# 50 MCQs on sample size calculation

By | April 23, 2024

1. Which of the following is NOT used in sample size calculation?

a) Type I error rate
b) Type II error rate
c) Randomization ratio
d) Hypothesized difference between groups

2. The Type I error rate is usually set at:

a) 0.05
b) 0.01
c) 0.1
d) 0.2

3. The Type II error rate is usually set at:

a) 0.05
b) 0.1
c) 0.2
d) 0.3

4. If the Type I error is 0.05 and power is 80%, the Type II error is:

a) 0.05
b) 0.1
c) 0.2
d) 0.3

5. Sample size is NOT affected by:

a) Type I error rate
b) Type II error rate
c) Variance of the outcome
d) Randomization ratio

6. A larger sample size is required if the variance of the outcome is:

a) Small
b) Large
c) Medium
d) Doesn’t depend on variance

7. Sample size calculation for equivalence/non-inferiority trials requires knowledge of:

a) Minimum clinically important difference
b) Hypothesized difference between groups
c) Both a and b
d) Neither a nor b

8. If the variances of the two groups being compared are different, then the sample size formula for:

a) Independent t-test is used
b) Pooled t-test is used
c) Either independent or pooled t-test can be used
d) No t-test formula applies

9. For a two group parallel design comparing means, which formula is used to calculate the total sample size if equal group sizes are assumed?

a) N = [Zα/2 + Zβ]2 * (σ12 + σ22) / (μ1 – μ2)2
b) N = 2 * [Zα/2 + Zβ]2 * (σ1 + σ2)2 / (μ1 – μ2)2
c) N = [Zα/2 + Zβ]2 * (σ1 + σ2)2 / (μ1 – μ2)2
d) N = 2 * [Zα/2 + Zβ]2 * (σ12 + σ22) / (μ1 – μ2)2

10. For a two group parallel design comparing proportions, which formula is used to calculate the total sample size if equal group sizes are assumed?

a) N = [Zα/2 + Zβ]2 * (p1(1-p1) + p2(1-p2)) / (p1 – p2)2
b) N = 2 * [Zα/2 + Zβ]2 * (√p(1-p)) / (p1 – p2)2
c) N = [Zα/2 + Zβ]2 * (√p1(1-p1) + √p2(1-p2)) / (p1 – p2)2
d) N = 2 * [Zα/2 + Zβ]2 * (p1(1-p1) + p2(1-p2)) / (p1 – p2)2

11. When using a one-sample t-test to compare a mean to a reference value, the sample size formula is:

a) N = [Zα/2 + Zβ]2 * σ2 / Δ2
b) N = 2 * [Zα/2 + Zβ]2 * σ2 / Δ2
c) N = [Zα/2 + Zβ] * σ / Δ
d) None of the above

12. For a binary outcome in a non-inferiority or equivalence trial, which value should be used for p in the sample size calculation?

a) Proportion in the control group
b) Proportion in the experimental group
c) Average of the expected proportions in both groups
d) It does not depend on the group proportions

13. In a two-arm parallel design comparing means, if the variance in one group is 1.5 times the variance in the other group, which formula should be used?

a) Independent t-test formula
b) Pooled t-test formula
c) Either formula can be used with an adjustment factor
d) No t-test formula applies in this case

14. For a study comparing three independent groups on a continuous outcome, which test should be used to calculate the sample size?

a) One-way ANOVA
b) Independent t-test
c) Chi-square test
d) McNemar’s test

15. The sample size needed for a one-way ANOVA with 3 groups and 80% power to detect an effect size of 0.5 between any two groups is:

a) 27 per group
b) 52 per group
c) 78 per group
d) 105 per group

16. If the standard deviation used in the sample size calculation is overestimated, then the actual study power will be:

a) Higher than anticipated
b) Lower than anticipated
c) Remain the same
d) Can’t say without knowing the extent of overestimation

17. If the difference between groups used in the sample size calculation is underestimated, then the actual study power will be:

a) Higher than anticipated
b) Lower than anticipated
c) Remain the same
d) Can’t say without knowing the extent of underestimation

18. For a two-arm superiority trial comparing proportions, if the hypothesized proportion in the control group is 0.2 and experimental group is 0.1, then the minimum sample size per group for 80% power is:

a) 64
b) 128
c) 256
d) 512

19. For a two-arm non-inferiority trial comparing proportions, if the control proportion is 0.2, non-inferiority margin is 0.05 and we want 90% power, the minimum total sample size is:

a) 198
b) 396
c) 792
d) 1584

20. If a multi-center randomized controlled trial is planned with 10 centers, the sample size needs to be:

a) Increased to account for center effect
b) Decreased to account for center effect
c) Not adjusted as center effect is averaged out
d) It depends on the degree of heterogeneity between centers

21. When the alternative hypothesis is two-sided, we use:

a) Smaller Z-values for power and type I error
b) Larger Z-values for power and type I error
c) Smaller Z-value for power, larger for type I error
d) Larger Z-value for power, smaller for type I error

22. For a paired t-test design comparing changes from baseline between two groups, the sample size formula is:

a) Same as independent t-test
b) Half the sample size of independent t-test
c) Twice the sample size of independent t-test
d) A different formula accounting for the correlation

23. If sample size estimation assumes a one-sided test but the actual analysis is two-sided:

a) Power will be higher than estimated
b) Power will be lower than estimated
c) Power remains the same

