Assessing normality: Applications in multi-group designs

Warr and erich (2013) compared a frequently recommended procedure in textbooks: the interquartile range divided by the sample standard deviation,against the shapiro-wilk's test in assessing normality of data. they found the shapiro-wilk's test to be far superior to the deficient interquartile range statistic. we look further into the issue of assessing non-normality by investigating the anderson-darling goodness-of-fit statistic for its sensitivity to detect non-normal data in a multi-group problem where type i error and power issues can be explored from perspectives not considered by warr and erich. in particular,we examined the sensitivity of this test for 23 non-normal distributions consisting of g- and h-distributions,contaminated mixed-normal distributions and multinomial distributions. in addition,we used a sequentially-rejective bonferroni procedure to limit the overall rate of type i errors across the multi-groups assessed for normality and defined the power of the procedure according to whether there was at least one rejection from among the three group tests,whether all three non-normal groups of data were detected and the average of the per-group power values. our results indicate that the anderson-darling test was generally effective in detecting varied types of non-normal data.