Statistical Power Analysis for the Behavioral Sciences

Motivated by surveys indicating that data analyses published in top behavioral science and psychology journals between 1960 and 1982 were [Page 1449]seriously lacking in statistical power, Jacob Cohen wrote the book Statistical Power Analysis for the Behavioral Sciences to draw attention to the problem and to provide a handbook of statistical power analysis for behavioral scientists.

The book covers power analysis based on various statistical tests commonly used in behavioral science. These tests include the following: (a) the t test for means, (b) significance test of a product-moment correlation coefficient, (c) test of the differences between correlation coefficients, (d) test to determine whether a proportion is 0.5 and the sign test, (e) test of the differences between proportions, (f) chi-square tests for goodness of fit and contingency tables, (g) analysis of variance (ANOVA) and covariance, (h) multiple regression and correlation analysis, and (i) a multivariate version of the multiple regression and correlation analysis.

Each test is discussed in a separate chapter, which starts with a description of the test, continues with a definition of the effect size index, and ends with a power table and a sample size table for the test, along with (for most tests) an explanation of how to use the power table for significance testing. Using the tables provided in the book, one can easily find the power and necessary sample size by locating the specified parameters. For example, given an effect size and a sample size for a t test for between-group means, one can find the power by locating the specified effect and sample sizes. Similarly, one can find the required sample size when the effect size and power are specified. In most power tables, a significance criterion in the form of the sample effect size is given to facilitate significance testing if data are available.

The book also discusses issues related to (a) understanding the magnitude of effect sizes, (b) the role of psychometric reliability, and (c) the efficacy of “qualifying” (differencing and partial-ling) dependent variables in the context of power analysis. A description of the computational procedures associated with each test is provided at the end of the book.

This book is useful in that it not only provides results for power and sample size calculations based on different tests but also describes the tests and the corresponding computational procedures so that interested readers can reproduce the results, presumably with additional computing aid. This

book does have limitations. The first edition of the book was published in 1969. Despite the addition of new material in the revised and second editions (published in 1977 and 1988, respectively), descriptions of power analysis for some important statistical methods currently in common use in behavioral research are missing. These methods include logistic regression analysis, repeated measures ANOVA, and McNemar's test for the difference between correlated proportions, among others. Thus, researchers might prefer to use one of the various software packages currently available that will conduct power and sample size calculations. Such software is typically user friendly and quickly generates results with complementary tables and/or graphics (e.g., provides power statements with visual demonstrations such as plots of power curves). In addition, current software packages incorporate power analysis for most of the recently developed statistical procedures that are not covered in the book. Individuals interested in understanding power and sample size calculations based on standard and conventional statistical tests might find this book useful. If instead the main goal is to calculate power and/or sample size, especially using modern advanced statistical techniques, then software might prove to be more convenient. Popular software of this sort includes nQuery, Power and Sample Size (PASS), and others.

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