Indian Kanoon - Search engine for Indian Law

A limitation of equipercentile equating:

One limitation of equipercentile equating is that the equating relationship cannot be determined for the parts of the score range above the highest score you observe and below the lowest score you observe. If you could observe the scores of the entire target population on both forms of the test, this limitation would not be a problem. In practice, it is not usually a problem for very low scores, because test users rarely need to discriminate at score levels below the lowest score observed. However, it can be a problem at high score levels on a difficult test, because some future test-taker may get a raw score higher than the highest score in the data used for the equating. Smoothing can help solve this problem because many smoothing methods will produce a smoothed distribution with nonzero probabilities (possibly very small, but not zero) at the highest and lowest score levels, even if no test-takers actually attained those scores. However, at those very high and very low score levels, the equating relationship computed from the smoothed distributions will be based on scores that were not actually observed! Equipercentile equating and the discreteness problem:

I said earlier that one limitation of equating comes from the discreteness of the score scale. That limitation applies to any type of equating. For linear equating, the discreteness of the scale does not cause a problem in computing the adjustmentonly in applying the adjustment after it is computed. But for equipercentile equating, the discreteness of the score scale causes a problem in computing the adjustment.

In handbook of Statistics 26, Psychometrics, Volume-26, First Edition 2007 published by Library of Congress Cataloging-in-Publication Data (ISBN-13:978-0-444-52103-3, ISBN-10:0-444-52103-8, ISSN (Series) : 0169-7161) edited by C.R. Rao and S. Sinharay, a paper titled Equating Test Scores authored by Paul W. Holland, Neil J. Dorans and Nancy S. Petersen, has been published wherein the authors of the study paper, observed as under:

3.1.1.3.-Presmoothing score distributions- Irregularities in the score distributions cause problems for equipercentile equating. They produce irregularities in the equipercentile equating function that do not generalize to other groups of test-takers. Consequently, it is generally considered advisable to presmooth the raw-score frequencies in some way prior to equipercentile equating. The purpose of this step is to eliminate some of the sampling variability present in the raw-score frequencies, in order to produce smoother edfs for computation of the equipercentile function. If presmoothing is done so as to preserve the essential features of the score frequencies, it will reduce the sampling variability in the estimated frequencies without introducing significant bias. The resulting estimates will be closer to the underlying frequencies in the target population, T. When presmoothing is done with a model that does not describe the data well, then the estimated frequencies will be biased estimates of the underlying frequencies in T. A limitation of equipercentile equating is that the equating relationship cannot be computed for any possible scores above the highest observed score or below the lowest observed score. If we could observe the scores of the entire target population, T, on both forms of the test, this limitation would not be a problem. Smoothing can help solve this problem because many smoothing methods will produce a smoothed distribution with probabilities (possibly very small) at the highest and lowest score levels, even if no test-takers actually attained those scores.