Pub Date : 2022-07-28DOI: 10.3102/10769986221111085
P. Zhan, K. Man, Stefanie A. Wind, Jonathan Malone
Respondents’ problem-solving behaviors comprise behaviors that represent complicated cognitive processes that are frequently systematically tied to one another. Biometric data, such as visual fixation counts (FCs), which are an important eye-tracking indicator, can be combined with other types of variables that reflect different aspects of problem-solving behavior to quantify variability in problem-solving behavior. To provide comprehensive feedback and accurate diagnosis when using such multimodal data, the present study proposes a multimodal joint cognitive diagnosis model that accounts for latent attributes, latent ability, processing speed, and visual engagement by simultaneously modeling response accuracy (RA), response times, and FCs. We used two simulation studies to test the feasibility of the proposed model. Findings mainly suggest that the parameters of the proposed model can be well recovered and that modeling FCs, in addition to RA and response times, could increase the comprehensiveness of feedback on problem-solving-related cognitive characteristics as well as the accuracy of knowledge structure diagnosis. An empirical example is used to demonstrate the applicability and benefits of the proposed model. We discuss the implications of our findings as they relate to research and practice.
{"title":"Cognitive Diagnosis Modeling Incorporating Response Times and Fixation Counts: Providing Comprehensive Feedback and Accurate Diagnosis","authors":"P. Zhan, K. Man, Stefanie A. Wind, Jonathan Malone","doi":"10.3102/10769986221111085","DOIUrl":"https://doi.org/10.3102/10769986221111085","url":null,"abstract":"Respondents’ problem-solving behaviors comprise behaviors that represent complicated cognitive processes that are frequently systematically tied to one another. Biometric data, such as visual fixation counts (FCs), which are an important eye-tracking indicator, can be combined with other types of variables that reflect different aspects of problem-solving behavior to quantify variability in problem-solving behavior. To provide comprehensive feedback and accurate diagnosis when using such multimodal data, the present study proposes a multimodal joint cognitive diagnosis model that accounts for latent attributes, latent ability, processing speed, and visual engagement by simultaneously modeling response accuracy (RA), response times, and FCs. We used two simulation studies to test the feasibility of the proposed model. Findings mainly suggest that the parameters of the proposed model can be well recovered and that modeling FCs, in addition to RA and response times, could increase the comprehensiveness of feedback on problem-solving-related cognitive characteristics as well as the accuracy of knowledge structure diagnosis. An empirical example is used to demonstrate the applicability and benefits of the proposed model. We discuss the implications of our findings as they relate to research and practice.","PeriodicalId":48001,"journal":{"name":"Journal of Educational and Behavioral Statistics","volume":"47 1","pages":"736 - 776"},"PeriodicalIF":2.4,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47269107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-18DOI: 10.3102/10769986221109208
Weimeng Wang, Yang Liu, Hongyun Liu
Differential item functioning (DIF) occurs when the probability of endorsing an item differs across groups for individuals with the same latent trait level. The presence of DIF items may jeopardize the validity of an instrument; therefore, it is crucial to identify DIF items in routine operations of educational assessment. While DIF detection procedures based on item response theory (IRT) have been widely used, a majority of IRT-based DIF tests assume predefined anchor (i.e., DIF-free) items. Not only is this assumption strong, but violations to it may also lead to erroneous inferences, for example, an inflated Type I error rate. We propose a general framework to define the effect sizes of DIF without a priori knowledge of anchor items. In particular, we quantify DIF by item-specific residuals from a regression model fitted to the true item parameters in respective groups. Moreover, the null distribution of the proposed test statistic using robust estimator can be derived analytically or approximated numerically even when there is a mix of DIF and non-DIF items, which yields asymptotically justified statistical inference. The Type I error rate and the power performance of the proposed procedure are evaluated and compared with the conventional likelihood-ratio DIF tests in a Monte Carlo experiment. Our simulation study has shown promising results in controlling Type I error rate and power of detecting DIF items. Even when there is a mix of DIF and non-DIF items, the true and false alarm rate can be well controlled when a robust regression estimator is used.
