Image Analysis, Classification and Change Detection in Remote Sensing, 3rd Edition

Hypothesis testing 65

In order to test such assertions on the basis of samples of the distributions

involved, it is also necessary to formulate alternative hypotheses. To distin-

guish these from the o riginal assertions, the latter are traditionally called null

hypotheses. Thus we might be interested in testing the simple null hypothesis

µ = 0 against the composite alternative hypothesis µ 6= 0. An appropriate

sample function for deciding whether or not to reject the null hypothesis in

favor of its alternative is referred to as a test statistic, often denoted by the

symbol Q. An appropria te test procedure will partition the possible realiza-

tions of the test statistic into two subsets: an acceptance region for the null

hypothesis and a rejection ...