A Study on Sensitivity and Robustness of One Sample Test Statistics to Outliers

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 z-test), 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).