ANOVA – one-way and two-way analysis MCQs With Answer

Analysis of variance (ANOVA) is a core statistical tool in pharmaceutical research that compares mean responses across multiple groups. B.Pharm students must master one-way ANOVA for single-factor experiments (e.g., comparing dissolution rates among formulations) and two-way ANOVA to evaluate two factors plus interaction effects (e.g., formulation and storage temperature). Key concepts include the F-test, sums of squares, degrees of freedom, assumptions of normality, independence and homogeneity of variance, and interpreting interactions and post hoc tests (Tukey, Bonferroni). Understanding fixed vs random effects, repeated measures, and proper experimental design ensures valid inference in formulation, stability, and bioequivalence studies. Now let’s test your knowledge with 30 MCQs on this topic.

Q1. What is the main purpose of one-way ANOVA in pharmaceutical experiments?

• To test equality of variances across groups
• To compare means of more than two independent groups on a single factor
• To assess correlation between two continuous variables
• To model time-to-event survival data

Correct Answer: To compare means of more than two independent groups on a single factor

Q2. Which assumption is NOT required for a standard one-way ANOVA?

• Independence of observations
• Normality of residuals
• Homogeneity of variance across groups
• Equal sample sizes in all groups

Correct Answer: Equal sample sizes in all groups

Q3. In an ANOVA table, the F-statistic is computed as:

• Mean Square Error divided by Mean Square Treatment
• Sum of Squares Total divided by degrees of freedom
• Mean Square Treatment divided by Mean Square Error
• Sum of Squares Between divided by Sum of Squares Within

Correct Answer: Mean Square Treatment divided by Mean Square Error

Q4. In a two-way ANOVA with interaction, what does a significant interaction term indicate?

• Both main effects are equal
• The effect of one factor depends on the level of the other factor
• Residuals are not normally distributed
• The overall mean is different from zero

Correct Answer: The effect of one factor depends on the level of the other factor

Q5. Which post hoc test controls family-wise error rate and is commonly used after ANOVA?

• Levene’s test
• Tukey’s HSD test
• Shapiro-Wilk test
• Chi-square test

Correct Answer: Tukey’s HSD test

Q6. In a pharmaceutical dissolution study comparing 4 formulations, which design element ensures validity of one-way ANOVA?

• Random assignment of samples to test runs
• Using only one replicate per formulation
• Measuring different endpoints for each formulation
• Mixing formulations in the same container

Correct Answer: Random assignment of samples to test runs

Q7. What is the between-group sum of squares (SSB) measuring?

• Variation of observations around their group means
• Variation attributable to differences between group means and the grand mean
• Total variability in the dataset without partitioning
• Random error due to measurement instruments

Correct Answer: Variation attributable to differences between group means and the grand mean

Q8. Degrees of freedom for treatment in one-way ANOVA with k groups is:

• n – k
• k – 1
• n – 1
• k

Correct Answer: k – 1

Q9. Which transformation is commonly used when ANOVA residuals show positive skew and unequal variances?

• Log transformation
• Square transformation
• No transformation is ever recommended
• Reciprocal of the mean

Correct Answer: Log transformation

Q10. Which test assesses homogeneity of variances prior to running ANOVA?

• Shapiro-Wilk test
• Levene’s test
• Mann-Whitney U test
• Cochran’s Q test

Correct Answer: Levene’s test

Q11. Eta-squared (η²) in ANOVA is used to:

• Test normality of residuals
• Measure effect size or proportion of variance explained by a factor
• Adjust p-values for multiple comparisons
• Estimate sample size

Correct Answer: Measure effect size or proportion of variance explained by a factor

Q12. In a two-way ANOVA without replication, which of the following cannot be tested?

• Main effect of factor A
• Main effect of factor B
• Interaction between A and B
• Grand mean

Correct Answer: Interaction between A and B

Q13. Which scenario describes a randomized block design commonly used in pharmaceutical experiments?

• Randomly assigning formulations to different analysts and treating analyst as block
• Using only one batch of each formulation
• Testing all formulations in one uncontrolled run
• Ignoring batch-to-batch variability

Correct Answer: Randomly assigning formulations to different analysts and treating analyst as block

Q14. If ANOVA yields a non-significant F for treatment, the appropriate conclusion is:

• All group means are exactly equal
• There is no evidence to conclude at least one mean differs from others
• The experiment failed and must be repeated
• The variances are unequal

Correct Answer: There is no evidence to conclude at least one mean differs from others

Q15. In repeated measures ANOVA, which assumption is specific compared to one-way ANOVA?

