Non-parametric tests – Wilcoxon Rank Sum Test MCQs With Answer

Non-parametric tests like the Wilcoxon Rank Sum Test are essential in B. Pharm biostatistics for comparing two independent groups when data are ordinal, skewed, or sample sizes are small. Also known as the Mann–Whitney U test, the rank-sum approach compares medians and distributions without assuming normality, making it ideal for pharmacology outcomes, drug efficacy scores, adverse event counts, and bioassay results. Understanding rank calculations, ties, test statistics (U and W), exact versus asymptotic p-values, and interpretation boosts your ability to analyze experimental and clinical data. This set of focused MCQs reinforces concepts, assumptions, calculations, and real-world applications for pharmacy students. Now let’s test your knowledge with 30 MCQs on this topic.

Q1. What is the primary purpose of the Wilcoxon Rank Sum Test in B. Pharm research?

• To compare means of two normally distributed groups using variances
• To compare two independent groups when data are non-normal or ordinal
• To compare more than two groups’ medians simultaneously
• To test correlation between two continuous variables

Correct Answer: To compare two independent groups when data are non-normal or ordinal

Q2. The Wilcoxon Rank Sum Test is also commonly known as which test?

• Student’s t-test
• Chi-square test
• Mann–Whitney U test
• Friedman test

Correct Answer: Mann–Whitney U test

Q3. Which type of data is most appropriate for the Wilcoxon Rank Sum Test?

• Paired nominal data
• Independent interval data that are strongly normal
• Independent ordinal or continuous data that may be skewed
• Time-to-event censored data

Correct Answer: Independent ordinal or continuous data that may be skewed

Q4. Which assumption is NOT required for the Wilcoxon Rank Sum Test?

• Observations are independent between groups
• Data come from continuous distributions (no excessive ties)
• Equality of variances in the two groups
• The measurement scale allows ranking

Correct Answer: Equality of variances in the two groups

Q5. What is the null hypothesis for the Wilcoxon Rank Sum Test in its common form?

• Group 1 has a larger mean than Group 2
• The two groups have identical distributions
• The variances of the two groups are equal
• There is a perfect correlation between groups

Correct Answer: The two groups have identical distributions

Q6. When comparing two independent drug-dose groups for median response, why might you choose Wilcoxon Rank Sum over unpaired t-test?

• Because sample size is extremely large and t-test loses power
• Because responses are ordinal, skewed, or small sample sizes make normality doubtful
• Because you want to compare variances not central tendency
• Because Wilcoxon requires normality which is always true for pharmacology data

Correct Answer: Because responses are ordinal, skewed, or small sample sizes make normality doubtful

Q7. What is the first computational step in performing the Wilcoxon Rank Sum Test?

• Calculate means and standard deviations for each group
• Combine all observations and assign ranks from smallest to largest
• Compute the chi-square statistic for grouped counts
• Apply logarithmic transformation to all data

Correct Answer: Combine all observations and assign ranks from smallest to largest

Q8. How are ties (identical values) handled in the rank-sum test?

• Tied values are discarded from analysis
• Each tied value receives the average of the ranks they would occupy
• Ties are broken randomly to avoid bias
• Tied values are given the maximum rank of the tie group

Correct Answer: Each tied value receives the average of the ranks they would occupy

Q9. The Mann–Whitney U statistic can be interpreted as:

• The sum of squared deviations of ranks from the mean rank
• The number of times a randomly chosen observation from group 1 exceeds one from group 2
• The pooled variance of the two groups
• The product of group sample sizes divided by two

Correct Answer: The number of times a randomly chosen observation from group 1 exceeds one from group 2

Q10. For sample sizes n1 and n2, the expected value of U under the null hypothesis equals:

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

Correct Answer: n1 * n2 / 2

Q11. Which test statistic is directly related to the Wilcoxon Rank Sum Test and often reported as W?

• Sum of ranks for one of the groups
• Difference of means divided by pooled SD
• Chi-square goodness-of-fit statistic
• Spearman rank correlation coefficient

Correct Answer: Sum of ranks for one of the groups

Q12. When both sample sizes are small, what p-value method is preferred for the Wilcoxon Rank Sum Test?

• Asymptotic normal approximation without ties adjustment
• Exact p-value obtained by permutation or exact tables
• Using bootstrap confidence intervals only
• Using chi-square approximation

Correct Answer: Exact p-value obtained by permutation or exact tables

Q13. In large samples the U statistic is approximately:

• Chi-square distributed
• Normally distributed after standardization
• Uniformly distributed between 0 and 1
• Exponential distributed

Correct Answer: Normally distributed after standardization

Q14. For a one-sided Wilcoxon Rank Sum Test, the alternative hypothesis states:

• The distributions are identical
• Group A tends to have larger values than Group B
• Group A has a larger variance than Group B
• Group A and Group B are perfectly correlated

Correct Answer: Group A tends to have larger values than Group B

Q15. Which of the following best describes what the test compares when distributions have similar shapes?

