An academic research group is designing a prospective cohort study to investigate the association between daily ultra-processed food consumption and the incidence of non-alcoholic fatty liver disease (NAFLD) in young adults. To ensure the study yields reliable conclusions, the principal investigator specifies an acceptable false-positive rate of . Through a pilot analysis and sample size estimation, the research team determines there is an probability that the study will fail to detect a true -fold increased risk of NAFLD, should one actually exist. Based on these specified parameters, what is the statistical power of this cohort study to detect the true association, expressed as a percentage?
Answer: 82 %
Answer
82
Statistical power is defined as the probability of correctly rejecting the null hypothesis when it is indeed false (i.e., the ability of a study to detect a true effect or association). Mathematically, power is calculated as , where is the Type II error rate. In this vignette, the researchers note an chance of failing to detect a true -fold increased risk. This failure to detect a true difference is a Type II error, meaning (or ). Therefore, the statistical power of the study is , or . The false-positive rate mentioned in the stem represents the Type I error rate (), which is used to set the significance level but is not used in the direct arithmetic calculation of power when is already known.
Step-by-Step Solution
Key Concept
Statistical power is calculated as , where represents the probability of committing a Type II error (failing to detect a true difference).
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