Test Score Equating Using a Mini‐Version Anchor and a Midi Anchor: A Case Study Using SAT® Data

This study explores an anchor that is different from the traditional miniature anchor in test score equating. In contrast to a traditional “mini” anchor that has the same spread of item difficulties as the tests to be equated, the studied anchor, referred to as a “midi” anchor (Sinharay & Holland), has a smaller spread of item difficulties than the tests to be equated. Both anchors were administered in an operational SAT administration and the impact of anchor type on equating was evaluated with respect to systematic error or equating bias. Contradicting the popular belief that the mini anchor is best, the results showed that the mini anchor does not always produce more accurate equating functions than the midi anchor; the midi anchor was found to perform as well as or even better than the mini anchor. Because testing programs usually have more middle difficulty items and few very hard or very easy items, midi external anchors are operationally easier to build. Therefore, the results of our study provide evidence in favor of the midi anchor, the use of which will lead to cost saving with no reduction in equating quality.     

A Comparison Between Linear IRT Observed‐Score Equating and Levine Observed‐Score Equating Under the Generalized Kernel Equating Framework

In this article, linear item response theory (IRT) observed‐score equating is compared under a generalized kernel equating framework with Levine observed‐score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when using data from IRT models, linear IRT observed‐score equating is virtually identical to Levine observed‐score equating. This leads to the conclusion that poststratification equating based on true anchor scores can be viewed as the curvilinear Levine observed‐score equating.     

Comparison of Item Preequating and Random Groups Equating Using IRT and Equipercentile Methods

An item-preequating design and a random groups design were used to equate forms of the American College Testing (ACT) Assessment Mathematics Test. Equipercentile and 3-parameter logistic model item-response theory (IRT) procedures were used for both designs. Both pretest methods produced inadequate equating results, and the IRT item preequating method resulted in more equating error than had no equating been conducted. Although neither of the item preequating methods performed well, the results from the equipercentile preequating method were more consistent with those from the random groups method than were the results from the IRT item pretest method. Item context and position effects were likely responsible, at least in part, for the inadequate results for item preequating. Such effects need to be either controlled or modeled, and the design further researched before the item preequating design can be recommended for operational use.     

A Comparison of Angoff's Design I and Design II for Vertical Equating Using Traditional and IRT Methodology

Practical considerations in conducting an equating study often require a trade-off between testing time and sample size. A counterbalanced design (Angoff's Design II) is often selected because, as each examinee is administered both test forms and therefore the errors are correlated, sample sizes can be dramatically reduced over those required by a spiraling design (Angoff's Design I), where each examinee is administered only one test form. However, the counterbalanced design may be subject to fatigue, practice, or context effects. This article investigated these two data collection designs (for a given sample size) with equipercentile and IRT equating methodology in the vertical equating of two mathematics achievement tests. Both designs and both methodologies were judged to adequately meet an equivalent expected score criterion; Design II was found to exhibit more stability over different samples.     

A Comparison of IRT Equating and Beta 4 Equating

Four equating methods (3PL true score equating, 3PL observed score equating, beta 4 true score equating, and beta 4 observed score equating) were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional-mean-squared-error (CMSE) difference, and the equipercentile equating property. True score equating more closely achieved estimated FOE than observed score equating when the true score distribution was estimated using the psychometric model that was used in the equating. Observed score equating more closely achieved estimated SOE, estimated CMSE difference, and the equipercentile equating property than true score equating. Among the four equating methods, 3PL observed score equating most closely achieved estimated SOE and had the smallest estimated CMSE difference, and beta 4 observed score equating was the method that most closely met the equipercentile equating property.     

等级记分模型下几种等值方法的比较研究

等值对考试具有重要意义,而我国的大部分考试却没有实现等值,在少数经过等值的考试中,大多只限于对二级记分题目的等值,鲜有对多级记分题目的等值研究。该研究针对包含多级记分题目的国内某大型语言类考试,探讨了等级反应模型下的同时校准法、固定共同题参数法以及链接独立校准法中的平均数标准差方法、平均数平均数方法、Haebara法和Stocking-Lord法六种等值方法的效果,从而优选最适合该考试的等值方法。     