• Homogeneity of variance
• Sphericity of the covariance matrix
• Normality of group means
• Independence between repeated measurements

Correct Answer: Sphericity of the covariance matrix

Q16. Which component is NOT part of the standard ANOVA table?

• Sum of Squares
• Mean Square
• Correlation Coefficient
• Degrees of Freedom

Correct Answer: Correlation Coefficient

Q17. In a two-way factorial design, “main effect” refers to:

• The effect of one factor averaged over levels of the other factor
• The combined interaction effect only
• The residual variability after fitting the model
• The mean of the error term

Correct Answer: The effect of one factor averaged over levels of the other factor

Q18. Which multiple comparison method is most conservative and reduces Type I error by adjusting alpha per comparison?

• Tukey’s HSD
• Bonferroni correction
• Dunnett’s test
• Fisher’s LSD without adjustment

Correct Answer: Bonferroni correction

Q19. For an ANOVA comparing 5 formulations with total sample size n=50, what is the error degrees of freedom?

• 45
• 49
• 5
• 44

Correct Answer: 45

Q20. Which situation suggests using a two-way ANOVA in formulation studies?

• Comparing a single formulation at one temperature
• Comparing dissolution across formulations and two storage conditions simultaneously
• Measuring only one batch repeatedly
• Comparing variances across replicates

Correct Answer: Comparing dissolution across formulations and two storage conditions simultaneously

Q21. If interaction is significant, best practice for interpreting results is:

• Ignore the interaction and focus on main effects
• Interpret main effects only if interaction is small
• Examine simple effects at specific levels of one factor
• Always pool all data and rerun analysis

Correct Answer: Examine simple effects at specific levels of one factor

Q22. In ANOVA, residuals are defined as:

• Differences between group means and grand mean
• Predicted values from the model
• Differences between observed values and their predicted/group means
• Sum of all squares

Correct Answer: Differences between observed values and their predicted/group means

Q23. Nested ANOVA is appropriate when:

• Levels of one factor are measured within levels of another factor (hierarchical structure)
• All factors are crossed and fully factorial
• There is only one observation per group
• Data are binary outcomes

Correct Answer: Levels of one factor are measured within levels of another factor (hierarchical structure)

Q24. Which measure indicates the proportion of total variance explained by the model in ANOVA?

• p-value
• R-squared or Omega-squared
• Standard error
• Skewness

Correct Answer: R-squared or Omega-squared

Q25. When sample sizes are unequal, which issue becomes more critical in ANOVA?

• Degrees of freedom for error are undefined
• Type I error inflation due to imbalance when variances differ
• Normality assumption is automatically satisfied
• Interaction effects disappear

Correct Answer: Type I error inflation due to imbalance when variances differ

Q26. Which software output element helps check ANOVA normality assumption visually?

• Boxplot of group means
• Residuals Q-Q plot
• ANOVA F-table
• Design matrix

Correct Answer: Residuals Q-Q plot

Q27. In a one-way ANOVA, Mean Square Error (MSE) estimates:

• Variance due to treatment effect
• Within-group variance or pooled estimate of error variance
• Total variance including between-group differences
• Grand mean squared

Correct Answer: Within-group variance or pooled estimate of error variance

Q28. A significant F-test at alpha=0.05 means:

• All groups differ from each other
• At least one group mean differs from others, requiring post hoc tests to locate differences
• The null hypothesis of equal variances is true
• The sample size is too large

Correct Answer: At least one group mean differs from others, requiring post hoc tests to locate differences

Q29. Which approach is recommended if ANOVA assumptions cannot be satisfied with transformations?

• Use nonparametric alternatives like Kruskal-Wallis or Friedman test
• Proceed with ANOVA regardless of assumptions
• Increase alpha to 0.10
• Remove the largest group

Correct Answer: Use nonparametric alternatives like Kruskal-Wallis or Friedman test

Q30. In two-way ANOVA with replication, the error term for interaction testing is based on:

• Mean Square of factor A
• Mean Square of factor B
• Mean Square Error (residual) pooled across replicates
• Grand mean squared

Correct Answer: Mean Square Error (residual) pooled across replicates

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