Robust comparisons of variation using ratios of interquantile ranges

01/01/2018

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by   Chandima N. P. G. Arachchige, et al.

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There are two major shortcomings of the F-test for testing the equality of two variances. Firstly, underlying normality of the populations from which the data is drawn is assumed and a violation of this assumption can lead to unreliable inference. Secondly, the usual sample variance estimators are non-robust and may be heavily influenced by outliers. In our study, we propose to use confidence intervals of ratios of interquantile ranges to compare the variation between two populations. We introduce interval estimators for the ratio that have excellent coverage properties for a wide range of distributions. Robustness properties of the estimator are studied using the influence function.