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In the type of recognition system under discussion, the physical sample to be recognized is first subjected to a battery of tests; on the basis of the test results, the sample is then assigned to one of a number of prespecified categories. The theory of how test results should be combined to yield an optimal assignment has been discussed in an earlier paper. Here, attention is focused on the tests themselves. At present, we usually measure the effectiveness of a set of tests empirically, i.e., by determining the percentage of correct recognitions made by some recognition device which uses these tests. In this paper, we discuss some of the theoretical problems encountered in trying to determine a more formal measure of the effectiveness of a set of tests; a measure which might be a practical substitute for the empirical evaluation. Specifically, the following question is considered: What constitutes an effective set of tests, and how is this effectiveness dependent on the correlations among, and the properties of, the individual tests in the set? Specific suggestions are considered for the case in which the test results are normally distributed, but arbitrarily correlated. The discussion is supported by the results of experiments dealing with automatic recognition of hand-printed characters.