Power of a study and statistical significance MCQs With Answer

Introduction: Understanding the power of a study and statistical significance is essential for B.Pharm students involved in research, clinical trials, and evidence-based pharmacy practice. This concise guide covers core keywords — p-value, alpha, Type I and Type II errors, power (1−β), effect size, sample size, confidence intervals, hypothesis testing, variance, and clinical versus statistical significance — with practical insight. Learn how sample size, effect magnitude, variability, and significance level influence power, and why appropriate planning prevents false negatives or positives in pharmacological studies. These concepts help design robust trials, interpret drug-effect evidence, and critique literature. Now let’s test your knowledge with 30 MCQs on this topic.

Q1. What does the statistical power of a study represent?

• The probability of observing a statistically significant result when the null hypothesis is true
• The probability of correctly rejecting a false null hypothesis
• The probability of making a Type I error
• The probability that the p-value is less than 0.05

Correct Answer: The probability of correctly rejecting a false null hypothesis

Q2. Which relationship between power and Type II error (β) is correct?

• Power = β
• Power = 1 − β
• Power = α + β
• Power = α − β

Correct Answer: Power = 1 − β

Q3. Which single change most directly increases the statistical power of a randomized clinical trial?

• Decreasing the chosen alpha level (e.g., from 0.05 to 0.01)
• Reducing the expected effect size
• Increasing the sample size
• Increasing variability in outcome measurements

Correct Answer: Increasing the sample size

Q4. How should you correctly interpret a p-value of 0.03?

• There is a 3% probability that the null hypothesis is true
• There is a 3% probability of observing the data, or more extreme, if the null hypothesis is true
• The result is clinically important
• The alternative hypothesis has a 97% probability of being true

Correct Answer: There is a 3% probability of observing the data, or more extreme, if the null hypothesis is true

Q5. The significance level α in hypothesis testing represents which of the following?

• The probability of a Type II error
• The acceptable probability of a Type I error
• The observed p-value threshold after study completion
• The probability that the alternative hypothesis is true

Correct Answer: The acceptable probability of a Type I error

Q6. Choosing a two-tailed test instead of a one-tailed test (with the same alpha) typically has what effect on power?

• Two-tailed tests are more powerful than one-tailed tests
• Two-tailed tests have the same power as one-tailed tests
• Two-tailed tests are less powerful than one-tailed tests
• Tail choice does not affect power

Correct Answer: Two-tailed tests are less powerful than one-tailed tests

Q7. How is Cohen’s d (standardized effect size) defined for comparing two means?

• Difference in means divided by pooled standard deviation
• Sum of means divided by pooled standard deviation
• Difference in means times pooled standard deviation
• Difference in variances divided by mean

Correct Answer: Difference in means divided by pooled standard deviation

Q8. Which statement best describes a 95% confidence interval for a mean difference?

• There is a 95% probability that the true mean lies in this specific interval
• If we repeat the study many times, 95% of calculated intervals will contain the true mean difference
• The mean difference is clinically significant if the interval is wide
• The p-value must be exactly 0.05 when the interval excludes zero

Correct Answer: If we repeat the study many times, 95% of calculated intervals will contain the true mean difference

Q9. If a trial reports p = 0.04 and α = 0.05, the correct conclusion is:

• Fail to reject the null hypothesis
• Reject the null hypothesis; result is statistically significant
• The null hypothesis is probably true
• The result is clinically meaningful regardless of effect size

Correct Answer: Reject the null hypothesis; result is statistically significant

Q10. Which statement correctly contrasts statistical significance and clinical significance?

• Statistical significance always implies clinical benefit
• Clinical significance is based only on p-values
• A statistically significant result may have negligible clinical importance
• Clinical significance can be determined from p-value alone

Correct Answer: A statistically significant result may have negligible clinical importance

Q11. Which inputs are necessary for an a priori sample size calculation?

• Desired alpha, desired power (or β), anticipated effect size, and estimate of outcome variability
• Observed p-value from the completed study and the desired alpha
• Only the expected effect size is required
• Only the budget and recruitment rate are required

Correct Answer: Desired alpha, desired power (or β), anticipated effect size, and estimate of outcome variability

Q12. Holding effect size constant, what is the likely impact of substantially increasing sample size on p-values?

• P-values will always increase
• P-values will always stay the same
• P-values may decrease, making statistical significance easier to achieve
• P-values become meaningless with large samples

Correct Answer: P-values may decrease, making statistical significance easier to achieve

Q13. What is a Type II error?

• Rejecting a true null hypothesis
• Failing to reject a false null hypothesis
• Using an incorrect statistical test
• Calculating the confidence interval incorrectly

Correct Answer: Failing to reject a false null hypothesis

Q14. How does increased variability (higher standard deviation) in outcome measurements affect study power, all else equal?

• Increases power
• Decreases power
• Does not affect power
• Makes alpha smaller

Correct Answer: Decreases power

Q15. Applying a stringent Bonferroni correction for multiple comparisons generally has which effect?

