Browsing by Author "Hanson, Bradley A."

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    A comparison of bivariate smoothing methods in common-item equipercentile equating
    (1991) Hanson, Bradley A.
    The effectiveness of smoothing the bivariate distributions of common and noncommon item scores in the frequency estimation method of common-item equipercentile equating was examined. The mean squared error of equating was computed for several equating methods and sample sizes, for two sets of population bivariate distributions of equating and nonequating item scores defined using data from a professional licensure exam. Eight equating methods were compared: five equipercentile methods and three linear methods. One of the equipercentile methods was unsmoothed equipercentile equating. Four methods of smoothed equipercentile (SEP) equating were considered : two based on log-linear models, one based on the four-parameter beta binomial model, and one based on the four-parameter beta compound binomial model. The three linear equating methods were the Tucker method, the Levine Equally Reliable method, and the Levine Unequally Reliable method. The results indicated that smoothed distributions produced more accurate equating functions than the unsmoothed distributions, even for the largest sample size. Tucker linear equating produced more accurate results than SEP equating when the systematic error introduced by assuming a linear equating function was small relative to the random error of the methods of SEP equating. Index terms: common-item equating, equating, log-linear models, smoothing, strong true score models.
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    Standard errors of a chain of linear equatings
    (1994) Zeng, Lingjia; Hanson, Bradley A.; Kolen, Michael J.
    A general delta method is described for computing the standard error (SE) of a chain of linear equatings. The general delta method derives the SEs directly from the moments of the score distributions obtained in the equating chain. The partial derivatives of the chain equating function needed for computing the SEs are derived numerically. The method can be applied to equatings using the common-items nonequivalent populations design. Computer simulations were conducted to evaluate the SEs of a chain of two equatings using the Levine and Tucker methods. The general delta method was more accurate than a method that assumes the equating processes in the chain are statistically independent. Index terms: chain equating, delta method, equating, linear equating, standard error of equating.
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    Standard errors of Levine linear equating
    (1993) Hanson, Bradley A.; Zeng, Lingjia; Kolen, Michael J.
    The delta method was used to derive standard errors (SEs) of the Levine observed score and Levine true score linear equating methods. SEs with a normality assumption as well as without a normality assumption were derived. Data from two forms of a test were used as an example to evaluate the derived SEs of equating. Bootstrap SEs also were computed for the purpose of comparison. The SEs derived without the normality assumption and the bootstrap SEs were very close. For the skewed score distributions, the SEs derived with the normality assumption differed from the SEs derived without the normality assumption and the bootstrap SEs. Index terms: equating, delta method, linear equating, score equating, standard errors of equating.