Sequentially Testing Three Hypotheses

Abstract

The sequential probability ratio test (SPRT) and 2-SPRT, discussed in Chapter 5, are sequential methods for deciding between two hypotheses. It is assumed here that the reader is familiar with the notation and concepts presented there. Increasingly ecologists are attempting to choose among three or more hypotheses. Morris (1954) and Waters (1955) appear to be the first in the biological literature to consider the problem of deciding among three or more hypotheses. Each developed sequential plans for determining whether the infestation of trees by spruce budworm egg masses was light, medium, or heavy. Waters also considered the infestation of spruce budworm larvae. The standard survey procedure in the northeastern United States had been to examine five 15-inch twigs from each of five balsam fir trees at every collection point (Waters, 1955). The twigs were cut by pole pruner from approximately the mid-crown height of the trees. In the study reported by Morris (1954), very tall trees for which the mid-crown could not be reached with pole pruners were felled and sample branches selected as follows: one branch from the apical quarter of the crown, one from the second quarter, one-half of a branch from the third quarter, and one-half from the basal quarter. These four values were averaged to give a mean for the tree. Alternately, Waters avoided including very tall trees in the sample. For sequential sampling, the tree was taken as the sampling unit. One observation per tree was recorded.