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On the Proportion of Missing Data in Classical Test Theory CTT

Mislevy, Robert J.
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Classical Test Theory (CTT), Design Effect, Effective Sample Size, Missing Data, Missing Information Principle


Knowing the proportion of missing response is critical in sample surveys for gauging its impact and, in some cases, implementing methods for dealing with it. A particular kind of missingness occurs in educational surveys, namely measurement error associated with an inherently unobservable, or latent, variable of interest. In this case, the variable is missing for every respondent—but not completely, because the observed responses provide information about it through the latent variable model. A characterization of missingness can be obtained with an analog of the design effect in survey sampling. In the case of classical test theory, the proportion of missingness with respect to estimating the population mean is shown to be the complement of test reliability. This result is an instance of Orchard and Woodbury’s (1972) missing information principle.

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