Testing for Three or Fewer Outliers in Two-Way Tables

Abstract

In John and Draper (1978), tests for outliers in two-way tables were discussed. A test statistic Q_K was considered (see Gentleman and Wilk, 1975b), and was shown to be the sum of squares of successive adjusted normalized uncorrelated residuals. Percentage points for a test statistic involving maximum Q_K in the one and two outlier cases were estimated by Monte Carlo generations. Formula approximations to these percentage points were suggested.

The present paper extends the previous work. Simulations to estimate percentage points for a test statistic involving maximum Q_K for the three outlier case are summarized, and approximations to these points suggested. An aspect of design of experiments in the general regression situation when it is feared that outliers may occur is also briefly discussed.

KEY WORDS:

• Residuals
• Outliers
• Tests for outliers
• Two-way tables
• Missing values
• Robust designs