Emrick’s model is a latent class or state model
for mastery testing that entails a simple rule for
separating masters from nonmasters with respect to
a homogeneous domain of items. His method for
estimating the model parameters has only restricted
applicability inasmuch as it assumes a mixing parameter
equal to .50 and an a priori known ratio of
the two latent success probabilities. The maximum
likelihood method is also available but yields an intractable
system of estimation equations which can
only be solved iteratively. The emphasis in this paper
is on estimates to be computed by hand but
nonetheless accurate enough for most practical situations.
It is shown how the method of moments can
be used to obtain such "quick and easy" estimates.
In addition, an endpoint method is discussed that
assumes that the parameters can be estimated from
the tails of the sample distribution. A monte carlo
experiment demonstrated that for a great variety of
parameter values, test lengths, and sample sizes,
the method of moments yields excellent results and
is uniformly much better than the endpoint method.