ALLOCATION OF ITEMS AND EXAMINEES IN ESTIMATING A NORM DISTRIBUTION BY ITEM‐SAMPLING

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Abstract
A norm distribution consisting of test scores received by 810 college students on a 150 item dichotomously‐scored 4‐alternative multiple‐choice test was empirically estimated through several item‐examinee sampling procedures. The post mortum item‐sampling investigation was specifically designed to manipulate systematically the variables of number of subtests, number of items per subtest, and number of examinees responding to each subtest. Defining one observation as the score received by one examinee on one item, the results suggest that as the number of observations increases beyond 1.23% of the data base all procedures produce stochastically equivalent results. The results of this investigation indicate that, in estimating a norm distribution by item‐sampling, the variable of importance is not the item‐sampling procedure per se but is instead the number of observations obtained by the procedure. It should be noted, however, that in this investigation the test score norm distribution was approximately symmetrical and the possibility should not be overlooked that item‐sampling as a procedure may be robust only for symmetrical norm distributions.