Standard Errors of Kernel Equating: Accounting for Bandwidth Estimation

In standardized testing, equating is used to ensure comparability of test scores across multiple test administrations. One equipercentile observed-score equating method is kernel equating, where an essential step is to obtain continuous approximations to the discrete score distributions by applying a kernel with a smoothing bandwidth parameter. When estimating the bandwidth, additional variability is introduced which is currently not accounted for when calculating the standard errors of equating. This poses a threat to the accuracy of the standard errors of equating. In this study, the asymptotic variance of the bandwidth parameter estimator is derived and a modified method for calculating the standard error of equating that accounts for the bandwidth estimation variability is introduced for the equivalent groups design. A simulation study is used to verify the derivations and confirm the accuracy of the modified method across several sample sizes and test lengths as compared to the existing method and the Monte Carlo standard error of equating estimates. The results show that the modified standard errors of equating are accurate under the considered conditions. Furthermore, the modified and the existing methods produce similar results which suggest that the bandwidth variability impact on the standard error of equating is minimal.     

On the reliability of the extreme score

Under the assumption of normality, a formula is derived for the reliability of the maximum score. It is shown that the maximum score is more reliable than each of the single observations, but less reliable than their composite score.     

The analysis of structural equation models by means of derivative free nonlinear least squares

It is shown that the PAR Derivative-Free Nonlinear Regression program in BMDP can be used to fit structural equation models, producing generalized least squares estimates, standard errors, and goodness-of-fit test statistics. Covariance structure models more general than LISREL can be analyzed. The approach is particularly useful for dealing with new non-standard models and experimenting with alternate methods of estimation. The research of the second author was supported by the NSF grant MCS 83-01587. We wish to thank our referees for some very valuable suggestions.     

Best linear prediction of composite universe scores

The problem of predicting universe scores for samples of examinees based on their responses to samples of items is treated. A general measurement procedure is described in which multiple test forms are developed from a table of specifications and each form is administered to a different sample of examinees. The measurement model categorizes items according to the cells of such a table, and the linear function derived for minimizing error variance in prediction uses responses to these categories. In addition, some distinctions are drawn between aspects of the approach taken here and the familiar regressed score estimates.The author thanks Robert L. Brennan, Michael J. Kolen, and Richard Sawyer for helpful comments and corrections, and anonymous reviewers for suggested improvements.     

On the standard error of the modified biserial correlation

A paradoxical implication of Kraemer's expression for the large-sample standard error of Brogden's form of the biserial correlation is identified, and a new expression is given which does not imply the paradox. However, numerical evidence is presented which calls into question the correctness of the expression.     

Individual distributions under ordinal measurement

For ordinal measurement the concept of an individual propensity distribution is developed. For any given individual the mean of this distribution is his true score, for which estimation procedures are discussed. Two measures of individual dispersion are considered and their distributions derived in the null case. These measures are shown to be counterparts at the individual level of Kendall's tau and Spearman's rho. Estimation of the two dispersion measures from sample data is investigated, and the relation of these estimates to the variance of the individual propensity distribution is derived.     

Ordinal data: An alternative distribution

To date, virtually all techniques appropriate for ordinal data are based on the uniform probability distribution over the permutations. In this paper we introduce and examine an alternative probability model for the distribution of ordinal data. Preliminary to deriving the expectations of Spearman's rho and Kendall's tau under this model, we show how to compute certain conditional expectations of rho and tau under the uniform distribution. The alternative probability model is then applied to ordinal test theory, and the calculation of true scores and test reliability are discussed.     

选择性颞叶梗塞对鼠学习记忆能力影响的定量研究

应用光化学的方法选择性诱导颞叶梗塞,同时测定学习记忆能力、神经功能缺失及梗塞面积。结果表明：颞叶梗塞鼠的学习记忆能力显著受损,但无明显感觉运动障碍;颞叶梗塞鼠的学习记忆受损程度与梗塞面积大小有关。结果提示选择性颞叶梗塞是一种理想的痴呆动物模型。     

Définir ou détecter des pathologies ? Utilisation et interprétation des scores seuils à la lumière du débat dimensions/catégories

A number of psychometric tests are aimed at locating the performance of an individual along a continuous range that goes from normal to worrying. In a different paradigm, there are tests whose goal is to assess whether or not an individual is healthy with respect to a psychological, psychiatric or neurological pathology that is defined independently from the test itself. The former rely on a dimensional concept of psychopathologies; the latter imply a categorical concept. The former require to compare the performance of the individual to a standard sample that is representative of the general population; the latter involve a standard sample representative of the healthy population only. The former might imply the use of a cut-off score to indicate that a certain degree of rarity of the performance has been reached, while the latter must involve a cut-off score to make a decision (whether the individual belongs to the “healthy” or “pathological” category), a score that is most often set so as to control the false-positive rate in making this decision. In the former paradigm, the cut-off score defines or contributes to define the pathology. In the latter, it only helps detecting it. This article aims at making clear the difference between these two realms and highlight their practical as well as theoretical impact on psychological practice.