Power and Sample Size
The term “power” in connection with scientific studies is used in a broad sense as well as in a narrow, statistical sense. The statistical term “power” refers to the probability of obtaining a significant result when testing the null hypothesis H0 : β j = 0 under the assumption of a certain (true) value for β j. This is the relevant concept if we are mainly interested in demonstrating that a certain covariate (after appropriate adjustment) has an effect. The more general term “power of a study” refers to the likelihood that a study can demonstrate or find what the study is intended to demonstrate or find. This may refer to a general aim like “Finding new genetic markers for diseases Y” or a more specific aim like “determining a critical threshold for exposure to X.” Typically statistical concepts to translate also such powers into probabilities or expectations can be found. The statistical “power” as the probability to be able to reject the null hypothesis of no effect is just one example. The most prominent alternative is to consider the expected length of a confidence interval.