A randomized controlled trial is designed with 90% power to detect a clinically meaningful difference in hemoglobin of 1 g/dL at alpha = 0.05. What does 90% power mean?
- A There is a 90% probability of correctly detecting a true difference of 1 g/dL if it exists ✓
- B There is a 90% probability that the null hypothesis is true
- C There is a 10% probability that the result is due to chance
- D The p-value will be less than 0.10
Correct answer: A. There is a 90% probability of correctly detecting a true difference of 1 g/dL if it exists
Explanation
Statistical power (1 - β) is the probability of correctly rejecting the null hypothesis when it is false, that is, detecting a true effect if it exists. 90% power means there is a 90% chance of finding a statistically significant difference if the true difference is actually 1 g/dL. Option B confuses power with the prior probability of the null. Option C describes alpha, not power.
Reference: Methods in Biostatistics by B. K. Mahajan, 7th ed.
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