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Qian, Jiahe – ETS Research Report Series, 2017
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…
Descriptors: Mathematical Formulas, Computation, Sampling, Research Design
Haberman, Shelby J. – ETS Research Report Series, 2008
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…
Descriptors: Equated Scores, Statistical Distributions, Probability, Computation
Haberman, Shelby J. – ETS Research Report Series, 2008
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…
Descriptors: Equated Scores, Probability, Statistical Distributions, Models
Xu, Xueli; von Davier, Matthias – ETS Research Report Series, 2008
Three strategies for linking two consecutive assessments are investigated and compared by analyzing reading data for the National Assessment of Educational Progress (NAEP) using the general diagnostic model. These strategies are compared in terms of marginal and joint expectations of skills, joint probabilities of skill patterns, and item…
Descriptors: National Competency Tests, Probability, Reading Achievement, Test Items
Oranje, Andreas – ETS Research Report Series, 2006
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…
Descriptors: Computation, Statistical Analysis, National Competency Tests, Comparative Analysis
Zhang, Jinming; Chang, Hua-Hua – ETS Research Report Series, 2005
This paper compares the use of multiple pools versus a single pool with respect to test security against large-scale item sharing among some examinees in a computer-based test, under the assumption that a randomized item selection method is used. It characterizes the conditions under which employing multiple pools is better than using a single…
Descriptors: Comparative Analysis, Test Items, Item Banks, Computer Assisted Testing
Yu, Lei; Livingston, Samuel A.; Larkin, Kevin C.; Bonett, John – ETS Research Report Series, 2004
This study compared essay scores from paper-based and computer-based versions of a writing test for prospective teachers. Scores for essays in the paper-based version averaged nearly half a standard deviation higher than those in the computer-based version, after applying a statistical control for demographic differences between the groups of…
Descriptors: Essays, Writing (Composition), Computer Assisted Testing, Technology Uses in Education