Maintaining Equivalent Cut Scores for Small Sample Test Forms

This study examines the effectiveness of three approaches for maintaining equivalent performance standards across test forms with small samples: (1) common‐item equating, (2) resetting the standard, and (3) rescaling the standard. Rescaling the standard (i.e., applying common‐item equating methodology to standard setting ratings to account for systematic differences between standard setting panels) has received almost no attention in the literature. Identity equating was also examined to provide context. Data from a standard setting form of a large national certification test (N examinees = 4,397; N panelists = 13) were split into content‐equivalent subforms with common items, and resampling methodology was used to investigate the error introduced by each approach. Common‐item equating (circle‐arc and nominal weights mean) was evaluated at samples of size 10, 25, 50, and 100. The standard setting approaches (resetting and rescaling the standard) were evaluated by resampling (N = 8) and by simulating panelists (N = 8, 13, and 20). Results were inconclusive regarding the relative effectiveness of resetting and rescaling the standard. Small‐sample equating, however, consistently produced new form cut scores that were less biased and less prone to random error than new form cut scores based on resetting or rescaling the standard.     

Use of Adjustment by Minimum Discriminant Information in Linking Constructed‐Response Test Scores in the Absence of Common Items

In many educational tests, both multiple‐choice (MC) and constructed‐response (CR) sections are used to measure different constructs. In many common cases, security concerns lead to the use of form‐specific CR items that cannot be used for equating test scores, along with MC sections that can be linked to previous test forms via common items. In such cases, adjustment by minimum discriminant information may be used to link CR section scores and composite scores based on both MC and CR sections. This approach is an innovative extension that addresses the long‐standing issue of linking CR test scores across test forms in the absence of common items in educational measurement. It is applied to a series of administrations from an international language assessment with MC sections for receptive skills and CR sections for productive skills. To assess the linking results, harmonic regression is applied to examine the effects of the proposed linking method on score stability, among several analyses for evaluation.     

Test Design and Speededness

A critical component of test speededness is the distribution of the test taker’s total time on the test. A simple set of constraints on the item parameters in the lognormal model for response times is derived that can be used to control the distribution when assembling a new test form. As the constraints are linear in the item parameters, they can easily be included in a mixed integer programming model for test assembly. The use of the constraints is demonstrated for the problems of assembling a new test form to be equally speeded as a reference form, test assembly in which the impact of a change in the content specifications on speededness is to be neutralized, and the assembly of test forms with a revised level of speededness.     

Assessing the Practical Equivalence of Conversions When Measurement Conditions Change

At times, the same set of test questions is administered under different measurement conditions that might affect the psychometric properties of the test scores enough to warrant different score conversions for the different conditions. We propose a procedure for assessing the practical equivalence of conversions developed for the same set of test questions but administered under different measurement conditions. This procedure assesses whether the use of separate conversions for each condition has a desirable or undesirable effect. We distinguish effects due to differences in difficulty from effects due to rounding conventions. The proposed procedure provides objective empirical information that assists in deciding to report a common conversion for a set of items or a different conversion for the set of items when the set is administered under different measurement conditions. To illustrate the use of the procedure, we consider the case where a scrambled test form is used along with a base test form. If section order effects are detected between the scrambled and base forms, a decision needs to be made whether to report a single common conversion for both forms or to report separate conversions.     

Evaluating Statistical Targets for Assembling Parallel Mixed‐Format Test Forms

Test assembly is the process of selecting items from an item pool to form one or more new test forms. Often new test forms are constructed to be parallel with an existing (or an ideal) test. Within the context of item response theory, the test information function (TIF) or the test characteristic curve (TCC) are commonly used as statistical targets to obtain this parallelism. In a recent study, Ali and van Rijn proposed combining the TIF and TCC as statistical targets, rather than using only a single statistical target. In this article, we propose two new methods using this combined approach, and compare these methods with single statistical targets for the assembly of mixed‐format tests. In addition, we introduce new criteria to evaluate the parallelism of multiple forms. The results show that single statistical targets can be problematic, while the combined targets perform better, especially in situations with increasing numbers of polytomous items. Implications of using the combined target are discussed.     

Detecting Local Item Dependence in Polytomous Adaptive Data

A rapidly expanding arena for item response theory (IRT) is in attitudinal and health‐outcomes survey applications, often with polytomous items. In particular, there is interest in computer adaptive testing (CAT). Meeting model assumptions is necessary to realize the benefits of IRT in this setting, however. Although initial investigations of local item dependence have been studied both for polytomous items in fixed‐form settings and for dichotomous items in CAT settings, there have been no publications applying local item dependence detection methodology to polytomous items in CAT despite its central importance to these applications. The current research uses a simulation study to investigate the extension of widely used pairwise statistics, Yen's Q₃ Statistic and Pearson's Statistic X², in this context. The simulation design and results are contextualized throughout with a real item bank of this type from the Patient‐Reported Outcomes Measurement Information System (PROMIS).     

