In a study with 95% power and 5% type I error (two-sided), if the investigators reduce the acceptable type I error to 1% while keeping all else constant, the required sample size will:
- A Increase, because a smaller alpha requires the test statistic to exceed a higher threshold, necessitating more data ✓
- B Decrease, because stricter criteria reduce the number of significant results
- C Remain unchanged — only power determines sample size
- D Decrease if the effect size is large
Correct answer: A. Increase, because a smaller alpha requires the test statistic to exceed a higher threshold, necessitating more data
Explanation
Sample size depends inversely on alpha (Type I error) and directly on power (1 − beta). Reducing alpha from 0.05 to 0.01 requires a larger critical value (Z_{alpha/2} increases from 1.96 to 2.576), which for the same power requires a larger sample to maintain sensitivity to detect the true effect. Stricter significance thresholds always require larger samples to maintain power.
Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.
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