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Standard Error of Linear Observed‐Score Equating for the NEAT Design With Nonnormally Distributed Data
Author(s) -
Zu Jiyun,
Yuan KeHai
Publication year - 2012
Publication title -
journal of educational measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.917
H-Index - 47
eISSN - 1745-3984
pISSN - 0022-0655
DOI - 10.1111/j.1745-3984.2012.00168.x
Subject(s) - equating , standard error , statistics , estimator , mathematics , resampling , normality , mean squared error , general linear model , linear model , sample size determination , multivariate normal distribution , multivariate statistics , rasch model
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.