A trial of a new antimalarial has 70% power at a 5% significance level. If the investigators repeat the study with a much larger sample size while keeping the true treatment effect and alpha unchanged, which statement is CORRECT?
- A Power will increase because the standard error of the difference decreases ✓
- B Power will decrease because more comparisons become possible
- C Power remains unchanged as it depends only on alpha
- D Beta error will increase proportionally with sample size
Correct answer: A. Power will increase because the standard error of the difference decreases
Explanation
Power equals 1 minus beta and increases with sample size because a larger n reduces the standard error of the estimated treatment difference, narrowing the confidence intervals and making a true effect easier to detect. Power depends on four quantities: alpha, sample size, the true effect size, and the underlying variability, not alpha alone. Beta is the complement of power, so as power rises beta necessarily falls, ruling out option D directly.
Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.
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