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Locating the Structural Zeros for Internal Anchor Tests: Including the Case of Rounded Formula Scores

Holland, Paul W.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Test Equating, Probability Models, Discrete Bivariate Distributions, Test Scores


When probability models are estimated for these joint distributions, it is usual to require the models to assign positive probability to the sampling zeros but to avoid assigning positive probability to the structural zeros. To do this, it is important to be able to locate where the structural zeros are in the bivariate distribution. When the scores on the tests are consecutive integers, it is easy to determine the location of the structural zeros. This report gives a solution to the problem of locating the structural zeros that arise for a class of bivariate distributions that includes both number-right scores and formula scores that have been rounded to integer values. The result for rounded formula scores is a simple alteration of the case where all the scores are consecutive integers.

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