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Reducing Type-2 Sampling Errors in the Estimation of Test Reliability

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Error of Measurement, Reliability Formulas, Split-Half Test Reliability, Test Reliability, Type II Errors


The formula and derivation are given for the sampling variance of the "random-halves" reliability coefficient when items, rather than examinees, are sampled. When the number of test items is large, this sampling variance is found to be larger than the Kuder-Richardson formula-20 coefficient by a factor equal to the number of test items. The usual matched-halves reliability coefficient will likewise usually have a large sampling variance, since it likewise is based on an arbitrary split of the test items. An adaptation of the Jackson-Ferguson "battery reliability coefficient," used as an estimate of the matched-forms reliability of the test, avoids this relatively large sampling variance.

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