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Mann-Whitney U Test — Previous Year Questions

📊 Topic Overview​

MetricValue
Papers Appeared20 of 27 (74.1%)
Priority🔴 VERY HIGH
Section DistributionSec A: ~4
Most Repeated"Compute Mann-Whitney U test for the following data"
ProbabilityExtremely High — the standard Section B computation from 2015 onward

🎯 Must-Know Concepts​

  1. Mann-Whitney U is the non-parametric alternative to the independent samples t-test
  2. Used when data is ordinal or not normally distributed
  3. Based on ranking all scores together from both groups
  4. Two U values computed: U₁ and U₂; the smaller is used
  5. Decision: compare U obtained with U critical (U obtained ≤ U critical = significant)

🔥 Core Computation Procedure​

Step-by-Step Mann-Whitney U Computation​

Step 1: State H₀ and H₁

  • H₀: There is no significant difference between Group 1 and Group 2
  • H₁: There is a significant difference between the two groups

Step 2: Rank all scores together Combine all scores from both groups, then rank them from lowest (rank 1) to highest. In case of ties, assign average ranks.

Step 3: Compute U₁ and U₂

U1=n1n2+n1(n1+1)2−R1U_1 = n_1 n_2 + \frac{n_1(n_1+1)}{2} - R_1

U2=n1n2+n2(n2+1)2−R2U_2 = n_1 n_2 + \frac{n_2(n_2+1)}{2} - R_2

Where:

  • n₁ = number of subjects in Group 1
  • n₂ = number of subjects in Group 2
  • R₁ = sum of ranks for Group 1
  • R₂ = sum of ranks for Group 2

Verification: U₁ + U₂ = n₁ × n₂

Step 4: Select the smaller U U = smaller of U₁ and U₂

Step 5: Find U critical from the Mann-Whitney U table Look up critical U at n₁ and n₂ at α = 0.05 (two-tailed)

Step 6: Decision

  • If U obtained ≤ U critical: Reject H₀ → Significant difference exists
  • If U obtained > U critical: Retain H₀ → No significant difference

Note: For Mann-Whitney U, the decision rule is reversed from most tests — the obtained value must be smaller than or equal to the critical value to be significant.

Worked Example Layout​

All Scores CombinedGroupRank
Score 1G11
Score 2G22
.........

Then compute R₁, R₂, U₁, U₂.

📝 Conceptual Questions​

When to use Mann-Whitney U Test (Section B — ~250 words)​

The Mann-Whitney U test is used when:

  1. The data are measured on an ordinal scale or the continuous data violates normality assumptions
  2. The researcher is comparing two independent groups
  3. Sample sizes are small
  4. The independent samples t-test assumptions cannot be met

Relationship to t-test: The Mann-Whitney U test is the non-parametric alternative to the independent samples t-test. Where the t-test requires interval/ratio data and assumes normality, the Mann-Whitney U test requires only ordinal-level data. When the normality assumption is met, the t-test is more powerful; when it is violated, Mann-Whitney U is preferred.

Assumptions of Mann-Whitney U:

  1. Two independent groups
  2. Data measured at least on ordinal scale
  3. Observations are independent

🧠 Memory Aid​

Mann-Whitney Steps (RRUC-D):

  • Rank all scores together
  • R₁ and R₂: sum ranks for each group
  • U₁ and U₂: apply the formulas
  • Choose smaller U
  • Decide: U obtained ≤ U critical → significant

📚 Related Content​

✅ Self-Assessment​

  1. What does the Mann-Whitney U test measure?
  2. If n₁ = 6, n₂ = 5, and R₁ = 40, what is U₁?
  3. If U₁ = 12 and U₂ = 18, which value is used for the decision?
  4. How does the decision rule for Mann-Whitney U differ from most other tests?
  5. When would you use Mann-Whitney U instead of a t-test?

💡 Exam Tips​

  • Always show the combined ranking table — this earns the most marks.
  • Verify your work: U₁ + U₂ must equal n₁ × n₂.
  • State H₀ before computing.
  • Remember: smaller U = more significant. The decision rule is the opposite of most tests.
  • Mention that Mann-Whitney U is the non-parametric equivalent of the t-test.