Assessing the significance of difference between two quick estimates of location

Abstract

Descriptive statistics such as means, standard deviations and quantiles are often the only records retained for long-term use from an exploratory, or otherwise, analyses of data. The problem of comparing locations of two populations with comparable dispersions on the basis of such records alone is addressed in this note. We construct analogues of the pooled t statistics by studentizing difference between two quick estimators such as trimeans, and Gastwirth estimators, using ranges of quantiles constituting the statistics. The null distributions of these statistics are then approximated by scaled Student's t distributions, and examined for validity robustness and compared with competitors. It is seen that the operating characteristics of tests based on studentized differences of quick estimators are superior to those of pooled t tests, which can also be performed on the basis of summaries, and are comparable to those of Wilcoxon-Mann-Whitney rank sum tests which require the complete data rather than the summaries.