On Using Empirical Distribution Function Plot for Checking the Normality Assumption of a Data Set

Since the normal distribution is the gate keeper to several statistical procedures, so conformity of a given data set to its normality assumptions is often of concern to the statisticians. Numerous parametric and non-parametric tests are available for testing the goodness of fit, some commonly used goodness of fit tests are chi-square goodness of fit test, Anderson Darling test, Kolmogorov-Smirnov (K-S) test, Wilks Shapiro Normality test, etc. Some graphical techniques are also available to check the goodness of fit to some of the hypothetical distributions under consideration like normal probability plot, quantile plot etc. The aim of this paper is to develop a graphical tool based on empirical distribution function and the Kolmogorov-Smirnov (K-S) statistic so that the normality of a given dataset can be checked as well as visualized