Q1. The primary purpose of ANOVA is to:
a) Compare the means of two groups
b) Compare the means of three or more groups
c) Measure correlation between variables
d) Test for normal distribution
Correct Answer: b) Compare the means of three or more groups
Explanation: ANOVA (Analysis of Variance) is mainly used when we want to check if there are significant differences among the means of three or more independent groups. For two groups, a t-test is usually used.
Q2. ANOVA compares:
a) Variances between samples only
b) Variances within samples only
c) Variance between groups to variance within groups
d) Standard deviations of samples
Correct Answer: c) Variance between groups to variance within groups
Explanation: ANOVA uses the F-ratio, which is the variance between group means divided by the variance within the groups. A higher F-ratio suggests a higher likelihood that at least one group mean is different.
Q3. Which of the following is NOT a type of ANOVA?
a) One-way ANOVA
b) Two-way ANOVA
c) Repeated Measures ANOVA
d) Logistic ANOVA
Correct Answer: d) Logistic ANOVA
Explanation: Common types include One-way (one factor), Two-way (two factors), and Repeated Measures (same subjects tested under multiple conditions). “Logistic ANOVA” is not a statistical term; logistic regression is a different method.
Q4. In ANOVA, the F-statistic represents:
a) The ratio of means to variances
b) The ratio of between-group variance to within-group variance
c) The sum of all squared deviations
d) The probability of Type I error
Correct Answer: b) The ratio of between-group variance to within-group variance
Explanation: F = Variance between groups / Variance within groups. A large F means that the differences between the group means are large relative to the variability inside the groups.
Q5. Which of the following is NOT an assumption of ANOVA?
a) Independence of observations
b) Normality of data within groups
c) Homogeneity of variances
d) Equal sample sizes in all groups
Correct Answer: d) Equal sample sizes in all groups
Explanation: ANOVA works best with equal sample sizes, but it is not a strict assumption. The three main assumptions are independence, normal distribution of residuals, and equal variances (homogeneity).
Q6. After finding a significant ANOVA result, which test is typically used to find where the differences lie?
a) Pearson’s correlation
b) Tukey’s HSD
c) Shapiro-Wilk test
d) Levene’s test
Correct Answer: b) Tukey’s HSD
Explanation: Post-hoc tests like Tukey’s Honestly Significant Difference, Bonferroni, or Scheffé are used after a significant ANOVA to identify which groups differ from each other.
Q7. A teacher wants to compare the exam scores of students taught with three different teaching methods. The best statistical test is:
a) Independent t-test
b) Paired t-test
c) One-way ANOVA
d) Chi-square test
Correct Answer: c) One-way ANOVA
Explanation: Since there are three groups (three teaching methods) and one dependent variable (exam score), a one-way ANOVA is the correct test.
Q8. In ANOVA, if the p-value is less than 0.05, it means:
a) All group means are equal
b) At least one group mean is significantly different
c) Variances are not equal
d) The data is not normally distributed
Correct Answer: b) At least one group mean is significantly different
Explanation: A significant p-value in ANOVA tells us that there’s evidence that at least one group mean differs, but it doesn’t tell which one — post-hoc testing is needed for that.
Q9. A researcher studies the effects of diet type (3 categories) and exercise frequency (2 categories) on weight loss. Which ANOVA should be used?
a) One-way ANOVA
b) Two-way ANOVA
c) Repeated Measures ANOVA
d) MANOVA
Correct Answer: b) Two-way ANOVA
Explanation: This situation has two independent variables (diet type and exercise frequency), so a two-way ANOVA is used to test for main effects and interaction effects.
Q10. Which test is an extension of ANOVA that can analyze multiple dependent variables at once?
a) MANOVA
b) ANCOVA
c) Kruskal-Wallis test
d) Friedman test
Correct Answer: a) MANOVA
Explanation: MANOVA (Multivariate Analysis of Variance) extends ANOVA to situations where there is more than one dependent variable. ANCOVA adds covariates; Kruskal-Wallis is the non-parametric alternative.
Q11. In ANOVA, the term “sum of squares” refers to:
a) The sum of all raw scores
b) The sum of squared deviations from the mean
c) The sum of standard deviations of groups
d) The square of the mean differences
Correct Answer: b) The sum of squared deviations from the mean
Explanation: ANOVA works with sum of squares (SS) to measure total variability. SS can be split into SS Between (variation due to group differences) and SS Within (variation due to individual differences inside groups).
Q12. In a one-way ANOVA, the total variability in the data is split into:
a) Between-groups variance only
b) Within-groups variance only
c) Between-groups variance + Within-groups variance
d) Mean squares and standard errors
Correct Answer: c) Between-groups variance + Within-groups variance
Explanation: Total Sum of Squares (SST) = Between-groups Sum of Squares (SSB) + Within-groups Sum of Squares (SSW). This partitioning is the foundation of ANOVA calculations.
MCQ 13 – Degrees of Freedom
Q13. In a one-way ANOVA with k groups and N total observations, the degrees of freedom for between-groups is:
a) k
b) N – k
c) k – 1
d) N – 1
Correct Answer: c) k – 1
Explanation:
- df(Between) = k – 1
- df(Within) = N – k
- df(Total) = N – 1
Q14. In ANOVA, the mean square is obtained by:
a) Dividing sum of squares by total N
b) Dividing sum of squares by its corresponding degrees of freedom
c) Dividing group means by total number of groups
d) Multiplying F by p-value
Correct Answer: b) Dividing sum of squares by its corresponding degrees of freedom
Explanation: Mean Square (MS) = SS / df.
