Power

Statistical power, or power for short, is the probability of rejecting a false null hypothesis in a hypothesis test, which involves the null hypothesis and the alternative hypothesis. The latter usually presents the researcher’s theory—the research hypothesis. As the null hypothesis and the alternative hypothesis are opposite to each other, either one or the other is plausible but not both. Rejecting the null hypothesis establishes the plausibility of the alternative hypothesis (i.e., the researcher’s theory). For example, a researcher hypothesizes that soothing music improves students’ ability to solve puzzles. This becomes the alternative hypothesis. On the contrary, the null hypothesis states that soothing music does not help improve students’ ability to solve puzzles. The probability of rejecting the null hypothesis represents the researcher’s chance of confirming the hypothesized effect of soothing music on solving puzzles. In this regard, statistical power is always sought after because it affects the odds of affirming the research hypothesis.

Statistical power is determined by the significance level, the effect size, error variance, and sample size in a statistical test. The smaller the significance level (or lower the α value), the less power the statistical test will produce, other things being equal, and the larger the effect size, the higher the statistical power. Larger variability generally works against statistical power because error variance can be viewed as the background noise in detecting an effect. Increased error variance makes it more difficult to substantiate the possible effect stated in the alternative hypothesis. Although error variance inherent to a research setting may be beyond human control, a researcher can always increase the sample size to raise the statistical power to the desired level (e.g., .80, or 80% power). Sample size determination is therefore synonymous with statistical power analysis.

[Page 1282]The general recommendation is that a power analysis be conducted to calculate statistical power prior to the study (a priori) rather than after the study (post hoc or a posteriori). A researcher should determine power a priori so as to ensure an adequate chance of affirming the research hypothesis in planning a study. Upon completion of the study, a researcher should refrain from using the sample estimates to determine power a posteriori. The post hoc power, thus computed, merely validates what has already been observed in the study: An insignificant result yields low power and a significant result returns high power. In other words, the post hoc power based on the sample estimates does not add any new information to the study.

See also Effect size; p Value; Power Analysis; Sample Size; Significance