A Study on Sensitivity and Robustness of One Sample Test Statistics to Outliers
Keywords:
outliers, type 1 error rate, sensitivity, robustness, inferential test statistics, levels of significance
Abstract
Outliers are observations that stand too different from others in a set of observations When present in a data set they affect both descriptive and inferential statistics This work therefore studies the sensitivity and robustness of one sample test statistics to outliers so as to know the appropriate one to test hypothesis about the population parameter when outliers are present One sample test statistics considered are parametrics test Student t-test and ztest non-parametric test Wilcoxon Sign test Distribution Sign test DST Asymptotic Sign test AST Wilcoxon Signed rank test Distribution Wilcoxon Signed rank test DWST and Asymptotic AWST t-test for rank transformation Rt-test and Trimmed t-test statistics Tt-test Monte Carlo experiments replicated five thousand 5000 times were conducted at eight 8 sample sizes 10 15 20 25 30 35 40 and 50 by simulating data from normal distribution At each of the sample sizes 10 and 20 of the generated data were randomly selected and invoked with various magnitude of outliers -10 -9 -8 8 9 10 The test statistics were compared at three levels of significance 0 1 0 05 and 0 01 A test is considered robust if its estimated error rate approximates the true error rate and has the highest number of times it approximates the error rate when counted over the percentage of outliers magnitudes of outliers and levels of significance and if the counts is minimum the test statistics is sensitive At all the three 3 levels of significance results revealed that Type 1 error rates of Student t-test Rt-test and AWST statistics are good and that z-test and Student t-test statistics are most sensitive to outliers The statistics robustness is affected by the levels of significance in that the sign test DST and AST is robust at 0 1 Tt-test and Wilcoxon Sign Rank test DWST and AWST at 0 05 and DST AWST Tttest and AST at 0 01 level of significance Consequently the Sign test
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Published
2016-05-15
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Copyright (c) 2016 Authors and Global Journals Private Limited
This work is licensed under a Creative Commons Attribution 4.0 International License.