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The Standard Error of Equating for the Kernel Method of Equating Score Distributions

Holland, Paul W.; King, Benjamin F.; Thayer, Dorothy T.
Publication Year:
Report Number:
RR-89-06, PSRTR-89-83
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Equated Scores, Kernel Method, Psychometrics, Standard Error of Measurement, Test Theory


Formulas for the standard error of equating (SEE) for a new equating technique, the kernel method, are developed in detail for three equating designs—two random groups, external anchor-test and internal anchor-test. The kernel method includes both linear and equipercentile methods as special cases. The SEEs developed in this paper make crucial use of log-linear models to pre-smooth (i.e., estimate) score distributions. The resulting SEEs reflect the method of estimation, the equating design and the final shape of the resulting equating function. An example is given that compares the SEEs for several applications of the kernel method.

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