When constructed-response items are administered for a second time, it is necessary to evaluate whether the current Time B administration's raters have drifted from the scoring of the original administration at Time A. To study this, Time A papers are sampled and rescored by Time B scorers. Commonly the scores are compared using the proportion of…

The finite population correction (FPC) factor is often used to adjust variance estimators for survey data sampled from a finite population without replacement. As a replicated resampling approach, the jackknife approach is usually implemented without the FPC factor incorporated in its variance estimates. A paradigm is proposed to compare the…

The variance formula derived for a two-stage sampling design without replacement employs the joint inclusion probabilities in the first-stage selection of clusters. One of the difficulties encountered in data analysis is the lack of information about such joint inclusion probabilities. One way to solve this issue is by applying Hájek's…

A general program for item-response analysis is described that uses the stabilized Newton-Raphson algorithm. This program is written to be compliant with Fortran 2003 standards and is sufficiently general to handle independent variables, multidimensional ability parameters, and matrix sampling. The ability variables may be either polytomous or…

Pseudo Bayes probability estimates are weighted averages of raw and modeled probabilities; these estimates have been studied primarily in nonpsychometric contexts. The purpose of this study was to evaluate pseudo Bayes probability estimates as applied to the estimation of psychometric test score distributions and chained equipercentile equating…

In operational equating, frequency estimation (FE) equipercentile equating is often excluded from consideration when the old and new groups have a large ability difference. This convention may, in some instances, cause the exclusion of one competitive equating method from the set of methods under consideration. In this report, we study the…

Continuous exponential families may be employed to find continuous distributions with the same initial moments as the discrete distributions encountered in typical applications of classical equating. These continuous distributions provide distribution functions and quantile functions that may be employed in equating. To illustrate, an application…

Continuous exponential families are applied to linking forms via a single-group design. In this application, a distribution from the continuous bivariate exponential family is used that has selected moments that match those of the bivariate distribution of scores on the forms to be linked. The selected continuous bivariate distribution then yields…

Some probabilistic illustrations of the reliability coefficient are provided to assist in interpretation of this measure. All explanations are derived under the assumption that the joint distribution of examinee scores from two parallel tests is well approximated by a bivariate normal distribution.

Latent-class item response models with small numbers of latent classes are quite competitive in terms of model fit to corresponding item-response models, at least for one- and two-parameter logistic (1PL and 2PL) models. Provided that care is taken in terms of computational procedures and in terms of use of only limited numbers of latent classes,…

Criteria for prediction of multinomial responses are examined in terms of estimation bias. Logarithmic penalty and least squares are quite similar in behavior but quite different from maximum probability. The differences ultimately reflect deficiencies in the behavior of the criterion of maximum probability.

Multinomial-response models are available that correspond implicitly to tests in which a total score is computed as the sum of polytomous item scores. For these models, joint and conditional estimation may be considered in much the same way as for the Rasch model for right-scored tests. As in the Rasch model, joint estimation is only attractive if…

Confidence intervals are an important tool to indicate uncertainty of estimates and to give an idea of probable values of an estimate if a different sample from the population was drawn or a different sample of measures was used. Standard symmetric confidence intervals for proportion estimates based on a normal approximation can yield bounds…

Weighting and variance estimation are two statistical issues involved in survey data analysis for large-scale assessment programs such as the Higher Education Information and Communication Technology (ICT) Literacy Assessment. Because survey data are always acquired by probability sampling, to draw unbiased or almost unbiased inferences for the…