Comparison of the One‐ and Bi‐Direction Chained Equipercentile Equating

This study investigated differences between two approaches to chained equipercentile (CE) equating (one‐ and bi‐direction CE equating) in nearly equal groups and relatively unequal groups. In one‐direction CE equating, the new form is linked to the anchor in one sample of examinees and the anchor is linked to the reference form in the other sample. In bi‐direction CE equating, the anchor is linked to the new form in one sample of examinees and to the reference form in the other sample. The two approaches were evaluated in comparison to a criterion equating function (i.e., equivalent groups equating) using indexes such as root expected squared difference, bias, standard error of equating, root mean squared error, and number of gaps and bumps. The overall results across the equating situations suggested that the two CE equating approaches produced very similar results, whereas the bi‐direction results were slightly less erratic, smoother (i.e., fewer gaps and bumps), usually closer to the criterion function, and also less variable.     

Equating Minimum-Competency Tests: Comparisons of Methods

The 1986 scores from Florida's Statewide Student Assessment Test, Part II (SSAT-II), a minimum-competency test required for high school graduation in Florida, were placed on the scale of the 1984 scores from that test using five different equating procedures. For the highest scoring 84 % of the students, four of the five methods yielded results within 1.5 raw-score points of each other. They would be essentially equally satisfactory in this situation, in which the tests were made parallel item by item in difficulty and content and the groups of examinees were population cohorts separated by only 2 years. Also, the results from six different lengths of anchor items were compared. Anchors of 25, 20, 15, or 10 randomly selected items provided equatings as effective as 30 items using the concurrent IRT equating method, but an anchor of 5 randomly selected items did not     

A Comparison of Two Procedures for Computing IRT Equating Coefficients

In order to equate tests under Item Response Theory (IRT), one must obtain the slope and intercept coefficients of the appropriate linear transformation. This article compares two methods for computing such equating coefficients–Loyd and Hoover (1980) and Stocking and Lord (1983). The former is based upon summary statistics of the test calibrations; the latter is based upon matching test characteristic curves by minimizing a quadratic loss function. Three types of equating situations: horizontal, vertical, and that inherent in IRT parameter recovery studies–were investigated. The results showed that the two computing procedures generally yielded similar equating coefficients in all three situations. In addition, two sets of SAT data were equated via the two procedures, and little difference in the obtained results was observed. Overall, the results suggest that the Loyd and Hoover procedure usually yields acceptable equating coefficients. The Stocking and Lord procedure improves upon the Loyd and Hoover values and appears to be less sensitive to atypical test characteristics. When the user has reason to suspect that the test calibrations may be associated with data sets that are typically troublesome to calibrate, the Stocking and Lord procedure is to be preferred.     

无锚题测验等值设计方法研究进展

由于测验安全性、试卷组卷不当等问题,有些测验的题本相互之间不能或者没有设置锚题。对作答不同题本的被试进行分数比较时,需要用到测验等值技术。不同于有锚题测验能通过题本之间的锚题进行等值,无锚题情境下的测验需要借助于一些特殊方法进行等值。目前,对无锚题测验进行等值主要有三种方式,一种是通过测验中具体的题目,也就是构建相同的"锚题"来进行等值,如构造随机等组测验法和利用题目先验信息进行等值的方法;一种是通过构建相同被试组来进行等值,即构造随机等组样本法;还有一种是借助于测验题目所考查的认知属性来进行等值,一般是基于一种认知诊断模型——规则空间模型来进行操作。     

Evaluation of Two New Smoothing Methods in Equating: The Cubic B-Spline Presmoothing Method and the Direct Presmoothing Method

This article considers two new smoothing methods in equipercentile equating , the cubic B-spline presmoothing method and the direct presmoothing method. Using a simulation study , these two methods are compared with established methods , the beta-4 method , the polynomial loglinear method , and the cubic spline postsmoothing method , under three sample sizes (300 , 1,000 , and 3,000) and for three test content areas (ITBS Maps and Diagrams , ITBS Reference and Materials , and ITBS Capitalization). Ten thousand random samples were simulated from population distributions , and the standard error , bias , and RMSE statistics were calculated. The cubic B-spline presmoothing method performed well in reducing total error of equating , whereas the direct presmoothing method appeared to need some modification for it to be as accurate as other smoothing methods.     

