Introduction to Power Analysis: Two-group Studies

This volume provides readers with enough background, examples and explanation that they can then read technical papers and materials that include complex power analyses. This book is an introduction to the core elements of power analysis. It does this through a case study of comparing the means of two groups, and walking the reader through the simple and complex considerations of this research question. From covariates to clusters, comparing two groups can sometimes be a complicated task, and so can the power analysis. The central theme of the book will be to explain the components of the test statistics and their sampling distributions. This will require a focus on the variance of the mean difference for the different situations in which this occurs: single level, multilevel, and with and without covariates. Once one understands the variances, the author shows how computation of noncentrality parameters, i.e. the expected test statistic, is straightforward. With the assistance of non-central distribution functions in R or commercial software packages such as Stata or SPSS, readers can compute exact power for a given design with relatively little effort. Advanced readers will be able to generate the presented graphs in their programs to provide a deeper understanding of the mathematical expressions.