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The Wilcoxon Test is a non-parametric statistical method used to compare two sets of data, either paired or independent, to determine if their population mean ranks differ significantly. It includes the Wilcoxon Signed Rank Test for paired data and the Wilcoxon Rank Sum Test for independent samples. This test is particularly useful when data does not follow a normal distribution, such as in small sample sizes or when dealing with outliers. It's a robust alternative to the t-test, offering reliable analysis for various research scenarios.

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## Introduction to the Wilcoxon Test

### Purpose of the Wilcoxon Test

The Wilcoxon Test is used to compare two sets of data and determine if their population mean ranks are significantly different

### Variants of the Wilcoxon Test

Wilcoxon Signed Rank Test

The Wilcoxon Signed Rank Test is used for paired data and examines if the median of the paired differences is significantly different from zero

Wilcoxon Rank Sum Test

The Wilcoxon Rank Sum Test is used for independent samples and assesses if two samples are likely to derive from the same distribution

### Advantages of the Wilcoxon Test

The Wilcoxon Test is a reliable method for statistical analysis when data does not follow a normal distribution

## Implementation of the Wilcoxon Test

### Steps for Implementing the Wilcoxon Test

The Wilcoxon Test involves ranking the data, calculating test statistics, and determining significance by comparing these statistics to critical values

### Wilcoxon Signed Rank Test Procedure

The Wilcoxon Signed Rank Test involves ranking and signing differences between pairs and summing the ranks of positive and negative differences separately

### Wilcoxon Rank Sum Test Procedure

The Wilcoxon Rank Sum Test involves ranking all observations together and using the sum of ranks for each group to compute the U statistic

## Applications of the Wilcoxon Test

### Practical Instances of the Wilcoxon Test

The Wilcoxon Signed Rank Test is often used in before-and-after studies, while the Wilcoxon Rank Sum Test is utilized in studies comparing two independent groups

### Comparison to Other Non-Parametric Tests

The Wilcoxon Test is a prominent method in statistical analysis and is often compared to other non-parametric tests, such as the Mann-Whitney U test

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