10Multiple Decision Problems
10.1 Introduction
We will make statements about a ≥ 2 populations (distributions). We first discuss selection procedures and later multiple comparisons of means. Gupta and Huang (1981) give a good overview of multiple decision problems.
10.2 Selection Procedures
We start with a set G of a populations, i.e. G = {Pi, i = 1, … , a}. These populations correspond with random variables with parameter vectors for which at least one component is unknown. This general approach is described in Rasch and Schott (2018). In this book we restrict ourselves to a special case. In Pi we consider stochastically independent random variables with a 
‐distribution.
It is our aim to select the population with the largest expectation or the populations with the t < a largest expectations. In Section 10.7 we discuss selection procedures for variances.
We first order the populations in G by magnitude of their expectations. For this, we need an order relation.
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