Investigations in Robust Analysis of Variance

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Designed experiments in the social and behavioral sciences (and other fields as well) customarily are handled by techniques associated with the analysis of variance (ANOVA). When the data may not be well behaved, applied statisticians and other practitioners should be able to obtain robust estimates of individual effects, accompanied by suitable summaries and aggregate measures of variability. By adding substantially to the limited number of available small-sample results that apply to the summaries and aggregates required for robust ANOVA, this project aims to provide the basis (including critical tables) for a unified body of basic inferential techniques for one-way and two-way layouts. For data that fail to satisfy the standard assumptions (for example, by containing some anomalous observations or by having heavy tails), ANOVA-like procedures are needed that perform well across a broad range of underlying distributions. A number of proposed robust procedures for the more general class of linear models, which also includes regression, may be applied in ANOVA situations, but evidence on their performance in small samples is still too limited to permit choice of a preferred technique or to make the necessary components (including estimates of effects and their standard errors, corresponding tests of hypotheses, and detailed critical tables) available for statistical applications. The proposed research will investigate several procedures for robust ANOVA, mainly based on M-estimation, using large-sample results and Monte Carlo to establish their properties in small samples. The work will at first emphasize the most widely used designs: two-way and one-way layouts. Previous work by Bickel, Draper, Fellner, Hampel, Hettmansperger, Hoaglin, Huber, Johnson, Kafadar, Lehmann, Mosteller, Rocke, Ronchetti, Rousseeuw, Schrader, Stahel, Tukey, Yohai, and Zamar will provide the main starting points. The research proposed by Mosteller and his associates will continue a line of work long supported by the Division of Social and Economic Science that has over the years produced many of the most innovative developments in statistical methods for making sense of social science data. The Principal Investigator has a most distinguished reputation among both social scientists and statisticians because of remarkable production of both technical and more accessible textbook materials describing and illustrating methods that continue to be developed.