Five Methods for Estimating Angoff Cut Scores with IRT

This article illustrates five different methods for estimating Angoff cut scores using item response theory (IRT) models. These include maximum likelihood (ML), expected a priori (EAP), modal a priori (MAP), and weighted maximum likelihood (WML) estimators, as well as the most commonly used approach based on translating ratings through the test characteristic curve (i.e., the IRT true‐score (TS) estimator). The five methods are compared using a simulation study and a real data example. Results indicated that the application of different methods can sometimes lead to different estimated cut scores, and that there can be some key differences in impact data when using the IRT TS estimator compared to other methods. It is suggested that one should carefully think about their choice of methods to estimate ability and cut scores because different methods have distinct features and properties. An important consideration in the application of Bayesian methods relates to the choice of the prior and the potential bias that priors may introduce into estimates.     

An Investigation of Undefined Cut Scores With the Hofstee Standard‐Setting Method

This article provides an overview of the Hofstee standard‐setting method and illustrates several situations where the Hofstee method will produce undefined cut scores. The situations where the cut scores will be undefined involve cases where the line segment derived from the Hofstee ratings does not intersect the score distribution curve based on actual exam performance data. Data from 15 standard settings performed by a credentialing organization are used to investigate how common undefined cut scores are with the Hofstee method and to compare cut scores derived from the Hofstee method with those from the Beuk method. Results suggest that when Hofstee cut scores exist that the Hofstee and Beuk methods often yield fairly similar results. However, it is shown that undefined Hofstee cut scores did occur in a few situations. When Hofstee cut scores are undefined, it is suggested that one extend the Hofstee line segment so that it intersects the score distribution curve to estimate cut scores. Analyses show that extending the line segment to estimate cut scores often yields similar results to the Beuk method. The article concludes with a discussion of what these results may imply for people who want to employ the Hofstee method.     

A Critical Look into the Beuk Standard-Setting Method

One commonly used compromise standard-setting method is the Beuk (1984) method. A key assumption of the Beuk method is that the emphasis given to the pass rate and the percent correct ratings should be proportional to the extent that the panelists agree on their ratings. However, whether the slope of Beuk line reflects the emphasis that panelists believe should be assigned to the pass rate and the percentage correct ratings has not be fully tested. In this article, I evaluate this critical assumption of the Beuk method by asking panelists to assign importance weights to their percentage correct and pass rate judgments. I show that in several cases that the emphasis suggested by the Beuk slope is noticeably different from what one would expect and is inconsistent with importance weight ratings. I also suggest two ways that the importance weights can be used to calculate alternate cut scores, and I show that one of the ways of calculating cut scores using the importance weights leads to larger potential differences in cut score estimates. I suggest that practitioners should consider collecting importance weights when the Beuk method is used for determining cut scores.     

Setting Performance Standards: Contemporary Methods

This module describes some common standard-setting procedures used to derive performance levels for achievement tests in education, licensure, and certification. Upon completing the module, readers will be able to: describe what standard setting is; understand why standard setting is necessary; recognize some of the purposes of standard setting; calculate cut scores using various methods; and identify elements to be considered when evaluating standard-setting procedures. A self-test and annotated bibliography are provided at the end of the module. Teaching aids to accompany the module are available through NCME.     

Modern Regression Discontinuity Analysis

Abstract

This article provides a detailed discussion of the theory and practice of modern regression discontinuity (RD) analysis for estimating the effects of interventions or treatments. Part 1 briefly chronicles the history of RD analysis and summarizes its past applications. Part 2 explains how in theory an RD analysis can identify an average effect of treatment for a population and how different types of RD analyses—“sharp” versus “fuzzy”—can identify average treatment effects for different conceptual subpopulations. Part 3 of the article introduces graphical methods, parametric statistical methods, and nonparametric statistical methods for estimating treatment effects in practice from regression discontinuity data plus validation tests and robustness tests for assessing these estimates. Section 4 considers generalizing RD findings and presents several different views on and approaches to the issue. Part 5 notes some important issues to pursue in future research about or applications of RD analysis.     