Detection of Test Collusion via Kullback–Leibler Divergence

The development of statistical methods for detecting test collusion is a new research direction in the area of test security. Test collusion may be described as large‐scale sharing of test materials, including answers to test items. Current methods of detecting test collusion are based on statistics also used in answer‐copying detection. Therefore, in computerized adaptive testing (CAT) these methods lose power because the actual test varies across examinees. This article addresses that problem by introducing a new approach that works in two stages: in Stage 1, test centers with an unusual distribution of a person‐fit statistic are identified via Kullback–Leibler divergence; in Stage 2, examinees from identified test centers are analyzed further using the person‐fit statistic, where the critical value is computed without data from the identified test centers. The approach is extremely flexible. One can employ any existing person‐fit statistic. The approach can be applied to all major testing programs: paper‐and‐pencil testing (P&P), computer‐based testing (CBT), multiple‐stage testing (MST), and CAT. Also, the definition of test center is not limited by the geographic location (room, class, college) and can be extended to support various relations between examinees (from the same undergraduate college, from the same test‐prep center, from the same group at a social network). The suggested approach was found to be effective in CAT for detecting groups of examinees with item pre‐knowledge, meaning those with access (possibly unknown to us) to one or more subsets of items prior to the exam.     

NCME 2008 Presidential Address: The Impact of Anchor Test Configuration on Student Proficiency Rates

Examined in this study were the effects of reducing anchor test length on student proficiency rates for 12 multiple‐choice tests administered in an annual, large‐scale, high‐stakes assessment. The anchor tests contained 15 items, 10 items, or five items. Five content representative samples of items were drawn at each anchor test length from a small universe of items in order to investigate the stability of equating results over anchor test samples. The operational tests were calibrated using the one‐parameter model and equated using the mean b‐value method. The findings indicated that student proficiency rates could display important variability over anchor test samples when 15 anchor items were used. Notable increases in this variability were found for some tests when shorter anchor tests were used. For these tests, some of the anchor items had parameters that changed somewhat in relative difficulty from one year to the next. It is recommended that anchor sets with more than 15 items be used to mitigate the instability in equating results due to anchor item sampling. Also, the optimal allocation method of stratified sampling should be evaluated as one means of improving the stability and precision of equating results.     

Research and Teaching in the Science Department of the University of London Institute of Education

This study was designed (1) to analyse the relationship between the answer profile from multiple‐choice questions on stoichiometric problems and the students’ reasoning patterns and (2) to examine the effect for certain variables on the facility values of test items. The instruments used were mainly paper‐and‐pencil tests. The subjects were 6262 grammar school students from all parts of the Federal Republic of Germany. They were randomly assigned to the test items.

The results indicated that many students arrived at their answers by mixing up amount and reacting mass, or molar mass and reacting mass. It was also found that the variables ‘easy/hard calculations’, and ‘formula given/to be developed’ determined the facility values of test items.

From the results, it was possible to make recommendations to practising teachers as well as to examiners. Knowing students’ ideas, the teacher can think of how to make use of them before entering the classroom. A teaching unit may start off with easy problems leaving the more difficult ones for later. Examiners developing new tests on stoichiometry should consider two essential preconditions for the formulae of chemical compounds, used in the item: formulae of the type AB should be avoided and the molar masses of the elements involved must be clearly different.     

An NCME Instructional Module on Using Differential Step Functioning to Refine the Analysis of DIF in Polytomous Items

Traditional methods for examining differential item functioning (DIF) in polytomously scored test items yield a single item‐level index of DIF and thus provide no information concerning which score levels are implicated in the DIF effect. To address this limitation of DIF methodology, the framework of differential step functioning (DSF) has recently been proposed, whereby measurement invariance is examined within each step underlying the polytomous response variable. The examination of DSF can provide valuable information concerning the nature of the DIF effect (i.e., is the DIF an item‐level effect or an effect isolated to specific score levels), the location of the DIF effect (i.e., precisely which score levels are manifesting the DIF effect), and the potential causes of a DIF effect (i.e., what properties of the item stem or task are potentially biasing). This article presents a didactic overview of the DSF framework and provides specific guidance and recommendations on how DSF can be used to enhance the examination of DIF in polytomous items. An example with real testing data is presented to illustrate the comprehensive information provided by a DSF analysis.     

