Wilcoxon Rank Sum 

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The Wilcoxon rank sum test, also known as the Mann-Whitney U test, is a non-parametric statistical test used in biostatistics to compare the distribution of two independent groups. It is particularly valuable when the assumptions required for parametric tests, such as the t-test, are not met, such as when the data is not normally distributed or when the sample sizes are small.
In biostatistics, the Wilcoxon rank sum test is commonly employed to assess differences between two groups in terms of their central tendency. Instead of comparing means like the t-test, this test compares the distributions of ranks between the two groups. Here's how it works:
Ranking: Combine the data from both groups and rank them from lowest to highest, assigning ranks based on their order.
Sum of Ranks: Calculate the sum of ranks for each group separately.
Test Statistic: The test statistic for the Wilcoxon rank sum test is the smaller of the two sums of ranks, denoted as U. It represents the likelihood that a randomly selected value from one group will be lower than a randomly selected value from the other group.
Hypothesis Testing: The null hypothesis (H0) typically states that there is no difference between the two groups. The alternative hypothesis (H1) asserts that there is a difference between the groups. The Wilcoxon rank sum test assesses whether the observed difference in ranks is statistically significant.
The Wilcoxon rank sum test is robust against outliers and does not rely on assumptions of normality, making it suitable for analyzing data with non-normal distributions or small sample sizes. It is widely used in biostatistics for comparing groups in clinical trials, epidemiological studies, and other research contexts where traditional parametric tests may not be appropriate.
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