• Reduces family-wise Type I error but increases Type II error (reduces power)
• Increases both Type I and Type II errors
• Eliminates the need for sample size calculation
• Ensures all individual tests have higher power

Correct Answer: Reduces family-wise Type I error but increases Type II error (reduces power)

Q16. Performing several interim analyses during a trial without statistical adjustment will most likely:

• Decrease the chance of a Type I error
• Leave overall alpha unchanged
• Increase the overall Type I error rate
• Guarantee higher power

Correct Answer: Increase the overall Type I error rate

Q17. What does a power curve typically illustrate?

• Relationship between sample size and variance only
• Relationship between effect size and p-value only
• Probability of detecting an effect (power) across different effect sizes or sample sizes
• Distribution of p-values under the null hypothesis

Correct Answer: Probability of detecting an effect (power) across different effect sizes or sample sizes

Q18. In many non-inferiority trials, which testing approach is commonly justified?

• Two-sided superiority test with α = 0.01
• One-sided test focusing on the prespecified direction of non-inferiority
• No hypothesis testing is needed for non-inferiority
• Testing both superiority and inferiority simultaneously without adjustment

Correct Answer: One-sided test focusing on the prespecified direction of non-inferiority

Q19. What is a major limitation of reporting post-hoc (observed) power after a study is completed?

• Observed power provides an independent check of sample size planning
• Observed power depends on the observed effect size and is redundant with the p-value
• Observed power always underestimates true power
• Observed power can determine clinical significance

Correct Answer: Observed power depends on the observed effect size and is redundant with the p-value

Q20. The parameter β in sample size planning denotes which quantity?

• The probability of a Type I error
• The desired power
• The probability of a Type II error
• The significance level multiplied by 100

Correct Answer: The probability of a Type II error

Q21. Besides increasing sample size, which practical strategy can increase a study’s power?

• Increasing outcome measurement error
• Using a less sensitive outcome measure
• Reducing variability by improving measurement precision
• Choosing a smaller anticipated effect size

Correct Answer: Reducing variability by improving measurement precision

Q22. What is a common consequence of conducting an underpowered clinical trial?

• High risk of false positive findings (Type I errors)
• High risk of false negative findings (Type II errors) and wide confidence intervals
• Guaranteed detection of clinically important effects
• P-values will always be below 0.05

Correct Answer: High risk of false negative findings (Type II errors) and wide confidence intervals

Q23. To detect a small but clinically meaningful effect, the required sample size will typically be:

• Very small
• Unrelated to the effect size
• Larger than for detecting a large effect
• Smaller than for detecting a large effect

Correct Answer: Larger than for detecting a large effect

Q24. What is the conventional target power used in many clinical trial sample size calculations?

• 50% (0.5)
• 80% (0.8)
• 100% (1.0)
• 10% (0.1)

Correct Answer: 80% (0.8)

Q25. If a study reports p = 0.07 and uses α = 0.05, the correct statistical action is to:

• Declare the result statistically significant because p is close to 0.05
• Fail to reject the null hypothesis (not statistically significant at α = 0.05)
• Automatically accept the alternative hypothesis
• Change α to 0.10 to claim significance without justification

Correct Answer: Fail to reject the null hypothesis (not statistically significant at α = 0.05)

Q26. When is it most appropriate to use a one-sided hypothesis test?

• When both directions of effect are clinically important and plausible
• When the effect direction was pre-specified and there is no interest in the opposite direction
• When you want to maximize the chance of any significant result after seeing data
• When sample size is too small for two-sided tests

Correct Answer: When the effect direction was pre-specified and there is no interest in the opposite direction

Q27. How does an intra-cluster correlation coefficient (ICC) > 0 in cluster randomized trials affect sample size needs?

• ICC reduces required sample size compared with an individually randomized trial
• ICC increases the effective sample size without adjustment
• ICC increases the required sample size because observations are correlated within clusters
• ICC has no impact on sample size calculations

Correct Answer: ICC increases the required sample size because observations are correlated within clusters

Q28. Which statement about the relationship between 95% confidence intervals and statistical significance at α = 0.05 is correct for a two-sided test?

• If the 95% CI for a mean difference excludes zero, the two-sided p-value will be greater than 0.05
• If the 95% CI for a mean difference excludes zero, the two-sided p-value will be less than 0.05
• Confidence intervals and p-values are unrelated
• A 95% CI excluding zero implies a one-sided p-value greater than 0.05

Correct Answer: If the 95% CI for a mean difference excludes zero, the two-sided p-value will be less than 0.05

Q29. In survival analysis, a hazard ratio (HR) of 0.8 with a 95% CI of 0.6–1.1 should be interpreted as:

• Statistically significant reduction in hazard because HR < 1
• Not statistically significant because the CI includes 1
• Clinically meaningless regardless of CI
• Sure evidence of superiority

Correct Answer: Not statistically significant because the CI includes 1

Q30. Which combination best helps ensure that a planned drug trial will have adequate power to detect a clinically important effect?

• Small sample size, high variability, and very small anticipated effect
• Large sample size, precise outcome measurement (low variability), and realistic anticipated effect size
• No prior estimate of variability, arbitrary alpha, and minimal recruitment
• Using post-hoc observed power instead of a priori calculations

Correct Answer: Large sample size, precise outcome measurement (low variability), and realistic anticipated effect size

Download