MONTE CARLO INVESTIGATION OF THE ROBUSTNESS OF DIXON'S CRITERIA FOR TESTING OUTLYING OBSERVATIONS.
ABERDEEN RESEARCH AND DEVELOPMENT CENTER ABERDEEN PROVING GROUND MD
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An investigation of the effect of non-normality on the distribution of Dixons criteria for detecting outlying observations is presented here. Monte Carlo techniques were used to determine the distribution of the Dixon statistics when observations are selected from specific non-normal distributions with varying degrees of abnormality. Two such distributions whose degree of abnormality, as determined by the coefficient of skewness, may be varied by changes in the parameters of the distributions are the beta and gamma distributions. A measure of the lack of robustness, that is the sensitivity to departures from normality, in the Dixon criteria may be determined by comparison of the frequency distributions of the Dixon type statistics computed from sampling the non-normal distributions with those values obtained by Dixon when sampling from the normal distribution. Based on the distributions of the Dixon statistics computed from the non-normal distributions, it has been shown that Dixons criteria is not robust and its wide use may result in incorrect decisions when the underlying distribution is asymmetric or skewed. Author
- Statistics and Probability