Mann–Whitney U test and its applications MCQs With Answer

Mann–Whitney U test is a nonparametric statistical method widely used in B.Pharm research to compare two independent groups when data are ordinal or not normally distributed. This rank-sum test (also called Wilcoxon rank-sum) assesses differences in central tendency or distribution without assuming normality, making it useful for pharmacology, clinical trials, dissolution studies, bioequivalence, and adverse event comparisons. Key concepts include U statistic, ranks, ties, exact versus asymptotic p-values, continuity correction, and effect size (r). Understanding assumptions, calculation steps, interpretation, and software implementation (R, SPSS, Python) helps B.Pharm students analyze real-world drug data robustly. Now let’s test your knowledge with 30 MCQs on this topic.

Q1. What is the primary purpose of the Mann–Whitney U test?

• Compare two independent samples when assumptions of t-test are not met
• Compare more than two groups
• Test for correlation between two variables
• Analyze paired data

Correct Answer: Compare two independent samples when assumptions of t-test are not met

Q2. Which alternative name is commonly used for the Mann–Whitney U test?

• Kruskal–Wallis test
• Wilcoxon signed-rank test
• Wilcoxon rank-sum test
• Kolmogorov–Smirnov test

Correct Answer: Wilcoxon rank-sum test

Q3. What types of data are appropriate for the Mann–Whitney U test?

• Nominal data only
• Ordinal or continuous non-normal data
• Only normally distributed continuous data
• Paired repeated measures

Correct Answer: Ordinal or continuous non-normal data

Q4. Which of the following is an important assumption of the Mann–Whitney U test?

• Normal distribution of raw data in each group
• Equal variances in raw data are required
• Observations are independent and distributions have similar shape
• Samples must be paired

Correct Answer: Observations are independent and distributions have similar shape

Q5. When should a B.Pharm student prefer Mann–Whitney U over independent t-test?

• When sample sizes are extremely large
• When data are binary
• When data are non-normal or ordinal
• When groups are paired

Correct Answer: When data are non-normal or ordinal

Q6. What is the null hypothesis in a two-sample Mann–Whitney U test?

• Both groups have equal sample sizes
• The two groups have identical distributions
• The two groups have equal variances
• The mean of group 1 is greater than mean of group 2

Correct Answer: The two groups have identical distributions

Q7. The U statistic can take values in which range?

• 0 to n1 + n2
• 0 to n1 * n2
• -∞ to +∞
• 1 to n1

Correct Answer: 0 to n1 * n2

Q8. How are tied values handled when ranking data for the Mann–Whitney U test?

• Discard all tied observations
• Assign the highest rank to all ties
• Assign average ranks to tied values
• Randomly assign distinct ranks

Correct Answer: Assign average ranks to tied values

Q9. What does a two-sided Mann–Whitney U test evaluate?

• Whether group 1 is strictly greater than group 2
• Whether there is any difference in distributions without direction
• Only differences in variances
• Only differences in medians ignoring distribution shape

Correct Answer: Whether there is any difference in distributions without direction

Q10. Which effect size measure is commonly used with Mann–Whitney U results?

• Cohen’s d
• Pearson’s r from raw scores
• Rank-biserial or r = Z / √N
• Odds ratio

Correct Answer: Rank-biserial or r = Z / √N

Q11. For large sample sizes, Mann–Whitney U is commonly approximated by which distribution?

• Chi-square distribution
• Student’s t-distribution
• Normal distribution (Z) with possible continuity correction
• F-distribution

Correct Answer: Normal distribution (Z) with possible continuity correction

Q12. If two groups have identical medians but different distribution shapes, Mann–Whitney may:

• Always fail to detect any difference
• Detect a significant difference because it compares distributions
• Only detect differences in variances
• Be invalid and return no result

Correct Answer: Detect a significant difference because it compares distributions

Q13. Which software tools commonly implement the Mann–Whitney U test?

• Only Excel
• R, SPSS, and Python libraries
• Only proprietary clinical software
• None; it must be computed by hand

Correct Answer: R, SPSS, and Python libraries

Q14. Which test should be used for paired nonparametric two-sample comparisons?

• Mann–Whitney U test
• Wilcoxon signed-rank test
• Kruskal–Wallis test
• Chi-square test

Correct Answer: Wilcoxon signed-rank test

Q15. For very small sample sizes in Mann–Whitney U, which p-value approach is preferred?

