John W. Tukey's contributions to multiple comparisons

Abstract

This article provides a historical overview of the philosophical, theoretical and practical contributions made by John Tukey to the field of simultaneous inference. His early work, culminating in the monograph "The Problem of Multiple Comparisons," established him as one of the pioneers in the field, investing it with both academic respectability and a focus on practical problems. For many years afterward, Tukey only published sporadically in the area but remained convinced that multiplicity issues were of fundamental importance. During the last decade of his life, Tukey again devoted substantial attention to multiplicity, experimenting with different graphical representations of multiple comparison procedures and exploring the implications of new approaches to controlling family-wise error rates. He leaves a rich legacy that should engage and inspire statisticians for many years to come.