1. What is the Wilcoxon Signed-Rank Test?

The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used to compare two related samples or repeated measurements on a single sample. It's an alternative to the paired Student's t-test when the data cannot be assumed to be normally distributed.

2. How Does the Calculator Work?

The calculator uses the Wilcoxon signed-rank formula:

Where:

• \( W \) — Wilcoxon test statistic (dimensionless)
• \( \text{ranks positive} \) — Sum of ranks for positive differences
• \( \text{ranks negative} \) — Sum of ranks for negative differences

Explanation: The test ranks the absolute differences between pairs, then sums the ranks where the differences were positive and negative separately.

3. Importance of W Statistic

Details: The W statistic is used to determine whether there is a statistically significant difference between two related samples. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis.

4. Using the Calculator

Tips: Enter the sum of positive ranks and negative ranks (both dimensionless values). These should be calculated from your paired data before using this calculator.

5. Frequently Asked Questions (FAQ)

Q1: When should I use the Wilcoxon signed-rank test?
A: Use it when you have paired data that doesn't meet the normality assumption required for a paired t-test.

Q2: What's the difference between W and Z in Wilcoxon test?
A: W is the raw test statistic. Z is a standardized version used for p-value calculation, especially with larger samples.

Q3: How do I interpret the W value?
A: The magnitude of W indicates the strength of the difference, while its sign shows the direction. Compare it to critical values or use for p-value calculation.

Q4: What are the assumptions of this test?
A: The test assumes that the differences between pairs are independent and symmetrically distributed around zero.

Q5: Can I use this for unpaired data?
A: No, for unpaired data you would use the Mann-Whitney U test (Wilcoxon rank-sum test) instead.