Non parametric test used to compare the medians of two independent samples
## Core Concept
The question tests understanding of non-parametric statistical tests used in comparing two independent samples, specifically focusing on median comparison. Non-parametric tests are essential in statistics as they don't require a normal distribution of the data, making them useful for skewed data or ordinal data. The test in question is used when the assumption of normality is violated, and the researcher aims to compare medians.
## Why the Correct Answer is Right
The correct answer, **Mann-Whitney U test**, also known as the Wilcoxon rank-sum test, is a non-parametric test used to compare two independent samples to assess whether their population mean ranks differ. It is particularly useful for comparing the medians of two independent samples when the data does not meet the assumptions for a t-test (e.g., normality of distribution). This test works by ranking all the data points together and then comparing the ranks of the two groups.
## Why Each Wrong Option is Incorrect
- **Option A: Paired t-test** is incorrect because it is a parametric test used for comparing two related samples, not independent samples, and it assumes normality of the data.
- **Option B: Kruskal-Wallis test** is incorrect because, although it is a non-parametric test, it is used to compare more than two independent samples, not just two.
- **Option D: Wilcoxon signed-rank test** is incorrect because it is used for paired data (related samples), not independent samples, and is a non-parametric alternative to the paired t-test.
## Clinical Pearl / High-Yield Fact
A key point to remember is that when dealing with **skewed data or ordinal data** from two independent groups, the **Mann-Whitney U test** is a suitable statistical test to compare medians. This test does not assume normality of the data distribution, making it a valuable tool in clinical research where data often does not follow a normal distribution.
## Correct Answer: C. Mann-Whitney U test