Validation of Group Domain Score Estimates Using a Test of Domain

Domain scores have been proposed as a user-friendly way of providing instructional feedback about examinees' skills. Domain performance typically cannot be measured directly; instead, scores must be estimated using available information. Simulation studies suggest that IRT-based methods yield accurate group domain score estimates. Because simulations can represent best-case scenarios for methodology, it is important to verify results with a real data application. This study administered a domain of elementary algebra (EA) items created from operational test forms. An IRT-based group-level domain score was estimated from responses to a subset of taken items (comprised of EA items from a single operational form) and compared to the actual observed domain score. Domain item parameters were calibrated both using item responses from the special study and from national operational administrations of the items. The accuracy of the domain score estimates were evaluated within schools and across school sizes for each set of parameters. The IRT-based domain score estimates typically were closer to the actual domain score than observed performance on the EA items from the single form. Previously simulated findings for the IRT-based domain score estimation procedure were supported by the results of the real data application.     

Gender Differences in Lunar‐related Scientific and Mathematical Understandings

This paper reports an examination on gender differences in lunar phases understanding of 123 students (70 females and 53 males). Middle‐level students interacted with the Moon through observations, sketching, journalling, two‐dimensional and three‐dimensional modelling, and classroom discussions. These lunar lessons were adapted from the Realistic Explorations in Astronomical Learning (REAL) curriculum. Students’ conceptual understandings were measured through analysis of pre‐test and post‐test results on a Lunar Phases Concept Inventory (LPCI) and a Geometric Spatial Assessment (GSA). The LPCI was used to assess conceptual learning of eight science and four mathematics domains. The GSA was used to assess learning of the same four mathematical domains; however, the GSA test items were not posed within a lunar context. Results showed both male and female groups to make significant gains in understanding on the overall LPCI test scores as well as significant gains on five of the eight science domains and on three of the four mathematics domains. The males scored significantly higher than the females on the science domain, phase—Sun/Earth/Moon positions, and on the mathematics domain geometric spatial visualisation. GSA results found both male and female groups achieving a significant increase in their test scores on the overall GSA. Females made significant gains on the GSA mathematics domains, periodic patterns and cardinal directions, while males made significant gains on only the periodic patterns domain. Findings suggest that both scientific and mathematical understandings can be significantly improved for both sexes through the use of spatially focused, inquiry‐oriented curriculum such as REAL.     

Use of Knowledge, Skill, and Ability Statements in Developing Licensure and Certification Examinations

The task inventory approach is commonly used in job analysis for establishing content validity evidence supporting the use and interpretation of licensure and certification examinations. Although the results of a task inventory survey provide job task-related information that can be used as a reliable and valid source for test development, it is often the knowledge, skills, and abilities (KSAs) required for performing the tasks, rather than the job tasks themselves, which are tested by licensure and certification exams. This article presents a framework that addresses the important role of KSAs in developing and validating licensure and certification examinations. This includes the use of KSAs in linking job task survey results to the test content outline, transferring job task weights to test specifications, and eventually applying the results to the development of the test items. The impact of using KSAs in the development of test specifications is illustrated from job analyses for two diverse professions. One method for transferring job task weights from the job analysis to test specifications through KSAs is also presented, along with examples. The two examples demonstrated in this article are taken from nursing certification and real estate licensure programs. However, the methodology for using KSAs to link job tasks and test content is also applicable in the development of teacher credentialing examinations.     

An Experimental Test of Student Verbal Reports and Teacher Evaluations as a Source of Validity Evidence for Test Development

The Standards for Educational and Psychological Testing indicate that test instructions, and by extension item objectives, presented to examinees should be sufficiently clear and detailed to help ensure that they respond as developers intend them to respond (Standard 3.20; AERA, APA, & NCME, 1999 American Educational Research Association (AERA), American Psychological Association (APA), National Council on Measurement in Education (NCME). 1999. Standards for educational and psychological testing, Washington, DC: Author.  [Google Scholar]). The present study investigates the use of verbal reports, one of many sources of evidence for validity arguments, as a way to evaluate the content clarity of 30 items from a large-scale science assessment. Student reports were used to edit items and create a student-modified test form. Evaluations from expert preservice teachers were used to edit the items and create an expert-modified test form. Both experimental forms, along with the original set of 30 items, were then randomly assigned to a sample of 264 examinees. Hierarchical regression analyses indicated that examinee performance on the student-modified and expert-modified forms was similar relative to performance on the original test items. Item statistics indicated that student-modified test items were equally difficult and discriminating as expert-modified test items. The implications of using student and teacher evaluations are discussed for informing test development.     

