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Analysis of Variance Is Easily Misapplied in the Analysis of Randomized Trials: A Critique and Discussion of Alternative Statistical Approaches

From the Integrative Medicine Service, Biostatistics Service, MSKCC, New York, NY.

Address correspondence and reprint requests to Andrew Vickers, PhD, Department of Medicine, Department of Epidemiology and Biostatistics, Memorial Sloan-Kettering Cancer Center, 1275 York Ave., New York, NY 10021. E-mail: vickersa{at}mskcc.org

Analysis of variance (ANOVA) is a statistical method that is widely used in the psychosomatic literature to analyze the results of randomized trials, yet ANOVA does not provide an estimate for the difference between groups, the key variable of interest in a randomized trial. Although the use of ANOVA is frequently justified on the grounds that a trial incorporates more than two groups, the hypothesis tested by ANOVA for these trials—"Are all groups equivalent?"—is often scientifically uninteresting. Regression methods are not only applicable to trials with many groups, but can be designed to address specific questions arising from the study design. ANOVA is also frequently used for trials with repeated measures, but the consequent reporting of "group effects," "time effects," and "time-by-group interactions" is a distraction from statistics of clinical and scientific value. Given that ANOVA is easily misapplied in the analysis of randomized trials, alternative approaches such as regression methods should be considered in preference.

Key Words: randomized controlled trials • analysis of variance • statistical interpretation of data

Abbreviations: ANOVA = analysis of variance; ANCOVA = analysis of covariance.

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