{"title":"Testing Differential Item Functioning Without Predefined Anchor Items Using Robust Regression","authors":"Weimeng Wang, Yang Liu, Hongyun Liu","doi":"10.3102/10769986221109208","DOIUrl":"https://doi.org/10.3102/10769986221109208","url":null,"abstract":"Differential item functioning (DIF) occurs when the probability of endorsing an item differs across groups for individuals with the same latent trait level. The presence of DIF items may jeopardize the validity of an instrument; therefore, it is crucial to identify DIF items in routine operations of educational assessment. While DIF detection procedures based on item response theory (IRT) have been widely used, a majority of IRT-based DIF tests assume predefined anchor (i.e., DIF-free) items. Not only is this assumption strong, but violations to it may also lead to erroneous inferences, for example, an inflated Type I error rate. We propose a general framework to define the effect sizes of DIF without a priori knowledge of anchor items. In particular, we quantify DIF by item-specific residuals from a regression model fitted to the true item parameters in respective groups. Moreover, the null distribution of the proposed test statistic using robust estimator can be derived analytically or approximated numerically even when there is a mix of DIF and non-DIF items, which yields asymptotically justified statistical inference. The Type I error rate and the power performance of the proposed procedure are evaluated and compared with the conventional likelihood-ratio DIF tests in a Monte Carlo experiment. Our simulation study has shown promising results in controlling Type I error rate and power of detecting DIF items. Even when there is a mix of DIF and non-DIF items, the true and false alarm rate can be well controlled when a robust regression estimator is used.","PeriodicalId":48001,"journal":{"name":"Journal of Educational and Behavioral Statistics","volume":"47 1","pages":"666 - 692"},"PeriodicalIF":2.4,"publicationDate":"2022-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42754815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-15DOI: 10.3102/10769986221108455
D. Molenaar, M. Curi, Jorge L. Bazán
Bounded continuous data are encountered in many applications of item response theory, including the measurement of mood, personality, and response times and in the analyses of summed item scores. Although different item response theory models exist to analyze such bounded continuous data, most models assume the data to be in an open interval and cannot accommodate data in a closed interval. As a result, ad hoc transformations are needed to prevent scores on the bounds of the observed variables. To motivate the present study, we demonstrate in real and simulated data that this practice of fitting open interval models to closed interval data can majorly affect parameter estimates even in cases with only 5% of the responses on one of the bounds of the observed variables. To address this problem, we propose a zero and one inflated item response theory modeling framework for bounded continuous responses in the closed interval. We illustrate how four existing models for bounded responses from the literature can be accommodated in the framework. The resulting zero and one inflated item response theory models are studied in a simulation study and a real data application to investigate parameter recovery, model fit, and the consequences of fitting the incorrect distribution to the data. We find that neglecting the bounded nature of the data biases parameters and that misspecification of the exact distribution may affect the results depending on the data generating model.
