Median Test
The median test is a non-parametric statistical test used to compare the medians of two or more groups. It is used to compare the distributions of two or more samples with respect to their median values. The median test is a type of non-parametric test because it makes no assumptions about the underlying distribution of the data.
The median test works by comparing the median values of each group. The null hypothesis for the median test states that the medians of the two or more groups are equal. The alternative hypothesis states that the medians of the two or more groups are not equal.
The median test can be used to determine whether the medians of two or more groups differ significantly. To perform the test, the data must first be arranged in ascending order. The median of each group is then calculated and compared. If there is a significant difference between the medians, the null hypothesis is rejected and the alternative hypothesis is accepted.
The median test can be used to compare the medians of three or more groups. The test is similar to the two-group median test, except that the medians of the three or more groups are compared. The Kruskal-Wallis test is an example of a three-group median test.
The median test can also be used to compare the medians of two or more independent samples. The Mann-Whitney U test is an example of a two-sample median test.
The median test is a useful tool for comparing the medians of two or more groups or samples. It is a non-parametric test that does not make assumptions about the underlying distribution of the data and is easy to implement.
References
Chen, L., & Gupta, S. (2015). Nonparametric statistical methods. John Wiley & Sons.
Kruskal, W. H., & Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47(260), 583-621.
Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics, 18(1), 50-60.