Review Question - QID 217250

Statistical power is given by 100% - false negative rate (FNR); thus, FNR = 100% - power = 100% - 80% = 20%. The threshold for statistical significance, often denoted as α, is the maximum acceptable false positive rate.

Statistical power is defined as the probability that a statistical test will detect an effect when there actually is an effect to be detected (i.e., the true positive rate). It is closely related to the probability that a statistical test will fail to detect an effect when there actually is an effect (i.e., a false negative). This relationship takes the following form: power = 100% - FNR. By adequately powering a study, investigators can impose an upper bound on the FNR. The threshold for statistical significance, α, is the probability that a statistical test will detect an effect when there actually is no effect (i.e., a false positive). By defining a statistical significance threshold (e.g., setting significance as p < 0.001), investigators directly impose an upper bound on the false positive rate (FPR).

Incorrect Answers:
Answer 1: The maximum acceptable FNR and FPR cannot be determined from this information is incorrect because these values can be obtained from the given power and statistical significance threshold.

Answer 2: The maximum acceptable FNR is 0.1% is incorrect because 0.1% is the maximum acceptable false positive rate. The maximum acceptable FNR = 100% - power = 100% - 80% = 20%.

Answers 4 & 5: The maximum acceptable FPR is 5% and the maximum acceptable FPR is 20% are incorrect because these would correspond to statistical significance thresholds of p < 0.05 and p < 0.20, respectively. In this study, the statistical significance threshold was p < 0.001, which denotes the maximum FPR (0.1%).

Bullet Summary:
Statistical power is the probability of detecting an effect when an effect actually exists, whereas statistical significance, which often takes the form of p < 0.05, is the probability of detecting an effect when an effect actually does not exist.