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…

When an assessment undergoes changes to the administration or instrument, bridge studies are typically used to try to ensure comparability of scores before and after the change. Among the most common and powerful is the common population linking design, with the use of a linear transformation to link scores to the metric of the original…

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…

In this study, we apply jackknifing to anchor items to evaluate the impact of anchor selection on equating stability. In an ideal world, the choice of anchor items should have little impact on equating results. When this ideal does not correspond to reality, selection of anchor items can strongly influence equating results. This influence does not…

Several factors could cause variability in item response theory (IRT) linking and equating procedures, such as the variability across examinee samples and/or test items, seasonality, regional differences, native language diversity, gender, and other demographic variables. Hence, the following question arises: Is it possible to select optimal…

Several complex sample standard error estimators based on linearization and resampling for the latent regression model of the National Assessment of Educational Progress (NAEP) are studied with respect to design choices such as number of items, number of regressors, and the efficiency of the sample. This paper provides an evaluation of the extent…

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…

At present, although the percentages of students with disabilities (SDs) and/or students who are English language learners (ELL) excluded from a NAEP administration are reported, no statistical adjustment is made for these excluded students in the calculation of NAEP results. However, the exclusion rates for both SD and ELL students vary…

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.

This report describes the derivation and evaluation of a method for comparing the performance standards for public school students set by different states. It is based on an approach proposed by McLaughlin and associates, which constituted an innovative attempt to resolve the confusion and concern that occurs when very different proportions of…

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…

This paper describes an approach to item analysis that is based on the estimation of a set of response curves for each item. The response curves show, at a glance, the difficulty and the discriminating power of the item and the popularity of each distractor, at any level of the criterion variable (e.g., total score). The curves are estimated by…

A multitude of methods has been proposed to estimate the sampling variance of ratio estimates in complex samples (Wolter, 1985). Hansen and Tepping (1985) studied some of those variance estimators and found that a high coefficient of variation (CV) of the denominator of a ratio estimate is indicative of a biased estimate of the standard error of a…

In this paper, a data perturbation method for minimizing the possibility of disclosure of participants' identities on a survey is described in the context of the National Assessment of Educational Progress (NAEP). The method distinguishes itself from most approaches because of the presence of cognitive tasks. Hence, a data edit should have minimal…