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 Test formula:

Where:

• \( T \) — The test statistic
• sum positive ranks — Sum of ranks for positive differences
• sum negative ranks — Sum of ranks for negative differences

Steps:

1. Calculate differences between paired observations
2. Rank the absolute values of the differences
3. Sum the ranks for positive and negative differences separately
4. The test statistic T is the smaller of the two sums

3. When to Use This Test

Details: Use this test when:

• Comparing two related samples (paired data)
• Data is not normally distributed
• Data is at least ordinal (can be ranked)
• You want to test for differences in medians

4. Using the Calculator

Tips: Enter pairs of measurements separated by commas, with each pair separated by spaces or new lines. For example: "5,6 7,8 9,10" or "5,6\n7,8\n9,10".

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Wilcoxon and t-test?
A: The t-test assumes normality and tests means, while Wilcoxon doesn't assume normality and tests medians.

Q2: How to interpret the T statistic?
A: Compare T to critical values from Wilcoxon tables. If T ≤ critical value, reject the null hypothesis.

Q3: What if there are ties in the data?
A: This calculator uses average ranks for tied values, which is the standard approach.

Q4: What's the minimum sample size needed?
A: Typically at least 6 pairs are needed for reliable results with this test.

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