Descriptive statistics, including mean, median, standard deviation, and coefficient of variation, and exploratory distributional plots (box-and-whisker plots and nonnal probability plots) were calculated on the individual samples for each treatment group, and probability values (P values) of univariate goodness-of-fit tests for normality were evaluated (Shapiro-Wilk, Anderson-Darling
, Kolmogorov-Smimov; Table 1).
Furthermore, a histogram plot and the results of an Anderson-Darling
test indicate that the normalized deviations are normally distributed, and that there is no significant bias between the NIST values and the reference values.
Where a transformation of the data for a particular test to a gaussian distribution was not possible or if the Anderson-Darling
test rejected normality, the reference interval was not computed and the appropriate cell was left blank.
They find empirical critical values for dimensions one through five for an Anderson-Darling type statistic and they also formulate a test based on the Kullback divergence statistic.
The Anderson-Darling methodology is then employed to assess the uniformity of the tail probabilities.
Note that this is nothing more than an application of the Anderson-Darling statistic to test uniformity of the [A.
A comparison of the asymptotic, Anderson-Darling critical values (recommended by Hawkins) and the empirically-derived critical values found in the appendix suggests that the asymptotic critical values may be quite conservative when applied to Hawkins' test statistic.
(A-D) goodness-of-fit test was used to determine if the distributions were appropriate for the datasets.