On the effect of rounding on hypothesis testing when sample size is large

Abstract

It is well known that sample moments are more sensitive and less robust than order statistics for robustness with respect to outliers. In this article, we show that the situation is exactly the opposite for robustness with respect to rounding. For large and very large sample sizes, statistical procedures based on order statistics become non-applicable even for very mild data rounding while procedures based on sample moments work perfectly for this rounding level. The comparison of sample moments and order statistics is made for tests for normality and tests for exponentiality.