纵向量表制作浅谈

等值(equating)和纵向量表化(vertical scaling)的功用是建立来自不同考试的分数之间的关系。等值是施用于相同年级,相同性质的试卷,而纵向量表化则用于不同年级而性质相似的试卷。纵向量表化是将不同年级的成绩放置于统一的成长分数量表之中。纵向量表(vertical scale)是一种延伸的分数,其度量跨越和串连不同年级之间,用以评估学生连继性的成就成长(Nitko,2004)。在教学中,学生的进度可以利用纵向量表来监察和评估。而在教育研究上,纵向量表可成为长期跟踪调查(longitudinal study)之有力工具。本文讨论纵向量表化的方法论,包括成长定义(definition of growth),数据收集(data collection)方法,试卷设计和使用项目反应理论(Item Response Theory)的方法以及对制作纵向量表提供一些实际的建议。     

A Nested Logit Approach for Investigating Distractors as Causes of Differential Item Functioning

In multiple‐choice items, differential item functioning (DIF) in the correct response may or may not be caused by differentially functioning distractors. Identifying distractors as causes of DIF can provide valuable information for potential item revision or the design of new test items. In this paper, we examine a two‐step approach based on application of a nested logit model for this purpose. The approach separates testing of differential distractor functioning (DDF) from DIF, thus allowing for clearer evaluations of where distractors may be responsible for DIF. The approach is contrasted against competing methods and evaluated in simulation and real data analyses.     

Equating Subscores under the Nonequivalent Anchor Test (NEAT) Design

The study examined two approaches for equating subscores. They are (1) equating subscores using internal common items as the anchor to conduct the equating, and (2) equating subscores using equated and scaled total scores as the anchor to conduct the equating. Since equated total scores are comparable across the new and old forms, they can be used as an anchor to equate the subscores. Both chained linear and chained equipercentile methods were used. Data from two tests were used to conduct the study and results showed that when more internal common items were available (i.e., 10–12 items), then using common items to equate the subscores is preferable. However, when the number of common items is very small (i.e., five to six items), then using total scaled scores to equate the subscores is preferable. For both tests, not equating (i.e., using raw subscores) is not reasonable as it resulted in a considerable amount of bias.     

The Relationship of Content Characteristics of GRE Analytical Reasoning Items to Their Difficulties and Discriminations

In actual test development practice, the number o f test items that must be developed and pretested is typically greater, and sometimes much greater, than the number that is eventually judged suitable for use in operational test forms. This has proven to be especially true for one item type–analytical reasoning-that currently forms the bulk of the analytical ability measure of the GRE General Test. This study involved coding the content characteristics of some 1,400 GRE analytical reasoning items. These characteristics were correlated with indices of item difficulty and discrimination. Several item characteristics were predictive of the difficulty of analytical reasoning items. Generally, these same variables also predicted item discrimination, but to a lesser degree. The results suggest several content characteristics that could be considered in extending the current specifications for analytical reasoning items. The use of these item features may also contribute to greater efficiency in developing such items. Finally, the influence of these various characteristics also provides a better understanding of the construct validity of the analytical reasoning item type.     

When Adaptation Is Not an Option: An Application of Multilingual Standard Setting

As an alternative to adaptation, tests may also be developed simultaneously in multiple languages. Although the items on such tests could vary substantially, scores from these tests may be used to make the same types of decisions about different groups of examinees. The ability to make such decisions is contingent upon setting performance standards for each exam that allow for comparable interpretations of test results. This article describes a standard setting process used for a multilingual high school literacy assessment constructed under these conditions. This methodology was designed to address the specific challenges presented by this testing program including maintaining equivalent expectations for performance across different student populations. The validity evidence collected to support the methodology and results is discussed along with recommendations for future practice.     

The Philosophical Aspects of IRT Equating: Modeling Drift to Evaluate Cohort Growth in Large‐Scale Assessments

Calibration and equating is the quintessential necessity for most large‐scale educational assessments. However, there are instances when no consideration is given to the equating process in terms of context and substantive realization, and the methods used in its execution. In the view of the authors, equating is not merely an exhibit of the statistical methodology, but it is also a reflection of the thought process undertaken in its execution. For example, there is hardly any discussion in literature of the ideological differences in the selection of an equating method. Furthermore, there is little evidence of modeling cohort growth through an identification and use of construct‐relevant linking items’ drift, using the common item nonequivalent group equating design. In this article, the authors philosophically justify the use of Huynh's statistical method for the identification of construct‐relevant outliers in the linking pool. The article also dispels the perception of scale instability associated with the inclusion of construct‐relevant outliers in the linking item pool and concludes that an appreciation of the rationale used in the selection of the equating method, together with the use of linking items in modeling cohort growth, can be beneficial to the practitioners.