The standard error of moving average smoothed equipercentile equating

The standard error of moving average smoothed equipercentile equating A very important aspect of virtually any kind of systematic investigation is to be able to identify whether two entities are different, and, almost equivalently, whether they are the same. We need to be sure that measurements made at different time in different places by different experimenters are equivalent. To do this in the social sciences, the procedure of equating is necessary to be able to compare measurements made using different instruments. Small sample sizes can lead to apparent jaggedness in the formulae for equating two quantities, and some kind of smoothing procedure is frequently necessary when dealing with relatively small samples. A large-sample formula is developed for the standard error of moving average smoothed equipercentile equating on a single sample. An example is given of the application in equating two versions of a reading test, and the results are verified using a bootstrap procedure. The large sample formula gives a result that is close to the bootstrap procedure, except at very sparse frequencies. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

The standard error of moving average smoothed equipercentile equating

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Publisher
Springer Journals
Copyright
Copyright © 2009 by Springer Science+Business Media B.V.
Subject
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1007/s11135-009-9231-1
Publisher site
See Article on Publisher Site

Abstract

A very important aspect of virtually any kind of systematic investigation is to be able to identify whether two entities are different, and, almost equivalently, whether they are the same. We need to be sure that measurements made at different time in different places by different experimenters are equivalent. To do this in the social sciences, the procedure of equating is necessary to be able to compare measurements made using different instruments. Small sample sizes can lead to apparent jaggedness in the formulae for equating two quantities, and some kind of smoothing procedure is frequently necessary when dealing with relatively small samples. A large-sample formula is developed for the standard error of moving average smoothed equipercentile equating on a single sample. An example is given of the application in equating two versions of a reading test, and the results are verified using a bootstrap procedure. The large sample formula gives a result that is close to the bootstrap procedure, except at very sparse frequencies.

Journal

Quality & QuantitySpringer Journals

Published: May 28, 2009

References

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