Appraising Minimum Effect of Standardized Contrasts in ANCOVA Designs: Statistical Power, Sample Size, and Covariate Imbalance Considerations

Abstract

The concepts and implementation of standardized mean differences and minimum effect tests have been emphasized in ANOVA. The corresponding processes and implications are, however, not yet well explicated in the context of ANCOVA. To enhance the usefulness of ANCOVA, this article describes the minimum effect tests of standardized contrast as a valuable alternative to the hypothesis testing of no effect difference and the conventional evaluation of unstandardized effects in ANCOVA. Power and sample size procedures are developed to accommodate covariate randomness and imbalance for randomized and nonrandomized designs. The data from a clinical study of comparing two treatments for gingivitis are used to illustrate the application of the suggested approaches. The emphases of numerical appraisal are on the merit of minimum effect detection in comparative analysis and the influence of covariate feature in power and sample size computation. The proposed power and sample size calculations improve upon approximate formulas by fully accounting for the stochastic property and intrinsic disparity of the covariate variables. Computer algorithms are available for calculating the p-value, power level, and sample size of one- and two-sided minimum effect tests.

KEYWORDS:

• Analysis of covariance
• Contrast
• Power
• Sample size
• Standardized effect size

Supplementary Materials

SAS/IML programs for performing the recommended test procedure, power computation, and sample size determination.

Acknowledgments

The author would like to thank the editor, the associate editor, and two referees for their constructive comments, which have led a substantial improvement of the article.

Additional information

Funding

This work was supported by the Ministry of Science and Technology, Taiwan grant MOST 107-2410-H-009-025-MY2.