# Abstract

DOLLINS, A. B. A computational guide to power analysis of fixed effects in balanced analysis of variance designs. September 1995, Report No. DoDPI95-R-0003. Department of Defense Polygraph Institute, Ft. McClellan, AL 36205.

This manuscript provides a step-by-step guide to statistical power calculation for the fixed effects of analysis of variance (ANOVA) designs with an equal number of observations in each cell. A brief history of ANOVA hypothesis testing theory is included to explain why power calculation is important and how the results can be used. The relationship between lambda, the noncentrality parameter used to calculate power in the ANOVA, and Cohen's (1988) measure of effect size is provided. Algorithms are provided for power calculation and for conversion between lambda, Cohen's measure of effect size, and phi--the parameter used in many tables of the noncentral F distribution. The appendices contain power of calculation examples for the main and interaction effects of 2 x 3 x 3 between- and within- subjects designs.

Key-words: computation guide, analysis of variance (ANOVA), statistical power, lambda, alpha, beta, effect size, algorithm

## Director's Foreword

The results of numerous published studies, both within and outside of the psychophysiological detection of deception (PDD) literature, are based on observation groups which are too small to provide results that are representative of the general population. Such studies are described as having low or insufficient statistical power. These publication not only represent a misuse of potentially useful resources, but may lead to unjustified, if not erroneous, conclusions. Among the potential reasons for the prevalence of such studies in the literature are the limited awareness of statistical power analysis, and difficulty associated with the calculation of statistical power.

This manuscript is the first of several computational guides to statistical power analysis to be developed at the Institute. It is designed to assist the investigator in designing, and understanding the analysis of, fixed effects in balanced factorial analysis of variance statistical designs. Future guides will address statistical power calculation for the commonly used student-t and chi-square inferential statistics. This and future documents should assist others, as they have the DoDPI faculty, in both the design and evaluation of PDD investigations.