Efficiency of Targeted Multistage Calibration Designs Under Practical Constraints: A Simulation Study

Calibration of an item bank for computer adaptive testing requires substantial resources. In this study, we investigated whether the efficiency of calibration under the Rasch model could be enhanced by improving the match between item difficulty and student ability. We introduced targeted multistage calibration designs, a design type that considers ability‐related background variables and performance for assigning students to suitable items. Furthermore, we investigated whether uncertainty about item difficulty could impair the assembling of efficient designs. The results indicated that targeted multistage calibration designs were more efficient than ordinary targeted designs under optimal conditions. Limited knowledge about item difficulty reduced the efficiency of one of the two investigated targeted multistage calibration designs, whereas targeted designs were more robust.     

Hybrid Computerized Adaptive Testing: From Group Sequential Design to Fully Sequential Design

Computerized adaptive testing (CAT) and multistage testing (MST) have become two of the most popular modes in large‐scale computer‐based sequential testing.  Though most designs of CAT and MST exhibit strength and weakness in recent large‐scale implementations, there is no simple answer to the question of which design is better because different modes may fit different practical situations. This article proposes a hybrid adaptive framework to combine both CAT and MST, inspired by an analysis of the history of CAT and MST. The proposed procedure is a design which transitions from a group sequential design to a fully sequential design. This allows for the robustness of MST in early stages, but also shares the advantages of CAT in later stages with fine tuning of the ability estimator once its neighborhood has been identified. Simulation results showed that hybrid designs following our proposed principles provided comparable or even better estimation accuracy and efficiency than standard CAT and MST designs, especially for examinees at the two ends of the ability range.     

计算机自适应考试系统研究

本文结合专家经验确定法和项目反应理论,设计出一种简明、实用的计算机自适应考试系统的试题难度确定方法,同时重点分析计算机自适应考试系统的测试起点、终点选择,选题策略和能力值估计方法。最后列举了一个自适应测试的步骤实例。本系统能够根据不同能力被试者随机选择试题项目,减少了测试长度,与传统在线考试系统相比提高了考试效率。     

Cognitive Diagnostic Multistage Testing by Partitioning Hierarchically Structured Attributes

In cognitive diagnostic models (CDMs), a set of fine-grained attributes is required to characterize complex problem solving and provide detailed diagnostic information about an examinee. However, it is challenging to ensure reliable estimation and control computational complexity when The test aims to identify the examinee's attribute profile in a large-scale map of attributes. To address this problem, this study proposes a cognitive diagnostic multistage testing by partitioning hierarchically structured attributes (CD-MST-PH) as a multistage testing for CDM. In CD-MST-PH, multiple testlets can be constructed based on separate attribute groups before testing occurs, which retains the advantages of multistage testing over fully adaptive testing or the on-the-fly approach. Moreover, testlets are offered sequentially and adaptively, thus improving test accuracy and efficiency. An item information measure is proposed to compute the discrimination power of an item for each attribute, and a module assembly method is presented to construct modules anchored at each separate attribute group. Several module selection indices for CD-MST-PH are also proposed by modifying the item selection indices used in cognitive diagnostic computerized adaptive testing. The results of simulation study show that CD-MST-PH can improve test accuracy and efficiency relative to the conventional test without adaptive stages.     

Skilled but unaware of it: CAT undermines a test taker's metacognitive competence

We investigated students' metacognitive experiences with regard to feelings of difficulty (FD), feelings of satisfaction (FS), and estimate of effort (EE), employing either computerized adaptive testing (CAT) or computerized fixed item testing (FIT). In an experimental approach, 174 students in grades 10 to 13 were tested either with a CAT or a FIT version of a matrices test. Data revealed that metacognitive experiences were not related to the resulting test scores for CAT: test takers who took the matrices test in an adaptive mode were paradoxically more satisfied with their performance the worse they had performed in terms of the resulting ability parameter. They also rated the test as easier the lower they had performed, but their estimates of effort were higher the better they had performed. For test takers who took the FIT version, completely different results were revealed. In line with previous results, test takers were supposed to base these experiences on the subjectively estimated percentage of items solved. This moderated mediation hypothesis was in parts confirmed, as the relation between the percentage of items solved and FD, FS, and EE was revealed to be mediated by the estimated percentage of items solved. Results are discussed with reference to feedback acceptance, errant self-estimations, and test fairness with regard to a possible false regulation of effort in lower ability groups when using CAT.     