{"title":"Zero and One Inflated Item Response Theory Models for Bounded Continuous Data","authors":"D. Molenaar, M. Curi, Jorge L. Bazán","doi":"10.3102/10769986221108455","DOIUrl":"https://doi.org/10.3102/10769986221108455","url":null,"abstract":"Bounded continuous data are encountered in many applications of item response theory, including the measurement of mood, personality, and response times and in the analyses of summed item scores. Although different item response theory models exist to analyze such bounded continuous data, most models assume the data to be in an open interval and cannot accommodate data in a closed interval. As a result, ad hoc transformations are needed to prevent scores on the bounds of the observed variables. To motivate the present study, we demonstrate in real and simulated data that this practice of fitting open interval models to closed interval data can majorly affect parameter estimates even in cases with only 5% of the responses on one of the bounds of the observed variables. To address this problem, we propose a zero and one inflated item response theory modeling framework for bounded continuous responses in the closed interval. We illustrate how four existing models for bounded responses from the literature can be accommodated in the framework. The resulting zero and one inflated item response theory models are studied in a simulation study and a real data application to investigate parameter recovery, model fit, and the consequences of fitting the incorrect distribution to the data. We find that neglecting the bounded nature of the data biases parameters and that misspecification of the exact distribution may affect the results depending on the data generating model.","PeriodicalId":48001,"journal":{"name":"Journal of Educational and Behavioral Statistics","volume":"47 1","pages":"693 - 735"},"PeriodicalIF":2.4,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45894141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-07DOI: 10.3102/10769986221104207
Su-Pin Hung, Hung-Yu Huang
To address response style or bias in rating scales, forced-choice items are often used to request that respondents rank their attitudes or preferences among a limited set of options. The rating scales used by raters to render judgments on ratees’ performance also contribute to rater bias or errors; consequently, forced-choice items have recently been employed for raters to rate how a ratee performs in certain defined traits. This study develops forced-choice ranking models (FCRMs) for data analysis when performance is evaluated by external raters or experts in a forced-choice ranking format. The proposed FCRMs consider different degrees of raters’ leniency/severity when modeling the selection probability in the generalized unfolding item response theory framework. They include an additional topic facet when multiple tasks are evaluated and incorporate variations in leniency parameters to capture the interactions between ratees and raters. The simulation results indicate that the parameters of the new models can be satisfactorily recovered and that better parameter recovery is associated with more item blocks, larger sample sizes, and a complete ranking design. A technological creativity assessment is presented as an empirical example with which to demonstrate the applicability and implications of the new models.
{"title":"Forced-Choice Ranking Models for Raters’ Ranking Data","authors":"Su-Pin Hung, Hung-Yu Huang","doi":"10.3102/10769986221104207","DOIUrl":"https://doi.org/10.3102/10769986221104207","url":null,"abstract":"To address response style or bias in rating scales, forced-choice items are often used to request that respondents rank their attitudes or preferences among a limited set of options. The rating scales used by raters to render judgments on ratees’ performance also contribute to rater bias or errors; consequently, forced-choice items have recently been employed for raters to rate how a ratee performs in certain defined traits. This study develops forced-choice ranking models (FCRMs) for data analysis when performance is evaluated by external raters or experts in a forced-choice ranking format. The proposed FCRMs consider different degrees of raters’ leniency/severity when modeling the selection probability in the generalized unfolding item response theory framework. They include an additional topic facet when multiple tasks are evaluated and incorporate variations in leniency parameters to capture the interactions between ratees and raters. The simulation results indicate that the parameters of the new models can be satisfactorily recovered and that better parameter recovery is associated with more item blocks, larger sample sizes, and a complete ranking design. A technological creativity assessment is presented as an empirical example with which to demonstrate the applicability and implications of the new models.","PeriodicalId":48001,"journal":{"name":"Journal of Educational and Behavioral Statistics","volume":"47 1","pages":"603 - 634"},"PeriodicalIF":2.4,"publicationDate":"2022-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46199623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-05DOI: 10.3102/10769986221150517
Patrícia Martinková, František Bartoš, M. Brabec
Inter-rater reliability (IRR), which is a prerequisite of high-quality ratings and assessments, may be affected by contextual variables, such as the rater’s or ratee’s gender, major, or experience. Identification of such heterogeneity sources in IRR is important for the implementation of policies with the potential to decrease measurement error and to increase IRR by focusing on the most relevant subgroups. In this study, we propose a flexible approach for assessing IRR in cases of heterogeneity due to covariates by directly modeling differences in variance components. We use Bayes factors (BFs) to select the best performing model, and we suggest using Bayesian model averaging as an alternative approach for obtaining IRR and variance component estimates, allowing us to account for model uncertainty. We use inclusion BFs considering the whole model space to provide evidence for or against differences in variance components due to covariates. The proposed method is compared with other Bayesian and frequentist approaches in a simulation study, and we demonstrate its superiority in some situations. Finally, we provide real data examples from grant proposal peer review, demonstrating the usefulness of this method and its flexibility in the generalization of more complex designs.
