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Analytic Smoothing for Equipercentile Equating Under the Common Item Nonequivalent Populations Design

Published online by Cambridge University Press:  01 January 2025

Michael J. Kolen  and
David Jarjoura
Michael J. Kolen*
Affiliation:
The American College Testing Program
David Jarjoura
Affiliation:
Northeastern Ohio Universities College of Medicine
*
Requests for reprints should be sent to Michael J. Kolen, Measurement Research Department, The American College Testing Program, PO Box 168, Iowa City, IA 52243.
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Abstract

A cubic spline method for smoothing equipercentile equating relationships under the common item nonequivalent populations design is described. Statistical techniques based on bootstrap estimation are presented that are designed to aid in choosing an equating method/degree of smoothing. These include: (a) asymptotic significance tests that compare no equating and linear equating to equipercentile equating; (b) a scheme for estimating total equating error and for dividing total estimated error into systematic and random components. The smoothing technique and statistical procedures are explored and illustrated using data from forms of a professional certification test.

Keywords

equatingequipercentile equatingequating errorbootstrap
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 1 , March 1987 , pp. 43 - 59
Copyright
Copyright © 1987 The Psychometric Society

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Footnotes

The authors thank Robert L. Brennan for reviewing an earlier draft of this manuscript. Most of the work was completed while the second author was at The American College Testing Program.

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