Introduction: The Kruskal–Wallis test and Friedman test are essential non-parametric statistical tools in B. Pharm and biostatistics for comparing group differences when data violate parametric assumptions. The Kruskal–Wallis test compares medians across three or more independent groups using rank sums, while the Friedman test evaluates differences across repeated measures or matched groups by ranking within subjects. Both tests use chi-square approximations, handle ordinal or skewed data, and require attention to ties and post-hoc pairwise comparisons (e.g., Dunn or Wilcoxon with adjustment). These methods are widely applied in pharmacology, clinical trials, and formulation studies for robust hypothesis testing. Now let’s test your knowledge with 30 MCQs on this topic.
Q1. What is the primary purpose of the Kruskal–Wallis test?
- To compare means of two independent groups assuming normality
- To compare medians across three or more independent groups using ranks
- To assess correlation between two continuous variables
- To analyze paired binary outcomes
Correct Answer: To compare medians across three or more independent groups using ranks
Q2. What type of data is most appropriate for the Friedman test?
- Independent continuous data with normal distribution
- Ordinal or continuous repeated measures within subjects
- Binary independent outcomes across groups
- Count data with Poisson distribution
Correct Answer: Ordinal or continuous repeated measures within subjects
Q3. Which assumption is NOT required for the Kruskal–Wallis test?
- Independent observations
- Same shape of distribution across groups
- Normal distribution within each group
- Ordinal or continuous data
Correct Answer: Normal distribution within each group
Q4. The Kruskal–Wallis test statistic H approximates which distribution for large samples?
- Student’s t-distribution
- Chi-square distribution
- F-distribution
- Binomial distribution
Correct Answer: Chi-square distribution
Q5. In a pharmacokinetic study comparing Cmax across three formulations with skewed data, which test is most appropriate?
- One-way ANOVA
- Kruskal–Wallis test
- Paired t-test
- Chi-square test
Correct Answer: Kruskal–Wallis test
Q6. How are ties handled in the Kruskal–Wallis test?
- Ties are ignored; test cannot be used with tied ranks
- Ties are assigned average ranks and a correction factor is applied
- Ties are broken randomly before ranking
- Ties automatically convert the test to ANOVA
Correct Answer: Ties are assigned average ranks and a correction factor is applied
Q7. Which post-hoc test is commonly used after a significant Kruskal–Wallis result?
- Dunnett’s test
- Dunn’s test with Bonferroni or Holm adjustment
- Tukey’s HSD
- McNemar’s test
Correct Answer: Dunn’s test with Bonferroni or Holm adjustment
Q8. What is the null hypothesis of the Friedman test?
- All group means are equal
- All treatment effects are zero across repeated measures (no differences)
- Data are normally distributed within subjects
- There is no association between two categorical variables
Correct Answer: All treatment effects are zero across repeated measures (no differences)
Q9. In a crossover study measuring blood pressure at three time points per subject, which test fits best?
- Kruskal–Wallis test
- Friedman test
- Chi-square test
- Independent samples t-test
Correct Answer: Friedman test
Q10. Which statistic is reported for the Kruskal–Wallis test result?
- H statistic with degrees of freedom and p-value
- T statistic with degrees of freedom and p-value
- Pearson correlation coefficient and p-value
- Odds ratio and confidence interval
Correct Answer: H statistic with degrees of freedom and p-value
Q11. When sample sizes are small and tied ranks are many, what is a recommended approach for Kruskal–Wallis?
- Use chi-square approximation regardless
- Use exact permutation or Monte Carlo methods for p-value
- Switch to parametric ANOVA without checks
- Discard tied observations
Correct Answer: Use exact permutation or Monte Carlo methods for p-value
Q12. Which effect size measure can be used with Kruskal–Wallis results?
- Cohen’s d for two groups only
- Eta-squared or epsilon-squared calculated from H
- Pearson’s r for correlations
- Relative risk
Correct Answer: Eta-squared or epsilon-squared calculated from H
Q13. For Friedman test post-hoc pairwise comparisons, which method is commonly applied?
- Independent samples t-test without adjustment
- Wilcoxon signed-rank test with Bonferroni correction
- Kruskal–Wallis on pairs without adjustments
- Chi-square test for each pair
Correct Answer: Wilcoxon signed-rank test with Bonferroni correction
Q14. Which of the following best describes data appropriate for Kruskal–Wallis?
- Nominal data with more than two categories
- Ordinal scores or continuous non-normal data across independent groups
- Paired continuous measurements
- Binary matched-pair outcomes
Correct Answer: Ordinal scores or continuous non-normal data across independent groups
Q15. If the Friedman test yields a significant p-value, what is the correct next step?