An Approach to Evaluating the Missing Data Assumptions of the Chain and Post-stratification Equating Methods for the NEAT Design

Two important types of observed score equating (OSE) methods for the non-equivalent groups with Anchor Test (NEAT) design are chain equating (CE) and post-stratification equating (PSE). CE and PSE reflect two distinctly different ways of using the information provided by the anchor test for computing OSE functions. Both types of methods include linear and nonlinear equating functions. In practical situations, it is known that the PSE and CE methods will give different results when the two groups of examinees differ on the anchor test. However, given that both types of methods are justified as OSE methods by making different assumptions about the missing data in the NEAT design, it is difficult to conclude which, if either, of the two is more correct in a particular situation. This study compares the predictions of the PSE and CE assumptions for the missing data using a special data set for which the usually missing data are available. Our results indicate that in an equating setting where the linking function is decidedly non-linear and CE and PSE ought to be different, both sets of predictions are quite similar but those for CE are slightly more accurate .     

A New Approach to Comparing Several Equating Methods in the Context of the NEAT Design

The nonequivalent groups with anchor test (NEAT) design involves missing data that are missing by design. Three equating methods that can be used with a NEAT design are the frequency estimation equipercentile equating method, the chain equipercentile equating method, and the item-response-theory observed-score-equating method. We suggest an approach to perform a fair comparison of the three methods. The approach is then applied to compare the three equating methods using three data sets from operational tests. For each data set, we examine how the three equating methods perform when the missing data satisfy the assumptions made by only one of these equating methods. The chain equipercentile equating method is somewhat more satisfactory overall than the other methods.     

实验数据的B样条压缩法

实验数据常归结为三种形式经验公式、表格和图形。利用B样条方法,对于图形数据给出了压缩方法,为CAD中的专家系统提供了一个有效的工具。     

Experimental Comparison of Virtual Reality with Traditional Teaching Methods for Teaching Radioactivity

Research at the University of Nottingham has been carried out to investigate the potential of Virtual Reality (VR) for teaching secondary school science. This paper describes the evaluation of VR to teach radioactivity at secondary school level. Evaluation was carried out in a local school and compared directly to the traditional teaching methods currently used in the school to teach radioactivity. Computer experience, computer attitudes, general attitudes and knowledge gained were measured to allow comparisons to be drawn. Individual differences of gender, ability and home computer use were also looked at in relation to the above measures. Results indicated that both ability level and the order in which the conditions were completed significantly affected the attitude scores. High ability students reported higher attitude scores, both overall and for the VR class in particular. As a result of the evaluation study, the Virtual Laboratory has been heavily modified and further evaluation studies were then carried out.     

成功编译LINUX内核的一种方法

文章说明了升级LINUX内核的重要性,并以REDHAT LINUX9的内核2.4.20-8编译升级内核到2.6.9为例介绍将LINUX内核进行重编译或升级的方法。     

A Comparison of Chained Linear and Poststratification Linear Equating Under Different Testing Conditions

In this study I compared results of chained linear, Tucker, and Levine-observed score equatings under conditions where the new and old forms samples were similar in ability and also when they were different in ability. The length of the anchor test was also varied to examine its effect on the three different equating methods. The three equating methods were compared to a criterion equating to obtain estimates of random equating error, bias, and root mean squared error (RMSE). Results showed that, for most studied conditions, chained linear equating produced fairly good equating results in terms of low bias and RMSE. Levine equating also produced low bias and RMSE in some conditions. Although the Tucker method always produced the lowest random equating error, it produced a larger bias and RMSE than either of the other equating methods. As noted in the literature, these results also suggest that either chained linear or Levine equating be used when new and old form samples differ on ability and/or when the anchor-to-total correlation is not very high. Finally, by testing the missing data assumptions of the three equating methods, this study also shows empirically why an equating method is more or less accurate under certain conditions .     

基于IRT的共同题非等组设计中五种项目参数等值方法的比较研究

本文采用共同题非等组设计,对五种基于IRT的项目参数等值方法进行比较研究。研究数据来自湖北某试点地区课改实验区和非课改区考生在标准化中考数学科目的考试数据,兼用大样本标准和其他标准作为各等值方法比较的检验标准,以RMSD指标作为操作性检验标准,利用STUIRT程序进行等值分析。研究结果表明,针对本研究所设置的等值情境,MS方法稳健性最差,对于项目难度参数的等值,同时校准方法最好,其次是SL特征曲线法,对于项目区分度参数的等值,MM方法精确性最好。     

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

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.     

纵向数据常用参数分析方法比较

分析了纵向数据的本质特点,对纵向数据常用的参数分析方法的优劣进行了比较。