Wilcoxon_Signed_Rank_Test.pptxxxxxxxxxxxx

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1. Wilcoxon Signed-Rank Test A Non-Parametric Test for Paired Data Analysis Presented by: [Your Name]

2. Introduction • The Wilcoxon Signed-Rank Test is a non-parametric test for comparing two paired samples. • It is used when data is not normally distributed. • The test ranks differences rather than using raw values.

3. When to Use the Wilcoxon Signed-Rank Test • When comparing two dependent (paired) samples. • When the data does not follow a normal distribution. • When the sample size is small. • When the differences between paired values can be meaningfully ranked.

4. Hypotheses • Null Hypothesis (H₀): The median difference between paired observations is zero. • Alternative Hypothesis (H₁): The median difference between paired observations is not zero.

5. Steps to Perform the Test 1. Calculate the differences between paired observations. 2. Rank the absolute differences (ignore the sign). 3. Sum the ranks for positive and negative differences. 4. Compute the test statistic W (smaller rank sum). 5. Compare W to a critical value or compute the p-value.

6. Example: Pain Relief Study • Patients rated pain before and after medication. • Differences were ranked and summed. • W was compared to the critical value. • Conclusion: No significant difference found (p > 0.05).

7. Conclusion • The Wilcoxon Signed-Rank Test is a useful alternative to the paired t-test for non-normal data. • It is based on ranking differences rather than using raw data. • Used for small samples where normality cannot be assumed.