Non-parametric tests: Wilcoxon, Chi-square MCQs With Answer

Introduction

Non-parametric tests are essential tools in biostatistics when data do not meet parametric assumptions such as normality or homogeneity of variance. This set of MCQs focuses on two widely used non-parametric methods in M.Pharm research: the Wilcoxon tests (signed-rank and rank-sum/Mann–Whitney) and the Chi-square family of tests (goodness-of-fit and tests of independence). The questions emphasize conceptual understanding, appropriate test selection, computation of test statistics, handling ties and zero differences, continuity corrections, degrees of freedom, and interpretation in contingency tables. These items are designed to prepare you for exam questions and practical data analysis decisions in pharmaceutical research.

Q1. Which situation is most appropriate for using the Wilcoxon signed-rank test?

• Comparing means of two independent normally distributed groups
• Comparing paired measurements when differences are not normally distributed
• Assessing association between two categorical variables in a 2×2 table
• Testing the goodness-of-fit for a single categorical variable

Correct Answer: Comparing paired measurements when differences are not normally distributed

Q2. The Wilcoxon rank-sum test (Mann–Whitney U) is best described as:

• A parametric test comparing paired samples
• A non-parametric test comparing two independent samples using ranks
• A test for homogeneity of variances
• A test for trend across ordered categories

Correct Answer: A non-parametric test comparing two independent samples using ranks

Q3. In the Wilcoxon signed-rank test, how are zero differences (ties at zero) commonly handled?

• They are assigned the average rank and included in the test statistic
• They are excluded from ranking and reduce the effective sample size
• They are converted to small positive values and kept
• They force the use of a parametric paired t-test instead

Correct Answer: They are excluded from ranking and reduce the effective sample size

Q4. Which assumption is NOT required for the Wilcoxon rank-sum (Mann–Whitney) test?

• Observations from the two groups are independent
• The two distributions have the same shape under the null
• The measurements are at least ordinal
• The samples must be of equal size

Correct Answer: The samples must be of equal size

Q5. For a 2×2 contingency table with small expected counts (<5 in any cell), which test is preferred over the Pearson Chi-square?

• Linear regression
• Wilcoxon signed-rank test
• Fisher’s exact test
• Mann–Whitney U test

Correct Answer: Fisher’s exact test

Q6. The Pearson Chi-square test for independence in a contingency table uses expected counts calculated from:

• Row totals only
• Column totals only
• The product of corresponding row and column totals divided by the grand total
• Sample variances of each cell

Correct Answer: The product of corresponding row and column totals divided by the grand total

Q7. Which of the following statements about the Wilcoxon signed-rank test statistic is TRUE?

• It compares sums of squared deviations from the median
• It is based on the signed ranks of differences between paired observations
• It requires normally distributed differences to be valid
• It uses contingency table counts to compute the statistic

Correct Answer: It is based on the signed ranks of differences between paired observations

Q8. When using Pearson Chi-square for goodness-of-fit, degrees of freedom are calculated as:

• Number of categories minus 1 minus number of estimated parameters
• Total sample size minus number of categories
• Number of categories multiplied by number of parameters
• Always equal to 1 for goodness-of-fit

Correct Answer: Number of categories minus 1 minus number of estimated parameters

Q9. In a 3×4 contingency table, how many degrees of freedom are used for the Pearson Chi-square test of independence?

• 3
• 6
• 8
• 12

Correct Answer: 6

Q10. Which adjustment is applied to the Pearson Chi-square statistic in a 2×2 table to improve approximation for small samples?

• Bonferroni correction
• Yates continuity correction
• Holm correction
• Fisher–Neyman correction

Correct Answer: Yates continuity correction

Q11. A researcher has paired pre- and post-treatment pain scores on an ordinal scale for 15 patients. Which test is most appropriate?

• Two-sample t-test
• Wilcoxon signed-rank test
• Mann–Whitney U test
• Pearson Chi-square test

Correct Answer: Wilcoxon signed-rank test

Q12. For the Mann–Whitney U test, a large U value corresponds to which outcome when comparing group A to group B?

• Group A has consistently larger ranks than group B
• Group A has consistently smaller ranks than group B
• There is no difference in rank distributions
• The test is invalid when U is large

Correct Answer: Group A has consistently larger ranks than group B

Q13. In Chi-square tests, standardized residuals help to:

• Determine which cells contribute most to a significant overall Chi-square
• Transform ordinal data to nominal
• Compute sample size for Wilcoxon tests
• Estimate effect size for Mann–Whitney U

Correct Answer: Determine which cells contribute most to a significant overall Chi-square

Q14. When ties are present in data for the Mann–Whitney U test, what is the recommended approach?

• Ignore ties; they do not affect the test
• Use a tie correction in the variance formula or use exact methods
• Convert tied values randomly to break ties
• Switch to a parametric t-test instead

Correct Answer: Use a tie correction in the variance formula or use exact methods

Q15. The null hypothesis for Pearson Chi-square test of independence states:

• Variables are linearly correlated
• Variables are independent (no association)
• The marginal totals are equal
• Row proportions equal column proportions exactly

Correct Answer: Variables are independent (no association)

Q16. In Wilcoxon signed-rank test, the test statistic is commonly compared to:

• A t-distribution critical value
• Theoretical critical values from Wilcoxon distribution or normal approximation for large samples
• The F-distribution
• The binomial distribution exclusively

Correct Answer: Theoretical critical values from Wilcoxon distribution or normal approximation for large samples

Q17. Which measure is an appropriate effect size for the Mann–Whitney U or Wilcoxon tests?

• Cohen’s d only
• Rank-biserial correlation or r (z/sqrt(N))
• Adjusted R-squared
• Hazard ratio

Correct Answer: Rank-biserial correlation or r (z/sqrt(N))

Q18. If expected frequencies in a contingency table are adequate, which property makes Pearson Chi-square test a large-sample test?

• It uses ranks instead of raw data
• Its sampling distribution approaches the Chi-square distribution with increasing sample size
• It estimates medians rather than means
• It requires normally distributed categorical data

Correct Answer: Its sampling distribution approaches the Chi-square distribution with increasing sample size

Q19. You want to test whether observed genotype frequencies match expected Hardy–Weinberg proportions. Which test is commonly used?

• Wilcoxon signed-rank test
• Pearson Chi-square goodness-of-fit test
• Mann–Whitney U test
• Paired t-test

Correct Answer: Pearson Chi-square goodness-of-fit test

Q20. When comparing more than two independent groups on an ordinal outcome, which non-parametric extension is appropriate instead of multiple pairwise Mann–Whitney tests?

• Kruskal–Wallis test
• Wilcoxon signed-rank test
• Pearson Chi-square test of independence
• Paired t-test

Correct Answer: Kruskal–Wallis test

Download