Median Test
The Median Test is a non-parametric statistical test used to determine if two or more independent groups have the same median. It is particularly useful when the data is ordinal or does not meet the assumptions of normality required by parametric tests like the t-test. The Median Test compares the medians of the groups by categorizing the data into values above and below the overall median, then using a chi-square test to assess whether the proportions differ significantly between the groups.
- Null Hypothesis (H₀): The medians of the two or more groups are equal.
- Alternative Hypothesis (H₁): The medians of the groups are not equal.
This test is simple and robust but is not very powerful compared to other non-parametric tests. It is typically used when the primary interest is whether the central tendencies of the groups differ.
Wilcoxon Rank-Sum Test (Equivalent to Mann-Whitney U-test)
The Wilcoxon Rank-Sum Test, also known as the Mann-Whitney U-test, is a non-parametric test used to compare two independent samples to determine if they come from the same distribution. It is used as an alternative to the independent t-test when the assumption of normality is violated. The test works by ranking all the data points from both groups together and comparing the sums of the ranks between the two groups.
- Null Hypothesis (H₀): The distributions of the two samples are the same.
- Alternative Hypothesis (H₁): The distributions of the two samples are different.
The Wilcoxon test is more powerful than the Median Test because it uses rank information and is sensitive to differences in location (medians) as well as other distributional differences between the groups. It is appropriate for continuous or ordinal data.
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