Normality

Data normality is focused on the premise that data is from one or more normally distributed populations. Characteristics of a distribution can be described by its moments (the average of its values which are then raised to a certain power). The normal distribution in standard form has a first moment (mean) of zero, a second moment (variance) of one, a third moment (skewness) of zero and a fourth moment (kurtosis) of three. Many statistical programs like SPSS subtract the three from the kurtosis value to normalize to zero for reporting purposes. These statistics are based on the distribution curve as a whole and not on individual cases. Data normality is usually focused on skewness and kurtosis which are measures of shape. A skewness and kurtosis of zero is indicative of a normal distribution. Skewness is associated with the symmetry of the distribution. Kurtosis is associated with how peaked or flat the distribution is. A kurtosis above zero is indicative of a peaked distribution while a negative value is indicative of a flat distribution. Some authors suggest that univariate values approaching at least 2.0 for skewness and 7.0 for kurtosis should be suspect (West et al., 1995; Yuan & Bentler, 1999). The descriptive statistics, including skewness and kurtosis are shown below in Table 1. Examination of the distributions indicated only one variable, cmit8 has a high negative skew, -2.179. Computing the log transformation reduced the skew to .851 and the kurtosis to.247. The transformed variable will be used in further analyses.