Clinical Trials

❘❙❚■ Chapter 17 | Types of Data and Normal DistributionAlthough visually appealing, these graphical methods do not provide objectivecriteria to determine the normality of variables, and interpretations are a matterof judgment. Numerical methods, such as the Kolmogorov–Smirnov, Shapiro–Wilk,Anderson–Darling, and Cramer–von Mises tests, are more formal [4,5]. The mostcommonly performed test is the Shapiro–Wilk test, which produces an S-W statistictogether with a P-value for testing the null hypothesis that the data are normallydistributed [4,5].ConclusionIn this chapter, we have described the different types of data and simple ways ofsummarizing and presenting them. Understanding these concepts and methods isimportant for using statistical methods properly. If you would like to understandmore about these concepts, references [1] and [2] provide a useful discussion ofthe topics and issues discussed.We have also provided an overview of the normal distribution. A normal distributionis characterized by a symmetrical bell curve defined by two parameters: mean (μ)and standard deviation (σ 2 ), expressed as N(μ,σ 2 ). The normal distribution is thefundamental basis of many statistical methods and models. The area under thenormal distribution curve, which represents the proportion of subjects in a range,can be derived from the standard normal distribution N(0,1) by transforming thegiven data distribution to the standard normal distribution.The use of histograms for checking normality of a sample is limited when the samplesize is small, and in this instance an inverse normal plot or numerical tests fornormality should be performed. When the given data are not normally distributedthen a more detailed transformation might be needed [1,2].References1. Altman DG. Practical Statistics for Medical Research. London: Chapman and Hall, 1999.2. Kirkwood B, Sterne J. Essential Medical Statistics, 2nd edition. Oxford: Blackwell Publishing, 2003.3. Armitage P, Colton T, editors. Encyclopaedia of Biostatistics: Statistical Theory and Methods.New York: John Wiley & Sons, 1998.4. Cramér H. Random Variables and Probability Distributions (Cambridge Tracts in Mathematics),New edition. Cambridge: Cambridge University Press, 2004.5. Shapiro SS, Wilk MB. An analysis of variance test for normality (complete samples).Biometrika 1965;52:591–611.184