# Statistical Power Analysis: A Simple and General Model for Traditional and Modern Hypothesis Tests

## Synopsis

This authored book presents a simple and general method for conducting statistical power analysis based on the widely used F statistic. The book illustrates how these analyses work and how they can be applied to problems of studying design, to evaluate others' research, and to choose the appropriate criterion for defining "statistically significant" outcomes. Statistical Power Analysis examines the four major applications of power analysis, concentrating on how to determine: the sample size needed to achieve desired levels of power; the level of power that is needed in a study; the size of effect that can be reliably detected by a study; and sensible criteria for statistical significance. Highlights of the second edition include: a CD with an easy-to-use statistical power analysis program; a new chapter on power analysis in multi-factor ANOVA, including repeated-measures designs; and a new One-Stop PV Table to serve as a quick reference guide. The previous edition was the first book to discuss in detail the application of power analysis to both traditional null hypothesis tests and to minimum-effect testing. This book demonstrates how the same basic model applies to both types of testing and explains how some relatively simple procedures allow researchers to ask a series of important questions about their research. Drawing from the behavioral and social sciences, the authors present the material in a nontechnical way so that readers with little expertise in statistical analysis can quickly obtain the values needed to carry out the power analysis for a range of hypotheses. Ideal for students and researchers of statistical and research methodology in the social, behavioral, and health sciences who want to know how to apply methods of power analysis to their research.

## Excerpt

One of the most common statistical procedures in the behavioral and social sciences is to test the hypothesis that treatments or interventions have no effect, or that the correlation between two variables is equal to zero, and so on (i.e., tests of the null hypothesis). Researchers have long been concerned with the possibility that they will reject the null hypothesis when it is in fact correct (i.e., make a Type I error), and an extensive body of research and data-analytic methods exists to help understand and control these errors. Substantially less attention has been devoted to the possibility that researchers will fail to reject the null hypothesis, when in fact treatments, interventions, and so forth, have some real effect (i.e., make a Type II error). Statistical tests that fail to detect the real effects of treatments or interventions might substantially impede the progress of scientific research.

The statistical power of a test is the probability that it will lead you to reject the null hypothesis when that hypothesis is in fact wrong. Because most statistical tests are done in contexts where treatments have at least some effect (although it might be minuscule), power often translates into the probability that the test will lead to a correct conclusion about the null hypothesis. Viewed in this light, it is obvious why researchers have become interested in the topic of statistical power, and in methods of assessing and increasing the power of their tests.

This book presents a simple and general model for statistical power analysis based on the widely used F statistic. A wide variety of statistics used in the social and behavioral sciences can be thought of as special applications of the general linear model (e.g., t tests, analysis of variance and covariance, correlation, multiple regression), and the F statistic can be used in testing hypotheses about virtually any of these specialized applications. The model for power analysis laid out here is quite simple, and it illustrates how these analyses work and how they can be applied to problems of study design, to evaluating others' research, and even to problems such as choosing the appropriate criterion for defining statistically significant outcomes.

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