The problem of mastery decisions and optimizing
cutoff scores on criterion-referenced tests is considered.
This problem can be formalized as an (empirical)
Bayes problem with decisions rules of a
monotone shape. Next, the derivation of optimal
cutoff scores for threshold, linear, and normal ogive
loss functions is addressed, alternately using such
psychometric models as the classical model, the
beta-binomial, and the bivariate normal model.
One important distinction made is between decisions
with an internal and an external criterion. A
natural solution to the problem of reliability and
validity analysis of mastery decisions is to analyze
with a standardization of the Bayes risk (coefficient
delta). It is indicated how this analysis proceeds
and how, in a number of cases, it leads to coefficients
already known from classical test theory. Finally,
some new lines of research are suggested
along with other aspects of criterion-referenced testing
that can be approached from a decision-theoretic
point of view.