Evaluating the Effects of Differences in Group Abilities on the Tucker and the Levine Observed-Score Methods for Common-Item Nonequivalent Groups Equating

Chen, Hanwei; Cui, Zhongmin; Zhu, Rongchun; Gao, Xueshan

doi:10.1037/e548302011-001

Cited by 3 publications

(7 citation statements)

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“…The TK method was introduced by Ledyard Tucker in an unpublished manuscript (Gulliksen, ). Details of the method are presented in numerous sources (e.g., Braun & Holland, ; Chen, Cui, Zhu, & Gao, ; Kolen & Brennan, , ). The TK method considers only observed scores and assumes that the linear regression function that regresses the scores on Form X onto the scores on a common item block are the same for both populations F and F* (using Braun and Holland's notation above).…”

Section: Literature Reviewmentioning

confidence: 99%

“…In general, the TK method may be preferable when the populations, F and F*, are similar and the scores on the two tests are less similar, that is, do not have a high correlation. In contrast, the LV method may be preferable when the populations, F and F*, are less similar, but the scores on the two tests are more similar, that is, have a high correlation (Chen et al., ; Kolen & Brennan, , ). If the two tests involved in the equating are designed to be parallel, both content‐wise and statistically, then both the TK and LV linear methods are likely unaffected by two forms having slightly unequal reliabilities.…”

Section: Literature Reviewmentioning

confidence: 99%

“…If the two tests involved in the equating are designed to be parallel, both content‐wise and statistically, then both the TK and LV linear methods are likely unaffected by two forms having slightly unequal reliabilities. When all assumptions are met, the LV method may be preferable over the TK method (Chen et al., ).…”

Section: Literature Reviewmentioning

confidence: 99%

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Effectiveness of Equating at the Passing Score for Exams With Small Sample Sizes

Wolkowitz¹,

Wright

2019

J Educational Measurement

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This article explores the amount of equating error at a passing score when equating scores from exams with small samples sizes. This article focuses on equating using classical test theory methods of Tucker linear, Levine linear, frequency estimation, and chained equipercentile equating. Both simulation and real data studies were used in the investigation. The results of the study supported past findings that as the sample sizes increase, the amount of bias in the equating at the passing score decreases. The research also highlights the importance for practitioners to understand the data, to have an informed expectation of the results, and to have a documented rationale for an acceptable amount of equating error.An examinee enters a testing center and scores a 45 out of 80 on Form A of an exam. Another examinee of the same ability completes a parallel form, Form B, of the exam and scores a 43 out of 80 on the exam. Form B is statistically equated to Form A. Based on the information provided thus far, Form B is seemingly more difficult than Form A. However, if additional information was provided that stated only 10 examinees completed each of the two forms, would you still believe that Form B is more difficult than Form A? How much confidence would you have in the interpretation of the equated Form B score? If the sample size increased to 25 on each form, how much more confidence would you have in the equated scores of Form B? How about 50 examinees on each form? 125? 250? At what point is the sample size for the equating great enough that you have enough confidence in interpreting the results? The likely answer is: It depends.There are multiple factors that play into the role of deciding when to equate two forms and determining the amount of acceptable equating error. One of the main factors is the purpose of the equating. Is the equating being performed for a low, medium, or high stakes exam? A program may tolerate more equating error in a low stakes exam than a high stakes exam. However, if two exam forms differ in difficulty and the sample size is small, what action should be taken? Should some form of equating be performed or should no equating be performed?The purpose of this article is to discuss the amount of error in equating small sample sizes at the passing score for credentialing exams. This differs from previous research on equating with small sample sizes because most such research focuses on equating accuracy across the entire range of possible scores. The goal of this article is to determine if equating two forms using methods normally recommended for higher sample sizes would effectively work for smaller sample sizes if the examinees' population distribution is centered near the passing score.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

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Effectiveness of Equating at the Passing Score for Exams With Small Sample Sizes

Wolkowitz¹,

Wright

2019

J Educational Measurement

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“…The first assumption requires the regression on the common item scores of total scores within both samples are equal. Conditional variance assumption requires variances of the total scores conditions are equal for both samples (Chen et al, 2010;Kolen & Brennan, 2014).…”

