A Study on Sensitivity and Robustness of one Sample and Matched-Pairs

The presence of outlier(s) in a data set may be inevitable as it can occur naturally in a population. Various test statistics have been developed, these are parametric (student t-test, z-test, paired t-test), non-parametric: Distribution Sign Test (DST), Asymptotic Sign Test (AST)Distribution, Wilcoxon Sign Rank test (DWST) and Asymptotic Wilcoxon Sign Rank Test (AWST), t-test for rank transformation which bridges the gap between the parametric and the non-parametric (Rt-test), and the Trimmed t-test statistic (Tt-test). Consequently, research carried out in this book examines the effect of outliers on one sample and paired sample inferential test statistics so as to determine the most sensitive and robust ones. At each sample size, 10% and 20% of the generated data were invoked with twenty-one (21) various magnitude of outliers (-10, -9,..., 9, 10). When there was no outlier in the data sets, the Type 1 error rate of the statistics was determined, while with outliers, the Power rate was determined to assess their sensitivity and robustness. Hence, end-user of statistics, researchers, policymakers among others will find this book viable and useful.