4 BOOTSTRAP CONFIDENCE-INTERVALS FOR THE BINOMIAL-ERROR MODEL

Confidence intervals for the mean function of the true proportion score (mu(zeta\x)), where zeta and x respectively denote the true proportion and observed test scores, can be approximated by the Efron, Bayesian, and parametric empirical Bayes (PEB) bootstrap procedures. The similarity of results yielded by all the bootstrap methods suggests the following: the unidentifiability problem of the prior distribution g(zeta) can be bypassed with respect to the construction of confidence intervals for the mean function, and a beta distribution for g(zeta) is a reasonable assumption for the test scores in compliance with a negative hypergeometric distribution. The PEB bootstrap, which reflects the construction of Morris intervals, is introduced for computing predictive confidence bands for zeta\x. It is noted that the effect of test reliability on the precision of interval estimates varies with the two types of confidence statements concerned