Section: Tucker Observed Score Equatingmentioning

confidence: 99%

“…Since a group can take only one form in non-equivalent groups common items pattern, linear equating also requires powerful statistical assumptions (Chen, Cui, Zhu & Gao, 2010). In this study, since Tucker and Levine observed score equating methods were used, only information about them was mentioned.…”

mentioning

confidence: 99%

An Investigation of Group Invariance in Test Equating According to Gender

Inal¹,

Arıkan²

2017

Eğitimde Ve Psikolojide Ölçme Ve Değerlendirme Dergisi

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The aim of this study is to investigate the group invariance condition according to Tucker and Levine observed score equating among linear equating methods. In the study, the 4 th and 6 th booklets of the PISA 2012 Mathematics subtest were used. Booklets were equated according to group and gender sub-variables, and then group invariance of each condition and WMSE values were calculated. Within this scope, REMSD and RMSD (x) group invariance indexes were employed. The results of the study indicated that, when WMSE values, obtained according to equating methods, were compared, Tucker observed score equating method with regard to whole-group and gender sub-groups produced the lowest error. When RMSD and REMSD values obtained according to gender sub-groups were examined by linear equating methods, it was found that group invariance value is smaller than criterion value for Tucker equating method, while it was greater than criterion value for Levine equating method. Eventually, group invariance condition was met for Tucker observed score equating, but not for Levine observed score equating.Keywords: Equating, group invariance, Tucker linear equating, Levine linear equating Öz Bu çalışmanın amacı doğrusal eşitleme yöntemlerinden Tucker ve Levine gözlenen puan eşitleme yöntemlerine göre eşitlemenin grup değişmezliği koşulunun incelenmesidir. Bu çalışmada PISA 2012 matematik alt testine ait 4. ve 6. kitapçıklardan elde edilen test puanları kullanılmıştır. Kitapçıklardan elde edilen puanlar tüm grup ve cinsiyet alt değişkenine göre eşitlenmiştir. Her bir koşula ait grup değişmezliği ve WMSE değerleri hesaplanmıştır. Bu bağlamda grup değişmezliği indekslerinden REMSD ve RMSD (x) kullanılmıştır. Araştırma sonucunda eşitleme yöntemlerine göre elde edilen WMSE değerleri karşılaştırıldığında hem tüm grup hem cinsiyet alt grubuna göre en az hata veren yöntemin Tucker gözlenen puan eşitleme olduğu görülmüştür. Doğrusal eşitleme yöntemleriyle cinsiyet alt grubuna göre elde edilen RMSD ve REMSD değerleri incelendiğinde, Tucker eşitleme yöntemi için kriter değerden küçük iken, Levine eşitleme yöntemi için kriter değerden daha yüksek çıkmıştır. Böylece grup değişmezliği koşulunun Tucker eşitleme yönteminde sağlanırken, Levine eşitleme yönteminde sağlanmadığı görülmüştür.

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New Insights Into Crustal Deformation of the Indonesia–Australia–New Guinea Collision Zone From a Broad‐Scale Kinematic Model

et al. 2023

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Regions with active tectonic activity like the IANGCZ are often delineated in global plate models as "deforming zones" (Kreemer et al., 2014) or "orogens" (Bird, 2003), for which crustal motion data are excluded from the determination of the otherwise rigid plate motion. Even as early as the 1970s, however, it was recognized that such areas of deformation are often themselves usefully described in terms of discrete "microplates" (e.g., Alvarez et al., 1974;Dewey et al., 1973), relatively small-scale blocks with little internal deformation except near

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Evaluating the Effects of Differences in Group Abilities on the Tucker and the Levine Observed-Score Methods for Common-Item Nonequivalent Groups Equating

Cited by 3 publications

References 10 publications

Effectiveness of Equating at the Passing Score for Exams With Small Sample Sizes

Effectiveness of Equating at the Passing Score for Exams With Small Sample Sizes

An Investigation of Group Invariance in Test Equating According to Gender

New Insights Into Crustal Deformation of the Indonesia–Australia–New Guinea Collision Zone From a Broad‐Scale Kinematic Model

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