Testing for an outlier in a linear model

Several authors have advocated the use of the maximum absolute studentized residual for the detection of a single outlier in a general linear model. An excellent survey of the work in this field is presented in Chapter 7 of Barnett and Lewis (1978). Ellenberg (1976) demonstrated that apparently different approaches based on the maximum reduction in the residual sum of squares are equivalent to the use of residuals. The main remaining problem is the determination of critical values. A number of authors use the first Bonferroni inequality. Ellenberg (1976) showed how to calculate the more precise second Bonferroni inequality. In this memorandum we show how the cumbersome computations required for this lower bound correction can be avoided in a large number of cases occurring in practice. When all the correlations between the residuals are absolutely smaller than the value tabulated in table II the approximate test based on the first Bonferroni inequality will result in a size of the test between (a - ½ a^2) and a. In table I critical values are given for a = 0.10; 0.05; 0.01 and 0.001.