Generalized wreath products of permutation groups

Abstract

John Tukey connected the theory underlying simple random sampling without replacement, cumulants, expected mean squares and spectrum analysis. He gave us one degree of freedom for nonadditivity, and he pioneered finite population models for understanding ANOVA. He wrote widely on the nature and purpose of ANOVA, and he illustrated his approach. In this appreciation of Tukey's work on ANOVA we summarize and comment on his contributions, and refer to some relevant recent literature.