{"title":"Assessing Inter-rater Reliability With Heterogeneous Variance Components Models: Flexible Approach Accounting for Contextual Variables","authors":"Patrícia Martinková, František Bartoš, M. Brabec","doi":"10.3102/10769986221150517","DOIUrl":"https://doi.org/10.3102/10769986221150517","url":null,"abstract":"Inter-rater reliability (IRR), which is a prerequisite of high-quality ratings and assessments, may be affected by contextual variables, such as the rater’s or ratee’s gender, major, or experience. Identification of such heterogeneity sources in IRR is important for the implementation of policies with the potential to decrease measurement error and to increase IRR by focusing on the most relevant subgroups. In this study, we propose a flexible approach for assessing IRR in cases of heterogeneity due to covariates by directly modeling differences in variance components. We use Bayes factors (BFs) to select the best performing model, and we suggest using Bayesian model averaging as an alternative approach for obtaining IRR and variance component estimates, allowing us to account for model uncertainty. We use inclusion BFs considering the whole model space to provide evidence for or against differences in variance components due to covariates. The proposed method is compared with other Bayesian and frequentist approaches in a simulation study, and we demonstrate its superiority in some situations. Finally, we provide real data examples from grant proposal peer review, demonstrating the usefulness of this method and its flexibility in the generalization of more complex designs.","PeriodicalId":48001,"journal":{"name":"Journal of Educational and Behavioral Statistics","volume":"48 1","pages":"349 - 383"},"PeriodicalIF":2.4,"publicationDate":"2022-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46141747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-04DOI: 10.3102/10769986221104800
Wendy Chan, L. Hedges
Multisite field experiments using the (generalized) randomized block design that assign treatments to individuals within sites are common in education and the social sciences. Under this design, there are two possible estimands of interest and they differ based on whether sites or blocks have fixed or random effects. When the average treatment effect is assumed to be identical across sites, it is common to omit site by treatment interactions and “pool” them into the error term in classical experimental design. However, prior work has not addressed the consequences of pooling when site by treatment interactions are not zero. This study assesses the impact of pooling on inference in the presence of nonzero site by treatment interactions. We derive the small sample distributions of the test statistics for treatment effects under pooling and illustrate the impacts on rejection rates when interactions are not zero. We use the results to offer recommendations to researchers conducting studies based on the multisite design.
{"title":"Pooling Interactions Into Error Terms in Multisite Experiments","authors":"Wendy Chan, L. Hedges","doi":"10.3102/10769986221104800","DOIUrl":"https://doi.org/10.3102/10769986221104800","url":null,"abstract":"Multisite field experiments using the (generalized) randomized block design that assign treatments to individuals within sites are common in education and the social sciences. Under this design, there are two possible estimands of interest and they differ based on whether sites or blocks have fixed or random effects. When the average treatment effect is assumed to be identical across sites, it is common to omit site by treatment interactions and “pool” them into the error term in classical experimental design. However, prior work has not addressed the consequences of pooling when site by treatment interactions are not zero. This study assesses the impact of pooling on inference in the presence of nonzero site by treatment interactions. We derive the small sample distributions of the test statistics for treatment effects under pooling and illustrate the impacts on rejection rates when interactions are not zero. We use the results to offer recommendations to researchers conducting studies based on the multisite design.","PeriodicalId":48001,"journal":{"name":"Journal of Educational and Behavioral Statistics","volume":"47 1","pages":"639 - 665"},"PeriodicalIF":2.4,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44462932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-27DOI: 10.3102/10769986221101624
J. R. Lockwood, K. Castellano, D. McCaffrey
Many states and school districts in the United States use standardized test scores to compute annual measures of student achievement progress and then use school-level averages of these growth measures for various reporting and diagnostic purposes. These aggregate growth measures can vary consequentially from year to year for the same school, complicating their use and interpretation. We develop a method, based on the theory of empirical best linear prediction, to improve the accuracy and stability of aggregate growth measures by pooling information across grades, years, and tested subjects for individual schools. We demonstrate the performance of the method using both simulation and application to 6 years of annual growth measures from a large, urban school district. We provide code for implementing the method in the package schoolgrowth for the R environment.
