A randomized controlled trial was designed with a statistical power of 80 percent to detect a 15 percent reduction in disease incidence. If the true effect actually exists, the probability that the trial will fail to detect it is:

• A 5 percent
• B 20 percent ✓
• C 95 percent
• D 80 percent

Explanation

Power is the probability of detecting a true effect, equal to 1 minus beta, where beta is the probability of a Type II error. With 80 percent power, beta is 20 percent, so there is a 1 in 5 chance of missing a real effect. The 5 percent figure corresponds to alpha, the Type I error risk of declaring an effect when none exists, which is a different quantity entirely.

Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.

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