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 computes the test statistic W using the formula:

Where:

• Calculate differences between paired observations
• Rank the absolute differences (ignoring zeros)
• Sum ranks for positive and negative differences separately
• Compute W as the difference between these sums

3. When to Use This Test

Details: Use when comparing two related samples or repeated measurements where the differences between pairs are not normally distributed. Common applications include before-and-after studies or matched case-control studies.

4. Using the Calculator

Tips: Enter paired data as comma-separated values, one pair per line. The calculator will compute the W statistic, sum of positive ranks (W+), and sum of negative ranks (W-).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Wilcoxon and Mann-Whitney tests?
A: Wilcoxon is for paired/matched data, while Mann-Whitney is for independent samples.

Q2: How to interpret the W value?
A: Compare the absolute value of W to critical values from Wilcoxon tables to determine significance.

Q3: What if I have ties in my data?
A: The calculator assigns average ranks to tied values, which is the standard approach.

Q4: Can I use this for small sample sizes?
A: Yes, Wilcoxon is particularly useful for small samples where normality assumptions may not hold.

Q5: What's the null hypothesis of this test?
A: The null hypothesis is that the median difference between pairs is zero.