- Declare all groups equal despite significance
- Conduct post-hoc pairwise comparisons with appropriate adjustment
- Switch to Kruskal–Wallis for confirmation
- Ignore the result because Friedman is non-parametric
Correct Answer: Conduct post-hoc pairwise comparisons with appropriate adjustment
Q16. How are ranks computed in the Friedman test?
- Ranks are computed across subjects for each treatment separately
- Within each subject, observations are ranked across treatments
- Global ranking across all observations ignoring subjects
- Only the largest value per subject is ranked
Correct Answer: Within each subject, observations are ranked across treatments
Q17. Which scenario would violate the independence assumption for Kruskal–Wallis?
- Randomly assigned independent treatment groups
- Repeated measures on the same subjects treated as separate groups
- Different patients in each treatment arm
- Independent laboratory replicates from different donors
Correct Answer: Repeated measures on the same subjects treated as separate groups
Q18. What does a large H statistic imply in Kruskal–Wallis?
- Strong evidence against the null hypothesis of equal distributions
- Evidence that all group medians are equal
- That the test assumptions are violated
- That sample size is too small
Correct Answer: Strong evidence against the null hypothesis of equal distributions
Q19. Which software command is commonly used to perform Kruskal–Wallis in R?
- lm()
- kruskal.test()
- friedman.test()
- t.test()
Correct Answer: kruskal.test()
Q20. For reporting Friedman test results in a manuscript, which elements should be included?
- Only the p-value without test name
- Test name, chi-square or Friedman statistic, degrees of freedom, p-value, and post-hoc methods
- Mean ± SD for each group only
- Only a figure without statistics
Correct Answer: Test name, chi-square or Friedman statistic, degrees of freedom, p-value, and post-hoc methods
Q21. Which is a limitation of Kruskal–Wallis compared with ANOVA?
- Cannot handle non-normal data
- Does not estimate group means or allow complex models with covariates easily
- Is only for paired data
- Requires equal variances strictly
Correct Answer: Does not estimate group means or allow complex models with covariates easily
Q22. When comparing more than three matched formulations across patients, which statistic indicates overall difference?
- Kruskal–Wallis H
- Friedman chi-square statistic
- Independent t-test
- Fisher’s exact test
Correct Answer: Friedman chi-square statistic
Q23. If tied ranks are frequent in Friedman test, what is recommended?
- Ignore tie effects; proceed normally
- Use tie corrections or exact methods and interpret cautiously
- Convert data to nominal categories and use chi-square
- Delete tied observations
Correct Answer: Use tie corrections or exact methods and interpret cautiously
Q24. Which of these is a correct null hypothesis for Kruskal–Wallis when applied to three drug dose groups?
- At least one dose group median differs
- All three dose group distributions are identical
- The highest dose has the largest mean
- Dose and response are perfectly correlated
Correct Answer: All three dose group distributions are identical
Q25. How does sample size affect the chi-square approximation for Kruskal–Wallis?
- Larger samples improve the accuracy of the chi-square approximation
- Sample size has no effect on approximation accuracy
- Smaller samples always improve approximation
- Chi-square approximation is invalid regardless of sample size
Correct Answer: Larger samples improve the accuracy of the chi-square approximation
Q26. Which measurement scale is least appropriate for Kruskal–Wallis or Friedman tests?
- Ordinal pain scores
- Continuous skewed concentration values
- Nominal categories without order
- Likert-scale questionnaire responses
Correct Answer: Nominal categories without order
Q27. In reporting a Kruskal–Wallis result, you obtained H = 7.82 with df = 2 and p = 0.02. What does this indicate?
- No evidence of difference among the three groups
- Significant difference among groups; at least one group differs
- Test failed due to ties
- All three groups have equal medians
Correct Answer: Significant difference among groups; at least one group differs
Q28. When would you prefer Friedman test over repeated measures ANOVA?
- When residuals are normally distributed and homoscedastic
- When repeated measures data are ordinal or violate parametric assumptions
- When there are only independent groups
- When comparing two unrelated samples
Correct Answer: When repeated measures data are ordinal or violate parametric assumptions
Q29. Which statement about degrees of freedom for Kruskal–Wallis is correct?
- df = total sample size minus one
- df = number of groups minus one
- df = number of observations per group
- df is not defined for Kruskal–Wallis
Correct Answer: df = number of groups minus one
Q30. In a repeated-measures drug efficacy trial with missing timepoints for some subjects, which issue affects Friedman test validity?
- Friedman requires balanced data without missing observations per block
- Missing data has no impact; proceed directly
- Friedman automatically imputes missing values
- Friedman is only for independent groups, so missing data is fine
Correct Answer: Friedman requires balanced data without missing observations per block
