The Wilcoxon Signed-Rank Test is a statistical method used to compare two related samples or repeated measurements on a single sample. It’s a non-parametric test, which means it doesn’t assume a normal distribution of the data. To simplify this process, a Wilcoxon Signed-Rank Calculator can be used. This calculator allows users to input their data and calculate the test statistic quickly.

## How It Works

The calculator takes two sets of data: pre-treatment and post-treatment values. These values are entered as comma-separated numbers. Additionally, users must input a significance level (α), typically set at 0.05. The calculator then performs the following steps:

**Calculate Differences:**It computes the differences between the pre-treatment and post-treatment values.**Rank the Differences:**The absolute differences are ranked, with ties receiving a rank equal to the average of their positions.**Sum the Ranks:**The ranks of the positive and negative differences are summed separately.**Calculate the Test Statistic (W):**The smaller of the two rank sums is the test statistic W.

## Example

Suppose we have the following data:

- Pre-treatment: 10, 12, 14, 16, 18
- Post-treatment: 11, 15, 13, 17, 19
- Significance Level (α): 0.05

The calculator will compute the differences, rank them, sum the ranks, and provide the value of W. For this example, the output might be something like “W = 3, Significance Level (α) = 0.05”.

## Relevant Information Table

Term | Description |
---|---|

Pre-treatment Values | The data before any intervention or treatment. |

Post-treatment Values | The data after the intervention or treatment. |

Significance Level (α) | The probability of rejecting the null hypothesis when it is true (typically set at 0.05). |

W | The test statistic calculated by the Wilcoxon Signed-Rank Test. |

## Conclusion

The Wilcoxon Signed-Rank Calculator is a valuable tool for researchers and statisticians who need to compare paired data without assuming a normal distribution. It simplifies the process of calculating the test statistic and helps in making informed decisions based on the significance level. By using this calculator, users can quickly determine whether there is a significant difference between two sets of related data.