Abstract
The analysis of covariance (ANCOVA) has notably proven to be an effective tool in a broad range of scientific applications. Despite the well-documented literature about its principal uses and statistical properties, the corresponding power analysis for the general linear hypothesis tests of treatment differences remains a less discussed issue. The frequently recommended procedure is a direct application of the ANOVA formula in combination with a reduced degrees of freedom and a correlation-adjusted variance. This article aims to explicate the conceptual problems and practical limitations of the common method. An exact approach is proposed for power and sample size calculations in ANCOVA with random assignment and multinormal covariates. Both theoretical examination and numerical simulation are presented to justify the advantages of the suggested technique over the current formula. The improved solution is illustrated with an example regarding the comparative effectiveness of interventions. In order to facilitate the application of the described power and sample size calculations, accompanying computer programs are also presented.
Highlights
The analysis of covariance (ANCOVA) was originally developed by Fisher (1932) to reduce error variance in experimental studies
It is essential to note that ANCOVA provides a useful approach for combining the advantages of two highly acclaimed procedures of analysis of variance (ANOVA) and multiple linear regression
ANCOVA provides a useful approach for combining the advantages of two widely established procedures of ANOVA and multiple linear regression
Summary
The analysis of covariance (ANCOVA) was originally developed by Fisher (1932) to reduce error variance in experimental studies. It is essential to note that ANCOVA provides a useful approach for combining the advantages of two highly acclaimed procedures of analysis of variance (ANOVA) and multiple linear regression. The importance and implications of statistical power analysis in scientific research are well demonstrated in Cohen (1988), Kraemer and Blasey (2015), Murphy et al (2014), and Ryan (2013), among others. It is of great practical value to develop theoretically sound and numerically accurate power and sample size procedures for detecting treatment differences within the context of ANCOVA. There are numerous published sources that address statistical theory and applications of power analysis for ANOVA and multiple linear regression. The corresponding results for multiple regression and correlation, especially the distinct notion of fixed and random regression settings, were given in Gatsonis
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