Can Examinees Use a Review Option to Obtain Positively Biased Ability Estimates on a Computerized Adaptive Test?

Part of the controversy about allowing examinees to review and change answers to previous items on computerized adaptive tests (CATs) centers on a strategy for obtaining positively biased ability estimates attributed to Wainer (1993) in which examinees intentionally answer items incorrectly before review and to the best of their abilities upon review. Our results, based on both simulated and live testing data, showed that there were instances in which the Wainer strategy yielded inflated ability estimates as well as instances in which it yielded deflated ability estimates. The success of the strategy in inflating ability estimates depended on the ability estimation method used (maximum likelihood versus Bayesian), the examinee's true ability level, the standard error of the ability estimate, the examinee's ability to implement the strategy, and the type of decision made from the ability estimate. We discuss approaches to dealing with the Wainer strategy in operational CAT settings.     

A Conditional Exposure Control Method for Multidimensional Adaptive Testing

In computerized adaptive testing (CAT), ensuring the security of test items is a crucial practical consideration. A common approach to reducing item theft is to define maximum item exposure rates, i.e., to limit the proportion of examinees to whom a given item can be administered. Numerous methods for controlling exposure rates have been proposed for tests employing the unidimensional 3-PL model. The present article explores the issues associated with controlling exposure rates when a multidimensional item response theory (MIRT) model is utilized and exposure rates must be controlled conditional upon ability. This situation is complicated by the exponentially increasing number of possible ability values in multiple dimensions. The article introduces a new procedure, called the generalized Stocking-Lewis method, that controls the exposure rate for students of comparable ability as well as with respect to the overall population. A realistic simulation set compares the new method with three other approaches: Kullback-Leibler information with no exposure control, Kullback-Leibler information with unconditional Sympson-Hetter exposure control, and random item selection.     

Item Review and the Rearrangement Procedure: Its process and its results

Permitting item review is to the benefit of the examinees who typically increase their test scores with item review. However, testing companies do not prefer item review since it does not follow the logic on which adaptive tests are based, and since it is prone to cheating strategies. Consequently, item review is not permitted in many adaptive tests. This study attempts to provide a solution that would allow examinees to revise their answers, without jeopardizing the quality and efficiency of the test. The purpose of this study is to test the efficiency of a “rearrangement procedure” that rearranges and skips certain items in order to better estimate the examinees' abilities, without allowing them to cheat on the test. This was examined through a simulation study. The results show that the rearrangement procedure is effective in reducing the standard error of the Bayesian ability estimates and in increasing the reliability of the same estimates.     

A Comparison of Procedures for Content-Sensitive Item Selection in Computerized Adaptive Tests

This simulation study compared two procedures to enable an adaptive test to select items in correspondence with a content blueprint. Trait level estimates obtained from testlet-based and constrained adaptive tests administered to 10,000 simulated examinees under two trait distributions and three item pool sizes were compared to the trait level estimates obtained from traditional adaptive tests in terms of mean absolute error, bias, and information. Results indicate that using constrained adaptive testing requires an increase of 5% to 11% in test length over the traditional adaptive test to reach the same error level and, using testlets requires an increase of 43% to 104% in test length over the traditional adaptive test. Given these results, the use of constrained computerized adaptive testing is recommended for situations in which an adaptive test must adhere to particular content specifications.     

A Closer Look at Using Judgments of Item Difficulty to Change Answers on Computerized Adaptive Tests

Recent studies have shown that restricting review and answer change opportunities on computerized adaptive tests (CATs) to items within successive blocks reduces time spent in review, satisfies most examinees' desires for review, and controls against distortion in proficiency estimates resulting from intentional incorrect answering of items prior to review. However, restricting review opportunities on CATs may not prevent examinees from artificially raising proficiency estimates by using judgments of item difficulty to signal when to change previous answers. We evaluated six strategies for using item difficulty judgments to change answers on CATs and compared the results to those from examinees reviewing and changing answers in the usual manner. The strategy conditions varied in terms of when examinees were prompted to consider changing answers and in the information provided about the consistency of the item selection algorithm. We found that examinees fared best on average when they reviewed and changed answers in the usual manner. The best gaming strategy was one in which the examinees knew something about the consistency of the item selection algorithm and were prompted to change responses only when they were unsure about answer correctness and sure about their item difficulty judgments. However, even this strategy did not produce a mean gain in proficiency estimates.     

Item Response Models for Examinee‐Selected Items

In some tests, examinees are required to choose a fixed number of items from a set of given items to answer. This practice creates a challenge to standard item response models, because more capable examinees may have an advantage by making wiser choices. In this study, we developed a new class of item response models to account for the choice effect of examinee‐selected items. The results of a series of simulation studies showed: (1) that the parameters of the new models were recovered well, (2) the parameter estimates were almost unbiased when the new models were fit to data that were simulated from standard item response models, (3) failing to consider the choice effect yielded shrunken parameter estimates for examinee‐selected items, and (4) even when the missingness mechanism in examinee‐selected items did not follow the item response functions specified in the new models, the new models still yielded a better fit than did standard item response models. An empirical example of a college entrance examination supported the use of the new models: in general, the higher the examinee's ability, the better his or her choice of items.     