What Do School‐Level Scores From Large‐Scale Assessments Really Measure?

Although assessments of mathematics, reading, and writing are assumed to measure distinct academic skills, this may be difficult owing to the pervasive influence of general ability on performance. Factor analyses of school-level data from 14 large-scale assessment programs revealed that 80% of the variance in mathematics, reading, and writing scores was due to a common, underlying factor. Multiple regression analyses confirmed that scores contribute little information that is unique to a particular subject (6% or less). Although different assessments may create the illusion of providing unique information, they may be tapping into generic cognitive abilities that cut across content areas. These results raise suspicions about the value and validity of interpretations based on school-level subject area scores.     

A Bayesian Hierarchical Selection Model for Academic Growth With Missing Data

Using a sample of schools testing annually in grades 9–11 with a vertically linked series of assessments, a latent growth curve model is used to model test scores with student intercepts and slopes nested within school. Missed assessments can occur because of student mobility, student dropout, absenteeism, and other reasons. Missing data indicators are modeled using logistic regression, with grade 9 and potentially unobserved growth scores used as covariates. Under a hierarchical selection model, estimates of school effects on academic growth and missingness are obtained. The results from the selection model are compared to a model that ignores the missing data process.     

A Comparison of Angoff and Bookmark Standard Setting Methods

This article presents a comparison of simplified variations on two prevalent methods, Angoff and Bookmark, for setting cut scores on educational assessments. The comparison is presented through an application with a Grade 7 Mathematics Assessment in a midwestem school district. Training and operational methods and procedures for each method are described in detail along with comparative results for the application. An alternative item ordering strategy for the Bookmark method that may increase its usability is also introduced. Although the Angoff method is more widely used, the Bookmark method has some promising features, specifically in educational settings. Teachers are able to focus on the expected performance of the "barely proficient" student without the additional challenge of estimating absolute item dificulty.     

The disjuncture between raw scores and pass rates in New York State public schools: Turning success into failure

This paper demonstrates that ‘failure’ is not a direct reflection of student knowledge. Using five years of New York State school-level data, we compare passing rates to raw-scores. We find, first, that when ‘cut scores’ are raised, more students fail even if raw scores are increasing. Second, increasing cut scores disproportionately fails more poor students than non-poor students, despite that poor students have the fastest rates of raw score improvement. Third, raised cut scores transform the smallest raw score gaps between high- and low-poverty schools into the largest passing gaps. Thus, while students in poor schools know more than they did previously, and although they have learned at superior rates, they are recast as the biggest ‘failures’ they have ever been.     

Estimating reliability of school-level scores using multilevel and generalizability theory models

The purpose of this study was to investigate the methods of estimating the reliability of school-level scores using generalizability theory and multilevel models. Two approaches, ‘student within schools’ and ‘students within schools and subject areas,’ were conceptualized and implemented in this study. Four methods resulting from the combination of these two approaches with generalizability theory and multilevel models were compared for both balanced and unbalanced data. The generalizability theory and multilevel models for the ‘students within schools’ approach produced the same variance components and reliability estimates for the balanced data, while failing to do so for the unbalanced data. The different results from the two models can be explained by the fact that they administer different procedures in estimating the variance components used, in turn, to estimate reliability. Among the estimation methods investigated in this study, the generalizability theory model with the ‘students nested within schools crossed with subject areas’ design produced the lowest reliability estimates. Fully nested designs such as (students:schools) or (subject areas:students:schools) would not have any significant impact on reliability estimates of school-level scores. Both methods provide very similar reliability estimates of school-level scores.     

Regression Discontinuity Designs With Multiple Rating-Score Variables

Abstract

In the absence of a randomized control trial, regression discontinuity (RD) designs can produce plausible estimates of the treatment effect on an outcome for individuals near a cutoff score. In the standard RD design, individuals with rating scores higher than some exogenously determined cutoff score are assigned to one treatment condition; those with rating scores below the cutoff score are assigned to an alternate treatment condition. Many education policies, however, assign treatment status on the basis of more than one rating-score dimension. We refer to this class of RD designs as “multiple rating score regression discontinuity” (MRSRD) designs. In this paper, we discuss five different approaches to estimating treatment effects using MRSRD designs (response surface RD; frontier RD; fuzzy frontier RD; distance-based RD; and binding-score RD). We discuss differences among them in terms of their estimands, applications, statistical power, and potential extensions for studying heterogeneity of treatment effects.     

