Comparisons between means

Abstract

We have not yet dealt adequately with the Gopain data. Chapter 7 discussed standard errors for a single mean and probabilistic inference based on this. Section 8.2 indicated how the methods of Chapter 7 can be used in a paired comparison experiment, but this is no help for Table 1.1 which had no planned pairing and unequal numbers in series D, E. We must consider what can be said about differences between means, their appropriate standard errors and subsequent probability statements, when the means are based on unequal numbers of observations. We need also to ask how this applies to the more complicated experimental designs of Chapter 8, where several treatments are under test simultaneously and various constraints on the organization and randomization of the experiment are deliberately introduced.