Lack of robustness in two tests of normality against autocorrelation in sample data

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Abstract
Robustness against autocorrelation in time-series data is investigated for two tests of normality: the Kolmogorov-Smirnov test, in the class of normality tests using statistics based on the empirical cu¬mulative distribution function, and the Shapiro-Wilk analysis-of-variance test, which regresses the ordered sample values on the corresponding expected normal order statistics. For a Gaussian first-order autoregressive process, it is shown by simulation that: 1. for short series, both tests are conservative for some range of negative values of first-order autocorrelation, and too liberal for medium-to-high positive and high negative values; 2. for moderate sample sizes, both tests are no longer conservative, but remain too liberal asymmetrically for high negative and positive values of first-order autocorrelation; 3. the Kolmogorov-Smirnov test, which traditionally suffers from lack of power in comparisons with the W test of Shapiro and Wilk, is more robust against autocorrelation in time-series data, whatever the sign of the first-order autocorrelation. We illustrate that these results also apply to spatially auto-correlated data along a transect.