A statistical-test-complemented graphical method for detecting multiple outliers in two-way tables

Abstract

A statistic Rk which has a simple relationship with Qk is proposed for the analysis of outliers in two-way tables and the rationale is discussed. The critical values of the test statistic, minimum Rk, can be well approximated by existing values based on univariate Grubbs-type outlier test statistics. The test statistics are complemented with plots of the largest Wk values, which have a simple monotonic inverse relationship with the values of Rk, against their expected quantiles which are approximated using a conditional independence argument. Two examples are analysed with satisfactory results.