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Abstract
Current clinical trials do not use random samples, but, instead, convenience samples. This raises the risk of non-normal data.
The aim of this paper is to review and describe for a non-mathematical readership common methods for testing the normal property, as well as methods for analyzing the data in case of non-normality.
With slight departures from the normal distribution, normality tests can be used even so. They include, among other tests, the normal-, t-, chi-square- tests, analysis of variance, and regression analyses. They should not be used if the chi-square goodness of fit is significant. Rank-testing is, then, an alternative, but, sometimes, distributions do not allow for this approach either. This can be checked by the Kolmogorov-Smirnov test. If the latter test is also positive, rank-testing is not warranted, and confidence intervals can be derived from the data without prior assumption about the type of frequency distribution. This can be done by calculating the range within which 95% of all possible outcomes lie. Another popular method for this purpose is bootstrapping, which resamples at random from the study's own data. This paper reviews methods to assess data for compliance with normality, and summarizes solutions for the analysis of non-normal data. We strongly believe that normality statistics, although the mainstay of statistical analysis for centuries, will rapidly be replaced with non-normal testing as the awareness of non-normal sampling distributions grows, and we hope that the paper will strengthen this awareness and affect the design and analysis of future clinical trials.
Notes
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