Do 45% of College Students Lack Critical Thinking Skills? Revisiting a Central Conclusion of Academically Adrift

The educational literature, the popular press, and educated laypeople have all echoed a conclusion from the book Academically Adrift by Richard Arum and Josipa Roksa (which has now become received wisdom), namely, that 45% of college students showed no significant gains in critical thinking skills. Similar results were reported by Pascarella, Blaich, Martin, and Hanson after the publication of Arum and Roksa's book in 2011. However, these authors' statistical tests were conducted incorrectly, and therefore this 45% finding is fundamentally untrue. We demonstrate that a correct statistical analysis would have found that far fewer students show significant gains in critical thinking. However, this does not reflect on student learning; instead, it reflects on how hard it is to find a statistically significant result when assessing student change on a student‐by‐student basis. This article discusses valid methods for testing the significance of gain scores of individual students.     

Estimating parallel form reliability from one administration of a criterion-referenced test: A computer program for practitioners

Reliability of a criterion-referenced test is often viewed as the consistency with which individuals who have taken two strictly parallel forms of a test are classified as being masters or nonmasters. However, in practice, it is rarely possible to retest students, especially with equivalent forms. For this reason, methods for making conservative approximations of alternate form (or test-retest “without the effects of testing”) reliability have been developed. Because these methods are computationally tedious and require some psychometric sophistication, they have rarely been used by teachers and school psychologists. This paper (a) describes one method (Subkoviak's) for estimating alternate-form reliability from one administration of a criterion-referenced test and (b) describes a computer program developed by the authors that will handle tests containing hundreds of items for large numbers of examinees and allow any test user to apply the technique described. The program is a superior alternative to other methods of simplifying this estimation procedure that rely upon tables; a user can check classification consistency estimates for several prospective cut scores directly from a data file, without having to make prior calculations.     

Repeater Analysis for Combining Information From Different Assessments

Admission decisions frequently rely on multiple assessments. As a consequence, it is important to explore rational approaches to combine the information from different educational tests. For example, U.S. graduate schools usually receive both TOEFL iBT^® scores and GRE^® General scores of foreign applicants for admission; however, little guidance has been given to combine information from these two assessments, even though the relationships between such sections as GRE Verbal and TOEFL iBT Reading are obvious. In this study, principles are provided to explore the extent to which different assessments complement one another and are distinguishable. Augmentation approaches developed for individual tests are applied to provide an accurate evaluation of combined assessments. Because augmentation methods require estimates of measurement error and internal reliability data are unavailable, required estimates of measurement error are obtained from repeaters, examinees who took the same test more than once. Because repeaters are not representative of all examinees in typical assessments, minimum discriminant information adjustment techniques are applied to the available sample of repeaters to treat the effect of selection bias. To illustrate methodology, combining information from TOEFL iBT scores and GRE General scores is examined. Analysis suggests that information from the GRE General and TOEFL iBT assessments is complementary but not redundant, indicating that the two tests measure related but somewhat different constructs. The proposed methodology can be readily applied to other situations where multiple assessments are needed.     

Conditional Standard Error of Measurement in Prediction

Previous methods for estimating the conditional standard error of measurement (CSEM) at specific score or ability levels are critically discussed, and a brief summary of prior empirical results is given. A new method is developed that avoids theoretical problems inherent in some prior methods, is easy to implement, and estimates not only a quantity analogous to the CSEM at each score but also the conditional standard error of prediction (CSEP) at each score and the conditional true score standard deviation (CTSSD) at each score, The new method differs from previous methods in that previous methods have concentrated on attempting to estimate error variance conditional on a fixed value of true score, whereas the new method considers the variance of observed scores conditional on a fixed value of an observed parallel measurement and decomposes these conditional observed score variances into true and error parts. The new method and several older methods are applied to a variety of tests, and representative results are graphically displayed. The CSEM-Iike estimates produced by the new method are called conditional standard error of measurement in prediction (CSEMP) estimates and are similar to those produced by older methods, but the CSEP estimates produced by the new method offer an alternative interpretation of the accuracy of a test at different scores. Finally, evidence is presented that shows that previous methods can produce dissimilar results and that the shape of the score distribution may influence the way in which the CSEM varies across the score scale.     