{"title":"Improving Accuracy and Stability of Aggregate Student Growth Measures Using Empirical Best Linear Prediction","authors":"J. R. Lockwood, K. Castellano, D. McCaffrey","doi":"10.3102/10769986221101624","DOIUrl":"https://doi.org/10.3102/10769986221101624","url":null,"abstract":"Many states and school districts in the United States use standardized test scores to compute annual measures of student achievement progress and then use school-level averages of these growth measures for various reporting and diagnostic purposes. These aggregate growth measures can vary consequentially from year to year for the same school, complicating their use and interpretation. We develop a method, based on the theory of empirical best linear prediction, to improve the accuracy and stability of aggregate growth measures by pooling information across grades, years, and tested subjects for individual schools. We demonstrate the performance of the method using both simulation and application to 6 years of annual growth measures from a large, urban school district. We provide code for implementing the method in the package schoolgrowth for the R environment.","PeriodicalId":48001,"journal":{"name":"Journal of Educational and Behavioral Statistics","volume":"47 1","pages":"544 - 575"},"PeriodicalIF":2.4,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46997238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-08DOI: 10.3102/10769986221099906
B. Domingue, K. Kanopka, B. Stenhaug, M. Sulik, Tanesia Beverly, Matthieu J. S. Brinkhuis, Ruhan Circi, Jessica Faul, Dandan Liao, Bruce McCandliss, Jelena Obradović, Chris Piech, Tenelle Porter, Project iLEAD Consortium, J. Soland, Jon Weeks, S. Wise, Jason D Yeatman
The speed–accuracy trade-off (SAT) suggests that time constraints reduce response accuracy. Its relevance in observational settings—where response time (RT) may not be constrained but respondent speed may still vary—is unclear. Using 29 data sets containing data from cognitive tasks, we use a flexible method for identification of the SAT (which we test in extensive simulation studies) to probe whether the SAT holds. We find inconsistent relationships between time and accuracy; marginal increases in time use for an individual do not necessarily predict increases in accuracy. Additionally, the speed–accuracy relationship may depend on the underlying difficulty of the interaction. We also consider the analysis of items and individuals; of particular interest is the observation that respondents who exhibit more within-person variation in response speed are typically of lower ability. We further find that RT is typically a weak predictor of response accuracy. Our findings document a range of empirical phenomena that should inform future modeling of RTs collected in observational settings.
{"title":"Speed–Accuracy Trade-Off? Not So Fast: Marginal Changes in Speed Have Inconsistent Relationships With Accuracy in Real-World Settings","authors":"B. Domingue, K. Kanopka, B. Stenhaug, M. Sulik, Tanesia Beverly, Matthieu J. S. Brinkhuis, Ruhan Circi, Jessica Faul, Dandan Liao, Bruce McCandliss, Jelena Obradović, Chris Piech, Tenelle Porter, Project iLEAD Consortium, J. Soland, Jon Weeks, S. Wise, Jason D Yeatman","doi":"10.3102/10769986221099906","DOIUrl":"https://doi.org/10.3102/10769986221099906","url":null,"abstract":"The speed–accuracy trade-off (SAT) suggests that time constraints reduce response accuracy. Its relevance in observational settings—where response time (RT) may not be constrained but respondent speed may still vary—is unclear. Using 29 data sets containing data from cognitive tasks, we use a flexible method for identification of the SAT (which we test in extensive simulation studies) to probe whether the SAT holds. We find inconsistent relationships between time and accuracy; marginal increases in time use for an individual do not necessarily predict increases in accuracy. Additionally, the speed–accuracy relationship may depend on the underlying difficulty of the interaction. We also consider the analysis of items and individuals; of particular interest is the observation that respondents who exhibit more within-person variation in response speed are typically of lower ability. We further find that RT is typically a weak predictor of response accuracy. Our findings document a range of empirical phenomena that should inform future modeling of RTs collected in observational settings.","PeriodicalId":48001,"journal":{"name":"Journal of Educational and Behavioral Statistics","volume":"47 1","pages":"576 - 602"},"PeriodicalIF":2.4,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48011887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-01DOI: 10.3102/10769986211072308
Wim J. van der Linden
The current literature on test equating generally defines it as the process necessary to obtain score comparability between different test forms. The definition is in contrast with Lord’s foundational paper which viewed equating as the process required to obtain comparability of measurement scale between forms. The distinction between the notions of scale and score is not trivial. The difference is explained by connecting these notions with standard statistical concepts as probability experiment, sample space, and random variable. The probability experiment underlying equating test forms with random scores immediately gives us the equating transformation as a function mapping the scale of one form into the other and thus supports the point of view taken by Lord. However, both Lord’s view and the current literature appear to rely on the idea of an experiment with random examinees which implies a different notion of test scores. It is shown how an explicit choice between the two experiments is not just important for our theoretical understanding of key notions in test equating but also has important practical consequences.
