Ophthalmic statistics note 9: parametric versus non-parametric methods for data analysis

With highly skewed or otherwise awkward data, the median may be more robust than the mean as a measure of central tendency and is used with nonparametric methods of analysis. However, it should be noted that this approach separates the p value from the effect size since the Mann-Whitney test, for example, tells us only whether there is a shift in location between samples and is by design divorced from the actual estimation of effect. CIs for the difference in medians should be presented to give an indication of the size of the effect. An alternative to non-parametric methods is given by bootstrapping or resampling, but such methods should not be considered without reference to a statistician. Where assumptions of normality are plausible, possibly following a transformation, parametric methods are preferable providing extra power and allowing adjustment for other factors such as differences between treatment groups at baseline in the case of clinical trials.