The crowd in mind and crowded minds: an experimental investigation of crowding effects on students’ views regarding tuition fees in Germany

In higher education, just amounts of tuition fees are often a topic of heated debate among different groups such as students, university teachers, administrative staff, and policymakers. We investigated whether unpleasant situations that students often experience at university due to social crowding can affect students’ views on the justified amount of tuition fees at universities. We report two experiments on whether conditions that lead to experienced crowding in higher education can affect how students cognitively deal with a given topic. Experiment 1 (N = 80) showed that the mere cognitive activation of crowdedness in text stories about situations related to student activities influenced prospective students’ estimates of what are justified university tuition fees. In Experiment 2 (N = 72), student participants wrote an essay on tuition fees in a small versus large room in groups of three versus six persons. Here, results showed that students together with relatively many others in a small room estimated higher tuition fees to be justified than participants in all other experimental conditions. We discuss the implications of the present findings for the configuration of classes in higher education.     

Evaluating the Operational Feasibility of Using Subsets of Items to Recommend Minimal Competency Cut Scores

Establishing cut scores using the Angoff method requires panelists to evaluate every item on a test and make a probability judgment. This can be time-consuming when there are large numbers of items on the test. Previous research using resampling studies suggest that it is possible to recommend stable Angoff-based cut score estimates using a content-stratified subset of ?45 items. Recommendations from earlier work were directly applied in this study in two operational standard-setting meetings. Angoff cut scores from two panels of raters were collected at each study, wherein one panel established the cut score based on the entire test, and another comparable panel first used a proportionally stratified subset of 45 items, and subsequently used the entire test in recommending the cut scores. The cut scores recommended for the subset of items were compared to the cut scores recommended based on the entire test for the same panel, and a comparable independent panel. Results from both studies suggest that cut scores recommended using a subset of items are comparable (i.e., within one standard error) to the cut score estimates from the full test.     

The Validity of Value-added Estimates from Low-Stakes Testing Contexts: The Impact of Change in Test-Taking Motivation and Test Consequences

Accountability mandates often prompt assessment of student learning gains (e.g., value-added estimates) via achievement tests. The validity of these estimates have been questioned when performance on tests is low stakes for students. To assess the effects of motivation on value-added estimates, we assigned students to one of three test consequence conditions: (a) an aggregate of test scores is used solely for institutional effectiveness purposes, (b) personal test score is reported to the student, or (c) personal test score is reported to faculty. Value-added estimates, operationalized as change in performance between two testing occasions for the same individuals where educational programming was experienced between testing occasions, were examined across conditions, in addition to the effects of test-taking motivation. Test consequences did not impact value-added estimates. Change in test-taking motivation, however, had a substantial effect on value-added estimates. In short, value-added estimates were attenuated due to decreased motivation from pretest to posttest.     

Putting dollars before scholars? Evidence from for-profit charter schools in Florida

This paper compares for- and non-profit management of charter schools in Florida using a unique dataset combining enrollment and student proficiency data with the annual independent financial audits filed by all charter schools. Comparisons reveal that independent for- and non-profit charter schools locate in similar markets and serve similar student bodies, whereas for-profits belonging to a network locate in lower income, denser, and more Hispanic areas. Bearing out the concerns of parents and policymakers, regression estimates indicate that, among independent charters, for-profits spend less per pupil on instruction and achieve lower student proficiency gains. By contrast, among charter schools belonging to a network, for-profits spend approximately 11% less per pupil, but expenses on student instruction are not being cut. The estimates, which control for differences across schools in student composition and other characteristics, imply that an equivalent level of per pupil expenses purchases about 0.03σ higher student proficiency at network for-profit charter schools.