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Statistical Power Analysis

Statistical power analysis (also referred to as sample size calculation) is a set of procedures to determine the appropriate number of participants for recruitment to a research study. Power analysis can be performed before or after the collection of data. When performed before, power analysis serves to aid researchers in their development of a desired sample size; when performed after, power analysis can reveal to researchers a reason for a nonsignificant result. In general, a power of .80 (or an 80% likelihood of rejecting the null hypothesis correctly) is acceptable, though there exists no formal standard. Many grant-awarding institutions as well as institutional review and ethics boards require power analysis and, as a result, it is most often conducted a priori, or before data are collected. This entry describes the nature of power, reviews some factors that influence statistical power, and concludes with a sampling of a few software packages used to conduct a statistical power analysis.

What Is Power?

The “power” of any statistical test is that test’s ability to appropriately reject the null hypothesis when, in fact, the alternative hypothesis is true. Said another way, a statistical test is said to have power when it can accurately detect an effect or result. Statistically speaking, a test’s power comes from a balance between Type I and Type II error, or alpha and beta error, respectively. Power is defined statistically as 1 – β (beta or Type-II error), where β is the chance of falsely failing to reject the null hypothesis (i.e., accepting the null falsely or missing the effect). Communication researchers covet power, because of its role in detecting results; simply put, without power, a researcher is unable to uncover any findings and, therefore, forward the progress of the communication discipline. The ability to detect an effect when that effect is real is paramount to all communication researchers.

Factors That Influence Power

Statistical power is not a static characteristic of tests; it is incorrect to say that a test “has” or “does not have” power. Instead, statistical tests can be “underpowered” or “powerful.” Because of this dynamic, several factors influence the extent to which a test is powerful. These include the statistical significance set for the test, the effect size, and the sample size. Each of these characteristics will be discussed in turn.

Statistical Significance

Power is firstly a function of Type I (α) and Type II (β) errors. More specifically, when a researcher controls for Type I error by decreasing the corresponding p-value (the numerical representation of Type I error in significance testing), he or she increases the chance of committing a Type II error and, concurrently, reducing a test’s power. By increasing the risk a researcher is willing to accept of committing a Type I error (i.e., increasing the p-value or α), the Type II or β decreases, providing a statistical test with more power. This co-movement of the α and β errors lead many communication researchers to set α to .05, which protects against Type I error while still providing a test with some power.

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