Normality is a distributional requirement of classical test statistics. In order for the test statistic to provide valid results leading to sound and reliable conclusions this requirement must be satisfied. In the not too distant past, it was claimed that violations of normality would not likely jeopardize scientific findings (See Hsu & Feldt, 1969; Lunney, 1970). Recent revelations suggest otherwise (See e.g., Micceri, 1989; Keselman, Huberty, Lix et al., 1998; Erceg-Hurn, Wilcox, & Keselman, 2013; Wilcox and Keselman, 2003; Wilcox, 2012a, b). Unfortunately the data obtained in psychological investigations rarely, if ever, meet the requirement of normally distributed data (Micceri, 1989; Wilcox, 2012a, b). Consequently, it could be the case that the results from many of the investigations conducted in psychology provide invalid results. Accordingly, authors recommend that researchers attempt to assess the validity of assuming data are normal in form prior to conducting a test of significance (Erceg-Hurn, et al., 2013; Keselman, et al., 1998). Present evidence suggests that a popular fit-statistic, the Kolmogorov-Smirnov test does a poor job of evaluating whether data are normal. Our investigation based on this statistic and other fit-statistics provides a more favorable picture of preliminary testing for normality.
Keselman, H. J.; Othman, Abdul R.; and Wilcox, Rand R.
"Preliminary Testing for Normality: Is This a Good Practice?,"
Journal of Modern Applied Statistical Methods:
2, Article 2.
Available at: http://digitalcommons.wayne.edu/jmasm/vol12/iss2/2