A single conceptual and theoretical framework for sampling any configuration of data from one or more population matrices is presented, integrating past designs and discussing implications for more general designs. The theory is based upon a generalization of the generalized symmetric mean approach for single matrix samples. (Author/CTM)

Procedures to be applicable in situations in which large numbers of individuals are tested or in situations where multiple measures are taken. (Author/CB)

The restrictions on item difficulties that must be met when binomial models are applied to domain-referenced testing are examined. Both a deterministic and a stochastic conception of item responses are discussed with respect to difficulty and Guttman-type items. (Author/BH)

In a situation where the population distribution of latent trait scores can be estimated, the ordinary maximum likelihood estimator of latent trait scores may be improved upon by taking the estimated population distribution into account. In this paper empirical Bayes estimators are compared with the liklihood estimator for three samples of 300…

A comparison was made between four different scoring procedures for the 45-item Reading Comprehension subtest, Level I, of the Comprehensive Test of Basic Skills, Form S, for a sample of 1,000 third grade students. These students were selected to have been among those who omitted from 3 to 22 of the 45 items. Another representative sample of 1,300…

Maximum likelihood factor analysis provides an effective method for estimation of factor matrices and a useful test statistic in the likelihood ratio for rejection of overly simple factor models. A reliability coefficient is proposed for analysis of factor solution. (Author/RK)

Multiple matrix sampling (MMS) theory indicates how data may be gathered to most efficiently convey information about levels of attainment in a population, but standard analyses of these data require random sampling of items from a fixed pool of items. This assumption proscribes the retirement of flawed or obsolete items from the pool as well as…

This report describes new statistical procedures for item response analysis using estimation of item response curves used in mental testing with ability parameters treated as a random sample. Modern computer technology and the EM algorithm make this solution possible. The research focused on the theoretical formulation and solution of maximum…

This study examined the effects of certain item selection methods on the classification accuracy and classification consistency of criterion-referenced instruments. Three item response data sets, representing varying situations of instructional effectiveness, were simulated. Five methods of item selection were then applied to each data set for the…

A test theory using only ordinal assumptions is presented, based on the idea that the test items are a sample from a universe of items. The sum across items of the ordinal relations for a pair of persons on the universe items is analogous to a true score. (SLD)

Formulas are presented for decision reliability and for classification validity for mastery/nonmastery decisions based on criterion referenced tests. Two item parameters are used: the probability of a master answering an item correctly, and the probability of a nonmaster answering an item incorrectly. The theory explores the relationships of…

Three statistical problems related to criterion-referenced testing are investigated: estimation of the likelihood of a false-positive or false-negative decision with a mastery test, estimation of true scores in the Compound Binomial Error Model, and comparison of the examinees to a control. Two methods for estimating the likelihood of…

California Assessment Program's application of matrix sampling and item response curve theory to the scaling and reporting of state assessment data is described. It is designed to express educational outcomes in an efficient and interpretable form that is both immediately informative and suited to analysis over extended periods of time.…

The concept under investigation was the reliability of estimates of mean scores of groups under various assumptions of multiple-matrix sampling when reliabilities are computed according to procedures based on generalizability theory. Four different cases were compared with respect to the generalizability coefficients depending upon whether pupils…