# What Type of Data Is Used in Wilcoxon Test?

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Heather Bennett

What Type of Data Is Used in Wilcoxon Test?

The Wilcoxon test, also known as the Wilcoxon signed-rank test, is a non-parametric statistical test used to determine whether there is a significant difference between two related samples. Unlike parametric tests, the Wilcoxon test does not assume any specific distribution for the data. Instead, it focuses on the order or rank of the observations.

## Types of Data

Before we delve into the details of the Wilcoxon test, let’s first understand the types of data it can be used for:

• Numerical Data: The Wilcoxon test can be applied to numerical data, which includes both continuous and discrete variables. These variables are measured on an interval or ratio scale.
• Paired Data: The Wilcoxon test is specifically designed to analyze paired or matched data.

Paired data consists of two sets of observations that are related in some way. For example, you might have measurements taken before and after a treatment intervention.

• Non-Normal Data: The Wilcoxon test is robust against departures from normality. This means it can handle data that do not follow a normal distribution.

## Hypotheses in the Wilcoxon Test

In the context of the Wilcoxon test, we typically have two hypotheses:

• Null Hypothesis (H0): This hypothesis states that there is no significant difference between the two related samples.
• Alternative Hypothesis (HA): This hypothesis states that there is a significant difference between the two related samples.

The Wilcoxon test calculates the signed ranks of the differences between the paired observations and determines whether these ranks are significantly different from zero. The test statistic is based on the sum of these ranks, and its significance is assessed using a critical value from the Wilcoxon signed-rank distribution.

## Interpreting the Results

Once you have performed the Wilcoxon test, you will obtain a p-value. This p-value represents the probability of observing a test statistic as extreme as or more extreme than what was observed, assuming that the null hypothesis is true.

If the p-value is less than your chosen significance level (e.g., 0.05), you can reject the null hypothesis and conclude that there is a significant difference between the two related samples. On the other hand, if the p-value is greater than your significance level, you fail to reject the null hypothesis, indicating that there is not enough evidence to suggest a significant difference.

### Conclusion

The Wilcoxon test is a powerful non-parametric statistical test used to analyze paired data when assumptions for parametric tests are violated or when dealing with non-normal data. It can handle numerical data measured on an interval or ratio scale and provides insight into whether there is a significant difference between two related samples.

Remember to consider both statistical significance and practical significance when interpreting the results of any statistical analysis.