Abstract
Often, in biology, a sequence of binary or polytomous tests is used to identify the population of origin of a specimen. The sequence is controlled by a diagnostic key which specifies the next test to be applied conditional on the responses to the tests so far performed. Provided that at least some tests are free from error for some of the populations, the tests performed serve to eliminate certain populations from contention. This leads to constructing the key by choosing the most useful next test. Here, usefulness is measured by a function of the vector of numbers of contending populations falling into various response categories. General desirable properties of such functions are developed and new functions recommended both in the error free situation and when error is present.
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