A Simulation and Comparison of Flexilevel and Bayesian Computerized Adaptive Testing

Computerized adaptive testing (CAT) is a testing procedure that adapts an examination to an examinee's ability by administering only items of appropriate difficulty for the examinee. In this study, the authors compared Lord's flexilevel testing procedure (flexilevel CAT) with an item response theory-based CAT using Bayesian estimation of ability (Bayesian CAT). Three flexilevel CATs, which differed in test length (36, 18, and 11 items), and three Bayesian CATs were simulated; the Bayesian CATs differed from one another in the standard error of estimate (SEE) used for terminating the test (0.25, 0.10, and 0.05). Results showed that the flexilevel 36- and 18-item CATs produced ability estimates that may be considered as accurate as those of the Bayesian CAT with SEE = 0.10 and comparable to the Bayesian CAT with SEE = 0.05. The authors discuss the implications for classroom testing and for item response theory-based CAT.     

A Comparison of Self-Adapted and Computerized Adaptive Tests

According to item response theory (IRT), examinee ability estimation is independent of the particular set of test items administered from a calibrated pool. Although the most popular application of this feature of IRT is computerized adaptive (CA) testing, a recently proposed alternative is self-adapted (SA) testing, in which examinees choose the difficulty level of each of their test items. This study compared examinee performance under SA and CA tests, finding that examinees taking the SA test (a) obtained significantly higher ability scores and (b) reported significantly lower posttest state anxiety. The results of this study suggest that SA testing is a desirable format for computer-based testing.     

Embedded Field Test Item Statistics: Can They Be Trusted for Estimating Student Proficiency?

Assessment items are commonly field tested prior to operational use to observe statistical item properties such as difficulty. Item parameter estimates from field testing may be used to assign scores via pre-equating or computer adaptive designs. This study examined differences between item difficulty estimates based on field test and operational data and the relationship of such differences to item position changes and student proficiency estimates. Item position effects were observed for 20 assessments, with items in later positions tending to be more difficult. Moreover, field test estimates of item difficulty were biased slightly upward, which may indicate examinee knowledge of which items were being field tested. Nevertheless, errors in field test item difficulty estimates had negligible impacts on student proficiency estimates for most assessments. Caution is still warranted when using field test statistics for scoring, and testing programs should conduct investigations to determine whether the effects on scoring are inconsequential.     

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.     

An NCME Instructional Module on Multistage Testing

Multistage tests are those in which sets of items are administered adaptively and are scored as a unit. These tests have all of the advantages of adaptive testing, with more efficient and precise measurement across the proficiency scale as well as time savings, without many of the disadvantages of an item-level adaptive test. As a seemingly balanced compromise between linear paper-and-pencil and item-level adaptive tests, development and use of multistage tests is increasing. This module describes multistage tests, including two-stage and testlet-based tests, and discusses the relative advantages and disadvantages of multistage testing as well as considerations and steps in creating such tests.     

Promising Areas for Psychometric Research

Many credentialing agencies today are either administering their examinations by computer or are likely to be doing so in the coming years. Unfortunately, although several promising computer-based test designs are available, little is known about how well they function in examination settings. The goal of this study was to compare fixed-length examinations (both operational forms and newly constructed forms) with several variations of multistage test designs for making pass-fail decisions. Results were produced for 3 passing scores. Four operational 60-item examinations were compared to (a) 3 new 60-item forms, (b) 60-item 3-stage tests, and (c) 40-item 2-stage tests; all were constructed using automated test assembly software. The study was carried out using computer simulation techniques that were set to mimic common examination practices. All 60-item tests, regardless of design or passing score, produced accurate ability estimates and acceptable and similar levels of decision consistency and decision accuracy. One interesting finding was that the 40-item test results were poorer than the 60-item test results, as expected, but were in the range of acceptability. This raises the practical policy question of whether content-valid 40-item tests with lower item exposure levels and/or savings in item development costs are an acceptable trade-off for a small loss in decision accuracy and consistency.     

