![]() ![]() In considering the use of such an approximation, the question arises as to whether the power analysis and study design are adequately aligned. The power analysis might be based on a test of group differences at the last time point, even though the research hypothesis involves changes across time. ![]() For example, consider a study involving repeated measurements across time on members of four treatment groups. The power of a repeated measures or other multivariate design can be approximated by the power of a reduced design and/or a reduced test. Consequently, the data analyst now has a broader range of tools with which to create the best power analysis to use in designing the best study. Recent work ( Muller and Barton 1989, 1991 Muller and Peterson 1984) has made power calculations for the general linear multivariate model (GLMM) convenient and readily available. Although multivariate models are widely used for data analysis, corresponding power methods are not. If the planned analysis includes hypothesis testing, then power analysis may be used to help choose the design and testing strategy (see, for example, Cohen 1977 Kraemer and Thiemann 1987 Lipsey 1990 Muller, Barton, and Benignus 1984). Helping design and plan research constitutes an important activity for many statisticians. Finally, we discuss the benefits and costs of power analysis in the practice of statistics. Fifth, we evaluate the tradeoffs in using reduced designs and tests to simplify power calculations. Fourth, we present the results of the power calculations. Third, we describe the design of the power analysis for the example, a longitudinal study of a child’s intellectual performance as a function of mother’s estimated verbal intelligence. ![]() The treatment includes coverage of the multivariate and univariate approaches to repeated measures, MANOVA, ANOVA, multivariate regression, and univariate regression. Second, we survey available methods for the general linear multivariate model (GLMM) with Gaussian errors and recommend those based on F approximations. First, we discuss the motivation for using detailed power calculations, focusing on multivariate methods in particular. Discussion of the example also highlights issues that typically must be considered in designing a study. Describing the development of the research proposal allows demonstrating the steps needed to conduct an effective power analysis. The focus is a complex but ubiquitous setting: repeated measures in a longitudinal study. We demonstrate how easily the methods can be applied by (1) reviewing their formulation and (2) describing their application in the preparation of a particular grant proposal. Recently developed methods for power analysis expand the options available for study design. ![]()
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