A Detection of Outliers in Random Sample from Normally Distributed Population Using Coefficient of Skewness
Abstract
The objective of this research is to the propose a detection of outliers in a test statistic. Such a test statistic is developed from the concept of GESD by Rosner, where the assumption of this test statistic is a normally distributed population. In this paper, we shall show a comparison of an ability of control type I error and power of the test under a simulation of normal distributions induced by the sample sizes 10, 20, 30, 50, 100 and 200. The outliers in this simulation are defined in many different situations, which the situations are replicated 1,000 times. The significance level is 0.05. The results show that the proposed test statistic can control the probability of type I error. The percentage of correct decision are greater than 95 when the alternative hypothesis is true.Keywords : outliers, normal distribution, coefficient of skewnessReferences
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Cochran, W.G. (1954). The combination of estimates from different experiments. Biometrics, 10(1), 101-129.
Cramér, H. (1946). Mathematical Methods of Statistics. Princeton: Princeton University Press.
Fisher, R. A. (1930). The moment of the distribution for normal samples of measures of departure from normality. In Proceedings of the Royal Society A. 130(812), 16-28.
Hawkin, D.M. (1980). Identification of Outliers. London: Chapman and Hall.
Joanes, D.N. & Gill C.A. (1998). Comparing measures of sample skewness and kurtosis. Journal of the
Royal Statistical Society (Series D): The Statistician, 47(1),183-189.
Rosner, B. (1975). On the Detection of Many Outliers. Technometrics, 17(2), 211-227.
Rosner, B. (1983). Percentage Points for a Generalized ESD Many-Outlier Procedure. Technometrics,
25(2), 165-172.
Suwattee, P. (2010). Theory of statistical inference. (3rd Edition). Bangkok: National Institute of
Development Administration. (in Thai)
Cochran, W.G. (1954). The combination of estimates from different experiments. Biometrics, 10(1), 101-129.
Cramér, H. (1946). Mathematical Methods of Statistics. Princeton: Princeton University Press.
Fisher, R. A. (1930). The moment of the distribution for normal samples of measures of departure from normality. In Proceedings of the Royal Society A. 130(812), 16-28.
Hawkin, D.M. (1980). Identification of Outliers. London: Chapman and Hall.
Joanes, D.N. & Gill C.A. (1998). Comparing measures of sample skewness and kurtosis. Journal of the
Royal Statistical Society (Series D): The Statistician, 47(1),183-189.
Rosner, B. (1975). On the Detection of Many Outliers. Technometrics, 17(2), 211-227.
Rosner, B. (1983). Percentage Points for a Generalized ESD Many-Outlier Procedure. Technometrics,
25(2), 165-172.
Suwattee, P. (2010). Theory of statistical inference. (3rd Edition). Bangkok: National Institute of
Development Administration. (in Thai)
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2020-01-14
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