One-way ANOVA is a fundamental statistical tool for comparing means across three or more groups, essential in pharmaceutical research and B. Pharm coursework. This concise, practical introduction covers assumptions (normality, independence, homogeneity of variances), calculation of sums of squares, mean squares, F-statistic, degrees of freedom, and interpretation of p-values. It also explains post-hoc tests (Tukey, Bonferroni), effect size (eta-squared), and real-world applications in drug formulation, stability testing and bioequivalence studies. These MCQs focus on data analysis, interpretation, common pitfalls and software outputs to strengthen your ability to choose, run and report one-way ANOVA results. Now let’s test your knowledge with 30 MCQs on this topic.
Q1. What is the primary objective of a one-way ANOVA?
- To compare means of three or more independent groups
- To assess correlation between two variables
- To compare variances of two groups only
- To predict a continuous outcome from multiple predictors
Correct Answer: To compare means of three or more independent groups
Q2. In one-way ANOVA the null hypothesis states:
- All group variances are equal
- All group means are equal
- At least one mean differs from the others
- There is a linear relationship between groups
Correct Answer: All group means are equal
Q3. Which assumption is NOT required for a valid one-way ANOVA?
- Independence of observations
- Normality of residuals
- Homogeneity of variances
- Equal sample sizes across groups
Correct Answer: Equal sample sizes across groups
Q4. The F-statistic in one-way ANOVA is computed as:
- Mean square within divided by mean square between
- Mean square between divided by mean square within
- Total sum of squares divided by degrees of freedom
- Difference between largest and smallest group mean
Correct Answer: Mean square between divided by mean square within
Q5. Which test is commonly used to check homogeneity of variances before ANOVA?
- Shapiro-Wilk test
- Levene’s test
- Durbin-Watson test
- Kruskal-Wallis test
Correct Answer: Levene’s test
Q6. In the ANOVA table, mean square (MS) is calculated by:
- SS × df
- SS divided by df
- df divided by SS
- F statistic divided by p-value
Correct Answer: SS divided by df
Q7. If the one-way ANOVA p-value is less than alpha (e.g., 0.05), you should:
- Fail to reject the null hypothesis
- Reject the null hypothesis and conclude at least one mean differs
- Conclude all group means are equal
- Immediately run a correlation analysis
Correct Answer: Reject the null hypothesis and conclude at least one mean differs
Q8. Which post-hoc test controls family-wise error rate and is often used after significant ANOVA?
- Tukey’s HSD test
- Shapiro-Wilk test
- Mann-Whitney U test
- Levene’s test
Correct Answer: Tukey’s HSD test
Q9. In pharmaceutical formulation studies comparing three batches, one-way ANOVA is used because:
- It compares the medians of paired samples
- It compares more than two group means simultaneously
- It predicts dissolution profile over time
- It tests for normality of data
Correct Answer: It compares more than two group means simultaneously
Q10. Total sum of squares (SST) is partitioned into:
- SSbetween and SSwithin
- SSerror and SSresidual only
- SSmodel only
- SSvariance and SSkurtosis
Correct Answer: SSbetween and SSwithin
Q11. Degrees of freedom between groups with k groups is:
- k
- k − 1
- n − k
- n − 1
Correct Answer: k − 1
Q12. Which nonparametric alternative is used when ANOVA assumptions are violated?
- Mann-Whitney U test
- Kruskal-Wallis test
- Chi-square test
- Paired t-test
Correct Answer: Kruskal-Wallis test
Q13. Eta-squared in ANOVA is a measure of:
- Statistical power only
- Effect size or proportion of variance explained
- Number of groups required
- Skewness of the distribution
Correct Answer: Effect size or proportion of variance explained
Q14. If sample sizes are unequal (unbalanced design), one-way ANOVA:
- Is completely invalid and cannot be used
- Still works but interpretation and post-hoc tests may require adjustments
- Automatically changes to two-way ANOVA
- Requires combining groups to equal sizes
Correct Answer: Still works but interpretation and post-hoc tests may require adjustments
Q15. Which outcome indicates a large F value in ANOVA?
- Between-group variance much larger than within-group variance
- Within-group variance much larger than between-group variance
- Total variance is zero
- All group means are identical
Correct Answer: Between-group variance much larger than within-group variance
Q16. One-way ANOVA is equivalent to which test when there are exactly two groups?
