chapter  2
General Concepts and Basic Multiple Comparison Procedures
Pages 30

The objective of this chapter is to introduce general concepts related to multiple testing as well as to describe basic strategies for constructing multiple comparison procedures. In Section 2.1 we introduce relevant error rates used for multiple hypotheses test problems. In addition, we discuss general concepts, such as adjusted and unadjusted p-values, single-step and stepwise test procedures, etc. In Section 2.2 we review different principles of constructing multiple comparison procedures, including union-intersection tests, intersection-union tests, the closure principle and the partitioning principle. We then review commonly used multiple comparison procedures constructed from marginal p-values. Methods presented here include Bonferroni-type methods and their improvements (Section 2.3) as well as modified Bonferroni methods based on the Simes inequality (Section 2.4). For each method, we describe its assumptions, advantages and limitations.