Detecting Outliers in a Two-Way Table: I. Statistical Behavior of Residuals

Abstract

This paper deals with some of the statistical properties of, and methods of analysis for, conventional residuals from additivity in two-way tables. Attention is given to three cases: (i) normal fluctuations superimposed on an additive model; (ii) one outlier added to the condition described in (i); and (iii) two outliers superimposed on the condition in (i). The results are based mainly on empirical sampling and involve average values, correlation properties, the use of the W-statistic (Shapiro and Wilk [24]) and of probability plotting methods. Generally speaking, in the null case of no outliers, the residuals do behave much like a normal sample. When one outlier is present, the direct statistical treatment of residuals provides a complete basis for data-analytic judgments, especially through judicious use of probability plots. When two outliers are present, however, the resulting residuals will often not have any noticeable statistical peculiarities.

KEY WORDS:

• Data Analysis
• Outliers
• Probability Plots
• Residuals
• Two-Way Tables
• W-Statistic