- Chi-square test
- Independent samples t-test
- Paired t-test
- Mann-Whitney U test
Correct Answer: Independent samples t-test
Q17. Which part of the ANOVA table gives the test statistic denominator?
- SSbetween
- MSwithin
- F statistic
- p-value
Correct Answer: MSwithin
Q18. When would you use one-way ANOVA in stability testing?
- To compare degradation rates across three storage conditions
- To estimate molecular weight distribution
- To calculate dissolution half-life from a single batch
- To determine sample contamination qualitatively
Correct Answer: To compare degradation rates across three storage conditions
Q19. Violating the homogeneity of variances assumption may lead to:
- Improved statistical power always
- Inflated Type I error rates or misleading p-values
- No effect on ANOVA results
- Automatic correction by software without options
Correct Answer: Inflated Type I error rates or misleading p-values
Q20. In reporting ANOVA results for a journal, which elements are essential?
- Only the p-value
- F statistic, degrees of freedom, p-value and effect size
- Raw data only without statistics
- Just the post-hoc table without ANOVA
Correct Answer: F statistic, degrees of freedom, p-value and effect size
Q21. Which software output component indicates whether group means differ overall?
- ANOVA F-test and its p-value
- Histograms only
- Boxplot medians only
- Descriptive statistics without tests
Correct Answer: ANOVA F-test and its p-value
Q22. For pairwise comparisons after ANOVA, Bonferroni correction is used to:
- Increase Type I error rate
- Control family-wise Type I error by adjusting significance level
- Test normality of residuals
- Replace Tukey’s test always
Correct Answer: Control family-wise Type I error by adjusting significance level
Q23. If residuals are markedly non-normal in a large sample, ANOVA is:
- Completely invalid and must be discarded
- Often robust to moderate non-normality due to central limit theorem
- Requires transforming degrees of freedom
- Automatically becomes nonparametric
Correct Answer: Often robust to moderate non-normality due to central limit theorem
Q24. Which scenario requires repeated measures ANOVA instead of one-way ANOVA?
- Comparing three independent drug batches
- Comparing the same subjects measured at baseline, 1 month and 3 months
- Comparing dissolution across three formulations with different subjects
- Comparing variances among groups
Correct Answer: Comparing the same subjects measured at baseline, 1 month and 3 months
Q25. The within-group sum of squares reflects:
- Variation due to differences between group means
- Variation due to differences within each group (residual error)
- Total variation in the entire dataset
- Average group mean squared
Correct Answer: Variation due to differences within each group (residual error)
Q26. Power of one-way ANOVA increases with:
- Smaller sample size and larger variance
- Larger sample size, larger effect size, and lower variance
- More groups with tiny differences
- Increasing alpha to 1.0
Correct Answer: Larger sample size, larger effect size, and lower variance
Q27. In ANOVA, a small p-value with a tiny effect size suggests:
- A practically important difference between groups
- Statistical significance but potentially trivial practical importance
- No difference between groups
- Violation of independence only
Correct Answer: Statistical significance but potentially trivial practical importance
Q28. Which statement about one-way ANOVA and multiple t-tests is correct?
- Multiple t-tests maintain family-wise error rate better than ANOVA
- ANOVA controls Type I error better than multiple separate t-tests
- ANOVA can only compare two groups while t-tests compare many
- They are unrelated methods
Correct Answer: ANOVA controls Type I error better than multiple separate t-tests
Q29. When designing an experiment for ANOVA in B. Pharm research, you should consider:
- Randomization, replication (sample size), and control of confounders
- Only the color of the packaging
- Eliminating variance by using identical samples always
- Avoiding any pre-study power calculation
Correct Answer: Randomization, replication (sample size), and control of confounders
Q30. Which output indicates the proportion of total variability explained by group membership?
- p-value
- Eta-squared (η²)
- Standard error
- Degrees of freedom
Correct Answer: Eta-squared (η²)
I am a Registered Pharmacist under the Pharmacy Act, 1948, and the founder of PharmacyFreak.com. I hold a Bachelor of Pharmacy degree from Rungta College of Pharmaceutical Science and Research. With a strong academic foundation and practical knowledge, I am committed to providing accurate, easy-to-understand content to support pharmacy students and professionals. My aim is to make complex pharmaceutical concepts accessible and useful for real-world application.
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