Some Practical Examples of Computer-Adaptive Sequential Testing

Computerized testing has created new challenges for the production and administration of test forms. Many testing organizations engaged in or considering computerized testing may find themselves changing from well-established procedures for handcrafiing a small number of paper-and-pencil test forms to procedures for mass producing many computerized test forms. This paper describes an integratedapproach to test development and administration called computer-adaptive sequential testing, or CAST. CAST is a structured approach to test construction which incorporates both adaptive testing methods with automated test assembly to allow test developers to maintain a greater degree of control over the production, quality assurance, and administration of different types of computerized tests. CAST retains much of the efficiency of traditional computer adaptive testing (CAT) and can be modified for computer mastery testing (CMT) applications. The CAST framework is described in detail and several applications are demonstrated using a medical licensure example.     

An Empirical Study of Computerized Adaptive Test Administration Conditions

This empirical study was designed to determine the impact of computerized adap- tive test (CAT) administration formats on student performance. Students in medical technology programs took a paper-and-pencil and an individualized, computerized adaptive test. Students were randomly assigned to adaptive test administration for- mats to ascertain the effect on student performance of altering: (a) the difficulty of the first item, (b) the targeted level of test difficulty, (c) minimum test length, and (d) the opportunity to control the test. Computerized adaptive test data were analyzed with ANCO VA. The paper-and.pencil test was used as a covariate to equalize abil- ity variance among cells. The only significant main effect was for opportunity to control the test. There were no significant interactions among test administration formats. This study provides evidence concerning adjusting traditional computer- ized adaptive testing to more familiar testing modalities.     

On the Issue of Item Selection in Computerized Adaptive Testing With Response Times

Many standardized tests are now administered via computer rather than paper‐and‐pencil format. The computer‐based delivery mode brings with it certain advantages. One advantage is the ability to adapt the difficulty level of the test to the ability level of the test taker in what has been termed computerized adaptive testing (CAT). A second advantage is the ability to record not only the test taker's response to each item (i.e., question), but also the amount of time the test taker spends considering and answering each item. Combining these two advantages, various methods were explored for utilizing response time data in selecting appropriate items for an individual test taker. Four strategies for incorporating response time data were evaluated, and the precision of the final test‐taker score was assessed by comparing it to a benchmark value that did not take response time information into account. While differences in measurement precision and testing times were expected, results showed that the strategies did not differ much with respect to measurement precision but that there were differences with regard to the total testing time.     

Stratified and Maximum Information Item Selection Procedures in Computer Adaptive Testing

In this study we evaluated and compared three item selection procedures: the maximum Fisher information procedure (F), the a-stratified multistage computer adaptive testing (CAT) (STR), and a refined stratification procedure that allows more items to be selected from the high a strata and fewer items from the low a strata (USTR), along with completely random item selection (RAN). The comparisons were with respect to error variances, reliability of ability estimates and item usage through CATs simulated under nine test conditions of various practical constraints and item selection space. The results showed that F had an apparent precision advantage over STR and USTR under unconstrained item selection, but with very poor item usage. USTR reduced error variances for STR under various conditions, with small compromises in item usage. Compared to F, USTR enhanced item usage while achieving comparable precision in ability estimates; it achieved a precision level similar to F with improved item usage when items were selected under exposure control and with limited item selection space. The results provide implications for choosing an appropriate item selection procedure in applied settings.     

