Confidence Intervals for the Differences between the Means Using Jackknife Method after ANOVA for Data with Outliers

Abstract

This study is a continuing investigation into the performance of confidence intervals for the differences between pairs of means based on the jackknife method for multiple comparisons after the ANOVA F-test. The main focus was to examine the jackknife based confidence intervals in detecting the differences between the means in multiple comparisons tests, especially when datasets contain outliers. A simulation with 5,000 runs each under various situations was conducted to investigate the performance of the jackknife based intervals. As equal sample sizes were considered in this study, we compared the performance of the jackknife based intervals with those obtained by the Tukey’s HSD (Honesty Significant Difference), a method that allows the comparison of all pairs of means, in terms of coverage probability and expected length. The results from a simulation study show that the jackknife based intervals enable better detection of differences between the means when outliers are present in the datasets. The intervals constructed by the jackknife method not only have shorter lengths but also offer control over the probability of a Type I error.