parametric statistical test that compares two independent samples to test if their underlying population distributions are different.
• The Wilcoxon test is used when the data are not normally distributed or the assumptions of the parametric tests, such as the t-test, are violated.
• The Wilcoxon test compares the ranks of the observations in the two samples, rather than their actual values, and thus is more robust to outliers and non-normality.
• The null hypothesis of the Wilcoxon test is that there is no difference between the population distributions of the two samples, while the alternative hypothesis is that the population distributions are different.
• The Wilcoxon test calculates a test statistic, called the U statistic or the sum of ranks, which measures the degree of difference between the two samples.
• The p-value of the Wilcoxon test indicates the probability of observing the U statistic, or a more extreme value, if the null hypothesis is true.
• A small p-value (<0.05) indicates strong evidence against the null hypothesis and in favor of the alternative hypothesis, while a large p-value (>0.05) indicates weak evidence against the null hypothesis and failure to reject it.
• The Wilcoxon test has some assumptions and limitations, such as requiring independent samples, equal variances, and random sampling, and being less powerful than the parametric tests when the assumptions are met.
• The Wilcoxon test can be one-tailed or two-tailed, depending on the direction of the alternative hypothesis and the research question.
• The Wilcoxon test can be used in a variety of applications, such as comparing the effectiveness of two treatments, testing for differences in medians or location, and examining the effects of categorical or nominal variables on a continuous outcome.