• Asymptotic p-value only
• Exact p-value calculation
• P-value is not needed for small samples
• Use bootstrap exclusively

Correct Answer: Exact p-value calculation

Q16. What is an effect of many tied observations on the Mann–Whitney U test?

• Increases test power substantially
• Has no effect on ranks or p-values
• Reduces power and requires tie-adjusted variance
• Converts test into a t-test automatically

Correct Answer: Reduces power and requires tie-adjusted variance

Q17. Which is an appropriate B.Pharm application of Mann–Whitney U?

• Comparing dissolution times between two formulations when data are skewed
• Comparing placebo and drug in a crossover paired design without accounting for pairing
• Estimating hazard ratios for time-to-event data with censoring
• Testing equality of more than two batch means simultaneously

Correct Answer: Comparing dissolution times between two formulations when data are skewed

Q18. How are ranks assigned when computing Mann–Whitney U?

• Rank each group separately
• Combine both groups and rank all observations together
• Use original data order as ranks
• Rank only the larger group

Correct Answer: Combine both groups and rank all observations together

Q19. When reporting Mann–Whitney U results in a paper, which elements are essential?

• Only p-value is necessary
• U value, sample sizes, p-value, and effect size
• Only group means and standard deviations
• Only test statistic without sample sizes

Correct Answer: U value, sample sizes, p-value, and effect size

Q20. If the Mann–Whitney U test yields p < 0.05, the proper interpretation is:

• There is strong evidence that distributions differ between groups
• The means of the groups are equal
• There is no evidence of any difference
• The result proves clinical significance

Correct Answer: There is strong evidence that distributions differ between groups

Q21. Which of the following is NOT required by the Mann–Whitney U test?

• Independence of observations
• Ordinal or continuous measurement
• Normality of the raw data
• Two independent groups

Correct Answer: Normality of the raw data

Q22. Under what condition does Mann–Whitney U test compare medians specifically?

• Always, regardless of distribution shape
• Only when distributions have similar shape and spread
• Only when sample sizes are equal
• Never; it only compares means

Correct Answer: Only when distributions have similar shape and spread

Q23. Which formula is a correct expression for U based on ranks R1 for group 1?

• U = R1 – n1(n1+1)/2
• U = n1*n2 + n1(n1+1)/2 – R1
• U = R1 + R2
• U = (R1/n1) – (R2/n2)

Correct Answer: U = n1*n2 + n1(n1+1)/2 – R1

Q24. What is the expected mean of the U distribution under the null hypothesis?

• n1 + n2
• n1*n2/2
• (n1 – n2)/2
• Zero

Correct Answer: n1*n2/2

Q25. The variance of U used in normal approximation is given by which base expression (before tie correction)?

• n1*n2*(n1+n2+1)/12
• n1*n2/(n1+n2)
• (n1+n2)^2/12
• n1*n2*(n1-n2)/12

Correct Answer: n1*n2*(n1+n2+1)/12

Q26. When should a continuity correction be applied?

• When using the exact distribution for U
• When approximating U by the normal distribution for discrete data
• Only for paired tests
• Continuity correction is never needed

Correct Answer: When approximating U by the normal distribution for discrete data

Q27. Is the Mann–Whitney U test valid with unequal sample sizes?

• No, sample sizes must be equal
• Yes, it remains valid with unequal sizes
• Only if the larger sample is more than twice the smaller
• Only when variances are equal

Correct Answer: Yes, it remains valid with unequal sizes

Q28. Can Mann–Whitney U test handle censored survival data?

• Yes, it is designed for censored data
• No, use survival analysis methods like Kaplan–Meier or log-rank test
• Yes, but only if censoring is random
• No, use paired t-test instead

Correct Answer: No, use survival analysis methods like Kaplan–Meier or log-rank test

Q29. When is a one-sided Mann–Whitney U test appropriate?

• When the data are normally distributed
• When a prior directional hypothesis exists
• Only when sample sizes are equal
• One-sided tests are never appropriate

Correct Answer: When a prior directional hypothesis exists

Q30. Which alternative test compares entire distributions between two samples (not just central tendency)?

• Kruskal–Wallis test
• Chi-square goodness-of-fit
• Kolmogorov–Smirnov test
• ANOVA

Correct Answer: Kolmogorov–Smirnov test

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