Parametric versus non-parametric statistics in the analysis of randomized trials with non-normally distributed data
By Andrew J. Vickers. BMC Medical Research Methodology, 2005
390 citations recorded by the source corpus.
BackgroundIt has generally been argued that parametric statistics should not be applied to data with non-normal distributions. Empirical research has demonstrated that Mann-Whitney generally has greater power than the t-test unless data are sampled from the normal. In the case of randomized trials, we are typically interested in how an endpoint, such as blood pressure or pain, changes following treatment. Such trials should be analyzed using ANCOVA, rather than t-test. The objectives of this study were: a) to compare the relative power of Mann-Whitney and ANCOVA; b) to determine whether ANCOVA provides an unbiased estimate for the difference between groups; c) to investigate the distribution of change scores between repeat assessments of a non-normally distributed variable.MethodsPolynomials were developed to simulate five archetypal non-normal distributions for baseline and post-treatment scores in a randomized trial. Simulation studies compared the power of Mann-Whitney and ANCOVA for analyzing each distribution, varying sample size, correlation and type of treatment effect (ratio or shift).ResultsChange between skewed baseline and post-treatment data tended towards a normal distribution. ANCOVA was generally superior to Mann-Whitney in most situations, especially where log-transformed data were entered into the model. The estimate of the treatment effect from ANCOVA was not importantly biased.ConclusionANCOVA is the preferred method of analyzing randomized trials with baseline and post-treatment measures. In certain extreme cases, ANCOVA is less powerful than Mann-Whitney. Notably, in these cases, the estimate of treatment effect provided by ANCOVA is of questionable interpretability.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/866ab09c3be52d921ddc649031a613f84f10279c
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Citations in the corpus
- An RCT Comparing Effect of Two Types of Support on Severity of Symptoms for People Completing Internet-Based Cognitive Behaviour Therapy for Social Phobia (2009, methodology): “Pre post-treatment changes in participant questionnaire scores were analysed using univariate analyses of covariance (ANCOVAs) [30,31].”
- Do Accounting Graduates’ Skills Meet The Expectations of Employers? A Matter of Convergence or Divergence (2009, methodology): “T-tests analysis was considered appropriate given the approximate normal distribution of the data (Heeren and D’Agostino, 1987; Vickers, 2005; Hair, Black, Babin, Anderson and Tatham, 2006).”
- Clinician-Assisted Internet-Based Treatment is Effective for Generalized Anxiety Disorder: Randomized Controlled Trial (2009, methodology): “Pre post-treatment changes in participant questionnaire scores were analysed using univariate analyses of covariance (ANCOVAs) [47,48].”
- Improving Middle School Students’ Science Literacy Through Reading Infusion (2010, methodology): “Finally, ANCOVA outperforms Mann-Whitney for most distributions under most circumstances (Vickers, 2005).”