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Univariate vs. Bivariate Smoothing in Frequency Estimation Equating

Livingston, Samuel A.; Feryok, Nancy J.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Equated Scores, Measurement Techniques, Statistical Analysis, Statistical Distributions


This study compared four variations of frequency estimation equating: (1) without smoothing; (2) with smoothing of the estimated distributions to be equated; (3 and 4) with smoothing of the observed joint distributions on the anchor test and each test to be equated. The tests consisted of 50 items, with an internal anchor of 19 common items. The criterion was accuracy in reproducing the results of equating in the population of 50,000 students. Smoothing the observed joint distributions substantially improved the equating in samples of 100 and 300 students. Smoothing offered little or no improvement in samples of 1000 and 3000 students. (26pp.)

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