Selection criteria for the construction of efficient diagnostic keys

A diagnostic key defines a hierarchial sequence of tests used to identify a specimen from a set of known taxa. The usual measure of the efficiency of a key, the expected number of tests per identification, may not be appropriate when the responses to tests are not known for all taxon/test pairs. An alternative measure is derived and it is shown that the test selected for use at each point in the sequence should depend on which measure is used. Two suggestions of Gower and Payne (1975), regarding test selection, are shown to be appropriate only to the new measure. Tests are usually selected by calculating the value of some selection criterion function. Functions are reviewed for use in each of the two situations, and new functions are derived. The functions discussed are shown to be interpretable in terms of the number of tests required to complete the key from the current point in the sequence, given that a particular test is selected. This interpretation enables the functions to be extended to select tests with different costs and allows recommendations to be made as to which function to use, depending on how many ‘good’ tests are available.