• Equality of means
• Equality of medians
• Equality of standard deviations
• Equality of sample sizes

Correct Answer: Equality of medians

Q16. How do ties affect the variance calculation for the Wilcoxon Rank Sum Test?

• Ties increase variance and require a correction term
• Ties do not affect variance and can be ignored
• Ties always decrease the test statistic value to zero
• Ties convert the test into a t-test automatically

Correct Answer: Ties increase variance and require a correction term

Q17. Which effect size is commonly reported with non-parametric tests like the Wilcoxon Rank Sum?

• Cohen’s d only
• Correlation coefficient r or common language effect size
• R-squared from linear regression
• Hazard ratio

Correct Answer: Correlation coefficient r or common language effect size

Q18. Which software packages provide built-in Wilcoxon Rank Sum / Mann–Whitney tests?

• Only specialized pharmacokinetic software
• R, SPSS, SAS, Stata, and Python (SciPy)
• Only Microsoft Excel without add-ins
• None; it must be coded manually in all software

Correct Answer: R, SPSS, SAS, Stata, and Python (SciPy)

Q19. You compare pain scores (0–10) between two independent drug groups using Wilcoxon Rank Sum and obtain p = 0.03 (two-sided). The best interpretation is:

• There is strong evidence of a difference in central tendency between the groups at α=0.05
• The two drugs have identical effects because p < 0.05
• The difference in means is clinically unimportant regardless of p-value
• The test proves causation of better pain control

Correct Answer: There is strong evidence of a difference in central tendency between the groups at α=0.05

Q20. Which scenario would violate the independence assumption required for the Wilcoxon Rank Sum Test?

• Two separate groups of patients each receiving a different drug
• Repeated measures on the same patient before and after treatment
• Random assignment of subjects to two groups
• Independent lab samples collected from different patients

Correct Answer: Repeated measures on the same patient before and after treatment

Q21. If sample sizes are equal and no ties occur, which of the following is true about U and the sum of ranks R1?

• U is always larger than R1
• U and R1 are unrelated statistics
• R1 can be converted to U using a simple formula
• U equals R1 divided by the larger sample size

Correct Answer: R1 can be converted to U using a simple formula

Q22. Which real-world B. Pharm example suits the Wilcoxon Rank Sum Test?

• Comparing mean blood concentrations assuming normality with large n
• Comparing ordinal pain relief scores between two independent treatments
• Estimating time-to-event for survival analysis with censoring
• Assessing agreement between two raters on the same subjects

Correct Answer: Comparing ordinal pain relief scores between two independent treatments

Q23. When the alternative is that group 1 values are greater than group 2, the test is:

• Two-sided
• Left-tailed
• Right-tailed
• Non-directional

Correct Answer: Right-tailed

Q24. If you observe many identical highest values in both groups, what practical effect might this have on the test?

• It increases the power dramatically
• It increases the number of permutations and reduces computation
• It creates many ties, which reduces precision and requires correction
• It allows the use of parametric tests instead

Correct Answer: It creates many ties, which reduces precision and requires correction

Q25. Which statement about Mann–Whitney and t-test is correct?

• Mann–Whitney always tests means while t-test tests medians
• Mann–Whitney is more powerful than t-test when normality holds
• Mann–Whitney is robust to non-normality and compares distributions, not strictly means
• Both tests require equal sample sizes to be valid

Correct Answer: Mann–Whitney is robust to non-normality and compares distributions, not strictly means

Q26. Which summary should you report when presenting Wilcoxon Rank Sum results in a research paper?

• Only the raw p-value without sample sizes or test statistic
• Sample sizes, median (or mean ranks) for each group, test statistic (U or W), and p-value
• Only the difference of means and standard deviations
• Only a bar chart with error bars

Correct Answer: Sample sizes, median (or mean ranks) for each group, test statistic (U or W), and p-value

Q27. The permutation interpretation of the Wilcoxon Rank Sum Test means:

• The test assumes data are normally distributed for permutations
• P-values derive from comparing observed rank sums to distribution of rank sums under random reassignment
• Permutation approach only applies when there are no ties
• The test estimates variance components via permutations

Correct Answer: P-values derive from comparing observed rank sums to distribution of rank sums under random reassignment

Q28. For a small example with group A: 2, 4, 7 and group B: 1, 3, 6, what is the combined rank of group A (sum of ranks) assuming ranks 1–6?

• 12
• 13
• 14
• 15

Correct Answer: 13

Q29. In comparing two formulations, the Wilcoxon Rank Sum Test rejects the null at α=0.05. Which additional information strengthens clinical inference?

• Effect size and confidence interval along with direction of difference
• Only the exact p-value without clinical context
• The number of decimal places used in ranks
• Only the sample means without variability

Correct Answer: Effect size and confidence interval along with direction of difference

Q30. A common mistake when using the Wilcoxon Rank Sum Test is:

• Using it for independent samples instead of paired samples
• Applying it to ordinal data
• Reporting medians instead of ranks
• Correctly adjusting for ties

Correct Answer: Using it for independent samples instead of paired samples

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