{"title":"What Is Actually Equated in “Test Equating”? A Didactic Note","authors":"Wim J. van der Linden","doi":"10.3102/10769986211072308","DOIUrl":"https://doi.org/10.3102/10769986211072308","url":null,"abstract":"The current literature on test equating generally defines it as the process necessary to obtain score comparability between different test forms. The definition is in contrast with Lord’s foundational paper which viewed equating as the process required to obtain comparability of measurement scale between forms. The distinction between the notions of scale and score is not trivial. The difference is explained by connecting these notions with standard statistical concepts as probability experiment, sample space, and random variable. The probability experiment underlying equating test forms with random scores immediately gives us the equating transformation as a function mapping the scale of one form into the other and thus supports the point of view taken by Lord. However, both Lord’s view and the current literature appear to rely on the idea of an experiment with random examinees which implies a different notion of test scores. It is shown how an explicit choice between the two experiments is not just important for our theoretical understanding of key notions in test equating but also has important practical consequences.","PeriodicalId":48001,"journal":{"name":"Journal of Educational and Behavioral Statistics","volume":"47 1","pages":"353 - 362"},"PeriodicalIF":2.4,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47910828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-11DOI: 10.3102/10769986221094789
W. van der Linden
Two independent statistical tests of item compromise are presented, one based on the test takers’ responses and the other on their response times (RTs) on the same items. The tests can be used to monitor an item in real time during online continuous testing but are also applicable as part of post hoc forensic analysis. The two test statistics are simple intuitive quantities as the sum of the responses and RTs observed for the test takers on the item. Common features of the tests are ease of interpretation and computational simplicity. Both tests are uniformly most powerful under the assumption of known ability and speed parameters for the test takers. Examples of power functions for items with realistic parameter values suggest maximum power for 20–30 test takers with item preknowledge for the response-based test and 10–20 test takers for the RT-based test.
{"title":"Two Statistical Tests for the Detection of Item Compromise","authors":"W. van der Linden","doi":"10.3102/10769986221094789","DOIUrl":"https://doi.org/10.3102/10769986221094789","url":null,"abstract":"Two independent statistical tests of item compromise are presented, one based on the test takers’ responses and the other on their response times (RTs) on the same items. The tests can be used to monitor an item in real time during online continuous testing but are also applicable as part of post hoc forensic analysis. The two test statistics are simple intuitive quantities as the sum of the responses and RTs observed for the test takers on the item. Common features of the tests are ease of interpretation and computational simplicity. Both tests are uniformly most powerful under the assumption of known ability and speed parameters for the test takers. Examples of power functions for items with realistic parameter values suggest maximum power for 20–30 test takers with item preknowledge for the response-based test and 10–20 test takers for the RT-based test.","PeriodicalId":48001,"journal":{"name":"Journal of Educational and Behavioral Statistics","volume":"47 1","pages":"485 - 504"},"PeriodicalIF":2.4,"publicationDate":"2022-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44049872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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