Power of a statistical test is defined as which of the following?

• A. The probability of a Type I error
• B. The probability of failing to detect a real effect
• C. The probability of demonstrating a significant effect if an effect really exists
• D. The probability of obtaining a p-value less than alpha

Answer: (C)

Power is the probability that a statistical test will reject the null hypothesis when there really is a true effect in the population. In other words, it’s the chance of detecting a real effect and obtaining a statistically significant result if the effect exists. This is different from the chance of a false positive (Type I error, alpha) or the chance of missing a real effect (Type II error, which power is 1 minus). It’s also not merely the probability of getting a p-value below alpha under any conditions; power specifically evaluates sensitivity under the alternative hypothesis. In practice, you can raise power by increasing sample size, boosting the true effect size (to the extent possible), reducing measurement variability, or sometimes adjusting alpha.