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Wilcoxon Matched Pair Signed Rank Test β€” Previous Year Questions

πŸ“Š Topic Overview​

MetricValue
Papers Appeared8 of 27 (29.6%)
Priority🟑 MEDIUM
Section DistributionSec A: ~1
Most Repeated"Explain in detail Wilcoxon matched pair signed rank test with suitable example."

🎯 Must-Know Concepts​

  1. Non-parametric alternative to paired samples t-test
  2. Based on ranks of absolute differences between paired scores
  3. Both magnitude and direction of differences are considered
  4. T statistic = smaller of sum of positive and negative ranks
  5. Decision: T obtained ≀ T critical = significant

πŸ”₯ Most Repeated Question​

Common phrasings:

  • "Explain in detail Wilcoxon matched pair signed rank test with suitable example."
  • "Describe Wilcoxon matched pair signed rank test."
  • "What do you mean by two sample tests? Write step by step procedure for Wilcoxon test for small sample."
  • "Wilcoxon matched pair signed rank test (short note)."

Answer (Section B β€” ~250 words):​

The Wilcoxon Matched Pair Signed Rank Test is a non-parametric statistical test used to compare two related (paired) samples. It is the non-parametric equivalent of the paired samples t-test.

When to Use:

  1. Data consists of paired observations (before-after, matched pairs, repeated measures)
  2. Data is at least ordinal
  3. Assumptions of the paired t-test (normality of difference scores) cannot be met
  4. Sample is small

Step-by-Step Procedure:

Step 1: Compute the difference (D) for each pair: D = Scoreβ‚‚ βˆ’ Score₁

Step 2: Exclude all pairs where D = 0 (zero differences are dropped). Update n accordingly.

Step 3: Rank the absolute values of the differences |D|, from smallest (rank 1) to largest. Handle ties with average ranks.

Step 4: Assign the sign of the original difference to each rank.

  • Positive differences β†’ positive ranks
  • Negative differences β†’ negative ranks

Step 5: Compute:

  • W⁺ = sum of positive ranks
  • W⁻ = sum of negative ranks

Verification: W⁺ + W⁻ = n(n+1)/2

Step 6: T = smaller of W⁺ and W⁻

Step 7: Find T critical from the Wilcoxon T table at the adjusted n and Ξ± = 0.05

Decision: If T obtained ≀ T critical β†’ Reject Hβ‚€ β†’ Significant difference between the two conditions

Note: Like Mann-Whitney U, the decision rule is reversed β€” smaller obtained value means more significant.

Example Table:

| Pair | Score₁ | Scoreβ‚‚ | D | |D| | Rank | Signed Rank | |------|--------|--------|---|----|------|-------------| | 1 | | | | | | | | ... | | | | | | |

Advantages:

  • Considers both magnitude and direction of differences (unlike sign test)
  • More powerful than the sign test
  • Suitable when t-test assumptions cannot be met

🧠 Memory Aid​

Wilcoxon Steps (DRZST):

  • Differences (compute D = Scoreβ‚‚ βˆ’ Score₁)
  • Remove zeros
  • Zero-free ranking of |D|
  • Sign the ranks (+ or βˆ’)
  • T = smaller of W⁺ and W⁻ β†’ compare with T critical

πŸ“š Related Content​

βœ… Self-Assessment​

  1. When is the Wilcoxon test preferred over the paired t-test?
  2. What is the purpose of the sign assigned to each rank?
  3. If W⁺ = 32 and W⁻ = 13, what is T?
  4. What should W⁺ + W⁻ equal?
  5. How does the Wilcoxon test differ from the sign test?

πŸ’‘ Exam Tips​

  • Section C (short note): Non-parametric paired test β†’ Based on ranks of |D| β†’ T = smaller of W⁺ and W⁻ β†’ T ≀ T critical = significant.
  • Section B (6 marks): Full procedure steps + the table + decision rule + comparison with paired t-test.
  • Show the complete signed rank table for computation questions.
  • Verification check (W⁺ + W⁻ = n(n+1)/2) is good practice and shows understanding.