24. The minimum clinically important difference is defined as:

a) The smallest change in outcome that would lead a patient to change management
b) Half the standard deviation of the outcome measure
c) One standard deviation of the outcome measure
d) None of the above

25. In a multicenter trial, sample size should be increased by what percentage to account for a design effect of 1.5?

a) 50%
b) 100%
c) 150%
d) 200%

26. For a non-inferiority trial, the non-inferiority margin is usually defined as a proportion of:

a) The treatment effect seen in previous superiority trials
b) Half the treatment effect seen in previous superiority trials
c) One standard deviation of the outcome measure
d) The minimum clinically important difference

27. For logistic regression with 6 predictor variables, a minimum of _____ subjects are needed in the smaller of the two outcome groups to ensure sufficient power:

a) 10 per predictor
b) 15 per predictor
c) 20 per predictor
d) 30 per predictor

28. If the hypothesized mean difference used in the sample size calculation is too large, then the actual study power will be:

a) Higher than anticipated
b) Lower than anticipated
c) Remain the same
d) Can’t determine without a precise amount

29. An interim analysis is planned for a randomized trial after half the target sample size has been recruited. To account for this interim look, the final target sample size needs to be:

a) Increased by 10%
b) Increased by 20%
c) Increased by 30%
d) Increased by 50%

30. If the true difference between groups is larger than hypothesized in the sample size calculation, then:

a) Power will be lower than anticipated
b) Power will be higher than anticipated
c) Power remains the same
d) Can’t determine without knowing the true difference

31. For a multi-arm trial with 3 experimental arms and 1 control arm comparing a continuous outcome, which design has the highest statistical power:

a) One-way ANOVA with 3 separate pairwise comparisons
b) One overall F-test from ANOVA with 3 separate t-tests if F is significant
c) Multiple linear regression with dummy variables for each arm
d) Repeated measures ANOVA

32. If the number of patients recruited exceeds the target sample size, then:

a) Statistical power remains the same
b) Statistical power increases marginally
c) Statistical power increases substantially
d) Oversampling has no effect on statistical power

33. All things remaining equal, a matched case-control study requires ____ the sample size of a randomized controlled trial:

a) Half
b) One-third
c) Twice
d) Three times

34. If binary outcome event rates are higher than expected, the required sample size ____ to maintain the same power:

a) Increases
b) Decreases
c) Remains the same
d) Cannot be determined without knowing actual event rates

35. Sample size estimation should use a ____ estimate of standard deviation rather than a best guess:

a) Conservative
b) Liberal
c) Precise
d) Unbiased

36. For sample size estimation, it is generally safer to assume the variance in the _____ arm will be larger:

a) Experimental
b) Active control
c) Placebo control
d) Either arm could be assumed

37. A crossover trial requires ____ the sample size compared to a parallel design:

a) Half
b) One-third
c) Twice
d) The same

38. In a multiple linear regression model with 4 predictors, the minimum required sample size for 90% power is ____ subjects:

a) 40
b) 50
c) 60
d) 75

39. If the absolute risk reduction seen in previous studies is smaller than hypothesized in sample size calculations, the actual study power will be:

a) Higher than anticipated
b) Lower than anticipated
c) Remain the same
d) Cannot determine without knowing the true risk reduction

40. If the variability (standard deviation) of the outcome is lower than assumed, the actual study power will be:

a) Higher than anticipated
b) Lower than anticipated
c) Remain the same
d) Cannot determine without knowing the true variability

41. Sample size recalculation is recommended during the trial if:

a) Actual event rates are significantly different than hypothesized
b) An interim analysis shows large treatment effect
c) Accrual is slower than predicted
d) Any of the above

42. In permutation testing, the required sample size is:

a) Larger than parametric tests as it is more conservative
b) Smaller than parametric tests as it is less conservative
c) The same as parametric tests
d) Cannot be determined without effect size parameters

43. When testing for non-inferiority or equivalence of two proportions, the sample size formula requires adding a ______ to the estimated control proportion:

a) Placebo effect
b) Margin of non-inferiority
c) Standard error term
d) None of the above

44. A trial using an ordinal multi-item outcome scale requires a larger sample size compared to a binary outcome if:

a) Between-subject variability is higher
b) Number of response options is greater
c) Internal consistency of the scale is lower
d) All of the above

45. When using linear mixed models for longitudinal data, the estimated sample size is usually:

a) Higher compared to standard techniques ignoring correlation
b) Lower compared to standard techniques ignoring correlation
c) The same
d) Cannot be determined without data parameters

46. According to the ‘rule of thumb’, the minimum subjects required for a factor analysis is:

a) 5 times the number of variables
b) 10 times the number of variables
c) 15 times the number of variables
d) 20 times the number of variables

47. When using ordinal logistic regression, sample size estimation requires assumption of:

a) Only the marginal proportions
b) Both marginal proportions and association parameters
c) Covariance structure of the predictors
d) Only variance of the outcomes

48. For a 2×2 factorial design, accounting for interaction requires sampling _____ compared to individual trials:

a) Half the number of subjects
b) The same number of subjects
c) Twice the number of subjects
d) Four times the number of subjects

49. When analyzing multiple primary outcomes, sample size inflation factors range from __ to account for Type I error:

a) 1.1 to 1.5
b) 1.5 to 2
c) 2 to 3
d) 3 to 5

50. For equivalence or non-inferiority trials, the required sample size is _____ compared to superiority trials with the same effect size:

a) Smaller
b) Larger