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. 2005 Nov 3:5:35.
doi: 10.1186/1471-2288-5-35.

Parametric versus non-parametric statistics in the analysis of randomized trials with non-normally distributed data

Andrew J Vickers  1
Affiliations

Parametric versus non-parametric statistics in the analysis of randomized trials with non-normally distributed data

Andrew J Vickers. BMC Med Res Methodol. .

Abstract

Background: It 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.

Methods: Polynomials 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).

Results: Change 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.

Conclusion: ANCOVA 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.

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Figures

Figure 1
Figure 1
Distribution of scores for a single die roll and the difference between two die rolls. The change score tends towards a more normal distribution.
Figure 2
Figure 2
Distribution of post-treatment and change scores from original and simulated data for headache severity ("moderate positive skew" distribution).
Figure 3
Figure 3
Distribution of post-treatment and change scores from original and simulated data for shoulder pain ("uniform" distribution).
Figure 4
Figure 4
Distribution of post-treatment and change scores from original and simulated data for Ki67, a biomarker of cell proliferation ("extreme asymmetry" distribution).
Figure 5
Figure 5
Distribution of post-treatment and change scores from original and simulated data for physical functioning scale of the SF36 ("extreme negative skew" distribution).
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