Showing papers by "Joseph W. McKean published in 1982"

The use and interpretation of robust analysis of variance

Abstract: Publisher Summary This chapter illustrates the use and interpretation of robust analysis of variance. The need for a robust analysis of variance follows from the advantages of classical analysis of varience (ANOVA). ANOVA is one of the principal statistical research tools in many scientific disciplines, its position probably more assured now than over 30 years ago when Eisenhart, 1947, made a similar observation. The primary reason for its popularity is that it provides a summary in convenient tabular form of complex patterns in data. This advantage accrues whether one regards the associated test statistics and p-values in an inferential or in a purely descriptive manner. The goal of robust analysis is to provide automatic detection and adjustment for outliers. As entries in a classical ANOVA table are functions of least squares estimates of regression coefficients and as least squares estimates are by now notorious for their lack of robustness, analogous procedures based upon robust estimates are needed. The chapter discusses robust analysis of variance procedures for the general non-full-rank linear model. The chapter describes the procedures in terms of their mathematical structure, demonstrating that the analysis has the same uses and interpretation as classical analysis of variance. This structure also leads to efficient computational algorithms. Necessary standardizing constants for the test statistics are motivated by consideration of likelihood ratio tests.