Can Examinees Use Judgments of Item Difficulty to Improve Proficiency Estimates on Computerized Adaptive Vocabulary Tests?

Recent simulation studies indicate that there are occasions when examinees can use judgments of relative item difficulty to obtain positively biased proficiency estimates on computerized adaptive tests (CATs) that permit item review and answer change. Our purpose in the study reported here was to evaluate examinees' success in using these strategies while taking CATs in a live testing setting. We taught examinees two item difficulty judgment strategies designed to increase proficiency estimates. Examinees who were taught each strategy and examinees who were taught neither strategy were assigned at random to complete vocabulary CATs under conditions in which review was allowed after completing all items and when review was allowed only within successive blocks of items. We found that proficiency estimate changes following review were significantly higher in the regular review conditions than in the strategy conditions. Failure to obtain systematically higher scores in the strategy conditions was due in large part to errors examinees made in judging the relative difficulty of CAT items.     

Item Selection in Computerized Adaptive Testing: Should More Discriminating Items be Used First?

During computerized adaptive testing (CAT), items are selected continuously according to the test-taker's estimated ability. The traditional method of attaining the highest efficiency in ability estimation is to select items of maximum Fisher information at the currently estimated ability. Test security has become a problem because high-discrimination items are more likely to be selected and become overexposed. So, there seems to be a tradeoff between high efficiency in ability estimations and balanced usage of items. This series of four studies with simulated data addressed the dilemma by focusing on the notion of whether more or less discriminating items should be used first in CAT. The first study demonstrated that the common maximum information method with Sympson and Hetter (1985) control resulted in the use of more discriminating items first. The remaining studies showed that using items in the reverse order (i.e., less discriminating items first), as described in Chang and Ying's (1999) stratified method had potential advantages: (a) a more balanced item usage and (b) a relatively stable resultant item pool structure with easy and inexpensive management. This stratified method may have ability-estimation efficiency better than or close to that of other methods, particularly for operational item pools when retired items cannot be totally replenished with similar highly discriminating items. It is argued that the judicious selection of items, as in the stratified method, is a more active control of item exposure, which can successfully even out the usage of all items.     

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.     

Minimizing the Influence of Item Parameter Estimation Errors in Test Development: A Comparison of Three Selection Procedures

In test development, item response theory (IRT) is a method to determine the amount of information that each item (i.e., item information function) and combination of items (i.e., test information function) provide in the estimation of an examinee's ability. Studies investigating the effects of item parameter estimation errors over a range of ability have demonstrated an overestimation of information when the most discriminating items are selected (i.e., item selection based on maximum information). In the present study, the authors examined the influence of item parameter estimation errors across 3 item selection methods—maximum no target, maximum target, and theta maximum—using the 2- and 3-parameter logistic IRT models. Tests created with the maximum no target and maximum target item selection procedures consistently overestimated the test information function. Conversely, tests created using the theta maximum item selection procedure yielded more consistent estimates of the test information function and, at times, underestimated the test information function. Implications for test development are discussed.     

Item Difficulty of Four Verbal Item Types and an Index of Differential Item Functioning for Black and White Examinees

In this study, the authors explored the importance of item difficulty (equated delta) as a predictor of differential item functioning (DIF) of Black versus matched White examinees for four verbal item types (analogies, antonyms, sentence completions, reading comprehension) using 13 GRE-disclosed forms (988 verbal items) and 11 SAT-disclosed forms (935 verbal items). The average correlation across test forms for each item type (and often the correlation for each individual test form as well) revealed a significant relationship between item difficulty and DIF value for both GRE and SAT. The most important finding indicates that for hard items, Black examinees perform differentially better than matched ability White examinees for each of the four item types and for both the GRE and SAT tests! The results further suggest that the amount of verbal context is an important determinant of the magnitude of the relationship between item difficulty and differential performance of Black versus matched White examinees. Several hypotheses accounting for this result were explored.     

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.     

计算机自适应测验中Rasch模型稳健性的模拟研究

本研究采用模拟数据的方法,在计算机自适应测验(Computer Adaptive Test,简称CAT)中分别采用Rasch及Birnbaum两种模型估计能力,通过比较两者的误差均方根(Root Mean Square Error,简称RMSE)、平均差异(Average Deviation,简称AD)及能力相关,对Rasch模型在CAT中的稳健性进行了研究。结果发现Rasch模型在区分度不等的条件下仍然能较准确地估计被试的能力水平,具有很强的稳健性。     

Psychometric and Cognitive Functioning of an Under-Determined Computer-Based Response Type for Quantitative Reasoning

We evaluated a computer-delivered response type for measuring quantitative skill. "Generating Examples" (GE) presents under-determined problems that can have many right answers. We administered two GE tests that differed in the manipulation of specific item features hypothesized to affect difficulty. Analyses related to internal consistency reliability, external relations, and features contributing to item difficulty, adverse impact, and examinee perceptions. Results showed that GE scores were reasonably reliable but only moderately related to the GRE quantitative section, suggesting the two tests might be tapping somewhat different skills. Item features that increased difficulty included asking examinees to supply more than one correct answer and to identify whether an item was solvable. Gender differences were similar to those found on the GRE quantitative and analytical test sections. Finally, examinees were divided on whether GE items were a fairer indicator of ability than multiple-choice items, but still overwhelmingly preferred to take the more conventional questions.     