A Comparison of Item-Selection Methods for Adaptive Tests with Content Constraints

In test assembly, a fundamental difference exists between algorithms that select a test sequentially or simultaneously. Sequential assembly allows us to optimize an objective function at the examinee's ability estimate, such as the test information function in computerized adaptive testing. But it leads to the non-trivial problem of how to realize a set of content constraints on the test—a problem more naturally solved by a simultaneous item-selection method. Three main item-selection methods in adaptive testing offer solutions to this dilemma. The spiraling method moves item selection across categories of items in the pool proportionally to the numbers needed from them. Item selection by the weighted-deviations method (WDM) and the shadow test approach (STA) is based on projections of the future consequences of selecting an item. These two methods differ in that the former calculates a projection of a weighted sum of the attributes of the eventual test and the latter a projection of the test itself. The pros and cons of these methods are analyzed. An empirical comparison between the WDM and STA was conducted for an adaptive version of the Law School Admission Test (LSAT), which showed equally good item-exposure rates but violations of some of the constraints and larger bias and inaccuracy of the ability estimator for the WDM.     

Computerized Adaptive Testing in Early Education: Exploring the Impact of Item Position Effects on Ability Estimation

Studies have shown that item difficulty can vary significantly based on the context of an item within a test form. In particular, item position may be associated with practice and fatigue effects that influence item parameter estimation. The purpose of this research was to examine the relevance of item position specifically for assessments used in early education, an area of testing that has received relatively limited psychometric attention. In an initial study, multilevel item response models fit to data from an early literacy measure revealed statistically significant increases in difficulty for items appearing later in a 20‐item form. The estimated linear change in logits for an increase of 1 in position was .024, resulting in a predicted change of .46 logits for a shift from the beginning to the end of the form. A subsequent simulation study examined impacts of item position effects on person ability estimation within computerized adaptive testing. Implications and recommendations for practice are discussed.     

Measuring and Validating Cognitive Modifiability as an Ability: A Study in the Spatial Domain

Measuring cognitive modifiability from the responsiveness of an individual's performance to intervention has long been viewed (e.g., Dearborne, 1921) as an alternative to traditional (static) ability measurement. Currently, dynamic testing, in which cues or instruction are presented with ability test items, is a popular method for assessing cognitive modifiability. Despite the long-standing interest, however, little data exists to support the validity of cognitive modifiability measures in any ability domain. Several special methodological difficulties have limited validity studies, including psychometric problems in measuring modifiability (i.e., as change), lack of appropriate validation criteria, and difficulty in linking modifiability to cognitive theory. In this article, relatively new developments for solving the validation problems are applied to measuring and validating spatial modifiability. Criterion-related validity for predicting learning in an applied knowledge domain, as well as construct validity, is supported.     

A Comparison of IRT Proficiency Estimation Methods Under Adaptive Multistage Testing

This inquiry is an investigation of item response theory (IRT) proficiency estimators’ accuracy under multistage testing (MST). We chose a two‐stage MST design that includes four modules (one at Stage 1, three at Stage 2) and three difficulty paths (low, middle, high). We assembled various two‐stage MST panels (i.e., forms) by manipulating two assembly conditions in each module, such as difficulty level and module length. For each panel, we investigated the accuracy of examinees’ proficiency levels derived from seven IRT proficiency estimators. The choice of Bayesian (prior) versus non‐Bayesian (no prior) estimators was of more practical significance than the choice of number‐correct versus item‐pattern scoring estimators. The Bayesian estimators were slightly more efficient than the non‐Bayesian estimators, resulting in smaller overall error. Possible score changes caused by the use of different proficiency estimators would be nonnegligible, particularly for low‐ and high‐performing examinees.     

How Well Can We Compare Scores on Test Forms That Are Constructed by Examinees Choice?

When an exam consists, in whole or in part, of constructed-response items, it is a common practice to allow the examinee to choose a subset of the questions to answer. This procedure is usually adopted so that the limited number of items that can be completed in the allotted time does not unfairly affect the examinee. This results in the de facto administration of several different test forms, where the exact structure of any particular form is determined by the examinee. However, when different forms are administered, a canon of good testing practice requires that those forms be equated to adjust for differences in their difficulty. When the items are chosen by the examinee, traditional equating procedures do not strictly apply due to the nonignorable nature of the missing responses. In this article, we examine the comparability of scores on such tests within an IRT framework. We illustrate the approach with data from the College Board's Advanced Placement Test in Chemistry