- MS Between = SSB / (k – 1)
- MS Within = SSW / (N – k)
Q15. The F-distribution used in ANOVA:
a) Is symmetric and bell-shaped
b) Is positively skewed
c) Can take negative values
d) Is identical to the t-distribution
Correct Answer: b) Is positively skewed
Explanation: The F-distribution is always positive (variance ratios can’t be negative) and skewed to the right, especially with small sample sizes.
Q16. If ANOVA assumptions are violated (especially normality), the non-parametric alternative for one-way ANOVA is:
a) Kruskal–Wallis test
b) Chi-square test
c) Mann–Whitney U test
d) Wilcoxon signed-rank test
Correct Answer: a) Kruskal–Wallis test
Explanation: Kruskal–Wallis is a rank-based non-parametric test for comparing three or more independent groups when ANOVA assumptions are not met.
Q17. In a two-way ANOVA, an interaction effect means:
a) The two factors influence each other’s effect on the dependent variable
b) Both factors are independent
c) The dependent variable affects the independent variable
d) Variance is equal across groups
Correct Answer: a) The two factors influence each other’s effect on the dependent variable
Explanation: An interaction occurs when the effect of one factor depends on the level of the other factor.
Q18. ANCOVA is an extension of ANOVA that:
a) Handles non-parametric data
b) Includes covariates to control for other variables
c) Compares only two groups
d) Requires no assumptions
Correct Answer: b) Includes covariates to control for other variables
Explanation: ANCOVA (Analysis of Covariance) adjusts the dependent variable for the influence of covariates, improving accuracy.
MCQ 19 – Repeated Measures ANOVA
Q19. Repeated Measures ANOVA is appropriate when:
a) Different participants are tested in each group
b) The same participants are tested under all conditions
c) There are no dependent variables
d) Samples are completely random
Correct Answer: b) The same participants are tested under all conditions
Explanation: Repeated measures ANOVA accounts for within-subject correlations when the same subjects are exposed to multiple treatments.
Q20. A significant ANOVA result means:
a) All group means are different from each other
b) At least one group mean is different from the others
c) Variances are unequal
d) Data is non-normal
Correct Answer: b) At least one group mean is different from the others
Explanation: ANOVA tells us if differences exist somewhere, but not exactly where — post-hoc tests are needed to find specific differences.
Q21. Which ANOVA assumption is considered most critical to avoid incorrect conclusions?
a) Independence of observations
b) Normality of data within groups
c) Equal sample sizes
d) Equal means across groups
Correct Answer: a) Independence of observations
Explanation: Independence is fundamental; violating it can severely bias results. ANOVA is somewhat robust to normality violations with large samples, but not to dependence between observations.
Q22. Which statistical test is commonly used before ANOVA to check homogeneity of variances?
a) Shapiro–Wilk test
b) Levene’s test
c) Tukey’s HSD
d) Bartlett’s test
Correct Answer: b) Levene’s test
Explanation: Levene’s test checks if the variances across groups are approximately equal — one of the key assumptions of ANOVA.
Q23. If homogeneity of variance is violated in a one-way ANOVA, an appropriate alternative is:
a) Kruskal–Wallis test
b) Welch’s ANOVA
c) Two-way ANOVA
d) ANCOVA
Correct Answer: b) Welch’s ANOVA
Explanation: Welch’s ANOVA adjusts the F-ratio to be more reliable when group variances are unequal.
Q24. A researcher finds that their ANOVA residuals are not normally distributed. One possible solution is:
a) Increase the number of groups
b) Perform a logarithmic or square-root transformation on the data
c) Reduce sample size
d) Change the p-value threshold to 0.10
Correct Answer: b) Perform a logarithmic or square-root transformation
Explanation: Transformations can help meet normality and variance assumptions before running ANOVA.
Q25. In ANOVA, a common measure of effect size is:
a) Pearson’s r
b) Cohen’s d
c) Eta-squared (η²)
d) Cronbach’s alpha
Correct Answer: c) Eta-squared (η²)
Explanation: Eta-squared indicates the proportion of total variance explained by the independent variable(s). Cohen’s d is for two-group differences.
Q26. The F-critical value in ANOVA is determined by:
a) Mean difference and variance ratio
b) Alpha level, df between, and df within
c) Sample means only
d) Number of dependent variables
Correct Answer: b) Alpha level, df between, and df within
Explanation: You find the F-critical from F-distribution tables using the degrees of freedom and the significance level.
Q27. If you want to control for Type I error very strictly when doing multiple comparisons after ANOVA, you might choose:
a) Tukey’s HSD
b) Bonferroni correction
c) Scheffé’s test
d) Fisher’s LSD
Correct Answer: b) Bonferroni correction
Explanation: Bonferroni adjusts the significance level by dividing alpha by the number of comparisons — making it very conservative.
Q28. Which of the following is a misuse of ANOVA?
a) Using it for 5 independent groups
b) Using it when dependent variable is categorical
c) Checking equal variances before analysis
d) Running post-hoc tests after a significant result
Correct Answer: b) Using it when dependent variable is categorical
Explanation: ANOVA requires a continuous dependent variable. For categorical outcomes, chi-square or logistic regression is used.
Q29. A study with one between-subjects factor (gender) and one within-subjects factor (pre- and post-training scores) should use:
a) One-way ANOVA
b) Two-way ANOVA
c) Mixed-design ANOVA
d) MANOVA
Correct Answer: c) Mixed-design ANOVA
Explanation: Mixed ANOVA handles a combination of between-subjects and within-subjects variables.
Q30. Why is ANOVA more robust to non-normality with large samples?
a) Because F-statistic becomes zero
b) Because the central limit theorem applies
c) Because variances automatically become equal
d) Because p-value is unaffected by normality
Correct Answer: b) Because the central limit theorem applies
Explanation: With large samples, the sampling distribution of the mean tends to be normal, making ANOVA more robust to violations of normality.