How to Equate Tests With Little or No Data

Standard procedures for equating tests, including those based on item response theory (IRT), require item responses from large numbers of examinees. Such data may not be forthcoming for reasons theoretical, political, or practical. Information about items' operating characteristics may be available from other sources, however, such as content and format specifications, expert opinion, or psychological theories about the skills and strategies required to solve them. This article shows how, in the IRT framework, collateral information about items can be exploited to augment or even replace examinee responses when linking or equating new tests to established scales. The procedures are illustrated with data from the Pre-Professional Skills Test (PPST).     

On the Relative Value of Multiple-Choice, Constructed Response, and Examinee-Selected Items on Two Achievement Tests

Using analyses based on fitting item response models to data from the College Board's Advanced Placement exams in chemistry and United States history, we found that the constructed response portion of the tests yielded little information over and above that provided by the multiple-choice sections. These tests also allow examinees to select subsets of the constructed response items; we found that scoring on the basis of the selections themselves provided almost as much information as did scoring on the basis of the answers     

Item Parameter Estimation Under Conditions of Test Speededness: Application of a Mixture Rasch Model With Ordinal Constraints

When tests are administered under fixed time constraints, test performances can be affected by speededness. Among other consequences, speededness can result in inaccurate parameter estimates in item response theory (IRT) models, especially for items located near the end of tests (Oshima, 1994). This article presents an IRT strategy for reducing contamination in item difficulty estimates due to speededness. Ordinal constraints are applied to a mixture Rasch model (Rost, 1990) so as to distinguish two latent classes of examinees: (a) a "speeded" class, comprised of examinees that had insufficient time to adequately answer end-of-test items, and (b) a "nonspeeded" class, comprised of examinees that had sufficient time to answer all items. The parameter estimates obtained for end-of-test items in the nonspeeded class are shown to more accurately approximate their difficulties when the items are administered at earlier locations on a different form of the test. A mixture model can also be used to estimate the class memberships of individual examinees. In this way, it can be determined whether membership in the speeded class is associated with other student characteristics. Results are reported for gender and ethnicity.     

A Method for Maintaining Scale Stability in the Presence of Test Speededness

Administering tests under time constraints may result in poorly estimated item parameters, particularly for items at the end of the test (Douglas, Kim, Habing, & Gao, 1998; Oshima, 1994). Bolt, Cohen, and Wollack (2002) developed an item response theory mixture model to identify a latent group of examinees for whom a test is overly speeded, and found that item parameter estimates for end-of-test items in the nonspeeded group were similar to estimates for those same items when administered earlier in the test. In this study, we used the Bolt et al. (2002) method to study the effect of removing speeded examinees on the stability of a score scale over an II-year period. Results indicated that using only the nonspeeded examinees for equating and estimating item parameters provided a more unidimensional scale, smaller effects of item parameter drift (including fewer drifting items), and less scale drift (i.e., bias) and variability (i.e., root mean squared errors) when compared to the total group of examinees.     

A New Stopping Rule for Computerized Adaptive Testing

The goal of the current study was to introduce a new stopping rule for computerized adaptive testing. The predicted standard error reduction stopping rule (PSER) uses the predictive posterior variance to determine the reduction in standard error that would result from the administration of additional items. The performance of the PSER was compared to that of the minimum standard error stopping rule and a modified version of the minimum information stopping rule in a series of simulated adaptive tests, drawn from a number of item pools. Results indicate that the PSER makes efficient use of CAT item pools, administering fewer items when predictive gains in information are small and increasing measurement precision when information is abundant.     

A COMPARISON OF EXAMINEE SAMPLING AND MULTIPLE MATRIX SAMPLING IN TEST DEVELOPMENT

For the purpose of obtaining data to use in test development, multiple matrix sampling (MMS) plans were compared to examinee sampling plans. Data were simulated for examinees, sampled from a population with a normal distribution of ability, responding to items selected from an item universe. Three item universes were considered: one that would produce a normal distribution of test scores, one a moderately platykurtic distribution, and one a very platykurtic distribution. When comparing sampling plans, total numbers of observations were held constant. No differences were found among plans in estimating item difficulty. Examinee sampling produced better estimates of item discrimination, test reliability, and test validity. As total number of observations increased, estimates improved considerably, especially for those MMS plans with larger subtest sizes. Larger numbers of observations were needed for tests designed to produce a normal distribution of test scores. With an adequate number of observations, MMS is seen as an alternative to examinee sampling in test development.