Standard Error of Linear Observed-Score Equating for the NEAT Design With Nonnormally Distributed Data.

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Bibliographic Details
Title:	Standard Error of Linear Observed-Score Equating for the NEAT Design With Nonnormally Distributed Data.
Authors:	Zu, Jiyun¹, Yuan, Ke-Hai²
Source:	Journal of Educational Measurement. Summer2012, Vol. 49 Issue 2, p190-213. 24p. 5 Charts, 7 Graphs.
Subject Terms:	*Errors, Estimation theory, Multivariable control systems, Mathematical statistics, Stochastic processes
Abstract:	In the nonequivalent groups with anchor test (NEAT) design, the standard error of linear observed-score equating is commonly estimated by an estimator derived assuming multivariate normality. However, real data are seldom normally distributed, causing this normal estimator to be inconsistent. A general estimator, which does not rely on the normality assumption, would be preferred, because it is asymptotically accurate regardless of the distribution of the data. In this article, an analytical formula for the standard error of linear observed-score equating, which characterizes the effect of nonnormality, is obtained under elliptical distributions. Using three large-scale real data sets as the populations, resampling studies are conducted to empirically evaluate the normal and general estimators of the standard error of linear observed-score equating. The effect of sample size (50, 100, 250, or 500) and equating method (chained linear, Tucker, or Levine observed-score equating) are examined. Results suggest that the general estimator has smaller bias than the normal estimator in all 36 conditions; it has larger standard error when the sample size is at least 100; and it has smaller root mean squared error in all but one condition. An R program is also provided to facilitate the use of the general estimator. [ABSTRACT FROM AUTHOR]
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Database:	Education Research Complete

Description
Abstract:	In the nonequivalent groups with anchor test (NEAT) design, the standard error of linear observed-score equating is commonly estimated by an estimator derived assuming multivariate normality. However, real data are seldom normally distributed, causing this normal estimator to be inconsistent. A general estimator, which does not rely on the normality assumption, would be preferred, because it is asymptotically accurate regardless of the distribution of the data. In this article, an analytical formula for the standard error of linear observed-score equating, which characterizes the effect of nonnormality, is obtained under elliptical distributions. Using three large-scale real data sets as the populations, resampling studies are conducted to empirically evaluate the normal and general estimators of the standard error of linear observed-score equating. The effect of sample size (50, 100, 250, or 500) and equating method (chained linear, Tucker, or Levine observed-score equating) are examined. Results suggest that the general estimator has smaller bias than the normal estimator in all 36 conditions; it has larger standard error when the sample size is at least 100; and it has smaller root mean squared error in all but one condition. An R program is also provided to facilitate the use of the general estimator. [ABSTRACT FROM AUTHOR]
ISSN:	00220655
DOI:	10.1111/j.1745-3984.2012.00168.x