Editor SANDIP SINHARAY, Educational Testing Service

Response time has started to play an increasingly important role in educational and psychological testing, which prompts many response time models to be proposed in recent years. However, response time modeling can be adversely impacted by aberrant response behavior. For example, test speededness can cause response time to certain items to deviate from the hypothesized model. In this article, we introduce

By tailoring test forms to the test‐taker's proficiency, Computerized Adaptive Testing (CAT) enables substantial increases in testing efficiency over fixed forms testing. When used for formative assessment, the alignment of task difficulty with proficiency increases the chance that teachers can derive useful feedback from assessment data. The application of CAT to formative assessment in the classroom

Editor SANDIP SINHARAY, Educational Testing Service

Van der Linden's hierarchical model for responses and response times can be used in order to infer the ability and mental speed of test takers from their responses and response times in an educational test. A standard approach for this is maximum likelihood estimation. In real‐world applications, the data of some test takers might be partly irregular, resulting from rapid guessing or item preknowledge

In his 2019 NCME Career Contributions Award address, Dr. Shelby Haberman uses examples of three kinds to illustrate how his training in theoretical statistics influenced his contributions to educational measurement. I bracket my comments on his address, and his contributions more generally, by considering two questions: Why might any theoretical statisticians receive this award? Why aren't all recipients

Examples of the impact of statistical theory on assessment practice are provided from the perspective of a statistician trained in theoretical statistics who began to work on assessments. Goodness of fit of item‐response models is examined in terms of restricted likelihood‐ratio tests and generalized residuals. Minimum discriminant information adjustment is used for linking with no anchors or problematic

In vertical scaling, results of tests from several different grade levels are placed on a common scale. Most vertical scaling methodologies rely heavily on the assumption that the construct being measured is unidimensional. In many testing situations, however, such an assumption could be problematic. For instance, the construct measured at one grade level may differ from that measured in another grade

Estimates of various variance components, universe score variance, measurement error variances, and generalizability coefficients, like all statistics, are subject to sampling variability, particularly in small samples. Such variability is quantified traditionally through estimated standard errors and/or confidence intervals. The paper derived new standard errors for all estimated statistics for two

There has been a growing research interest in the identification and management of disengaged test taking, which poses a validity threat that is particularly prevalent with low‐stakes tests. This study investigated effort‐moderated (E‐M) scoring, in which item responses classified as rapid guesses are identified and excluded from scoring. Using achievement test data composed of test takers who were

This study proposed a recursion‐based analytical approach to assess measurement precision of ability estimation and classification accuracy in multistage adaptive tests (MSTs). A simulation study was conducted to compare the proposed recursion‐based analytical method with an analytical method proposed by Park, Kim, Chung, and Dodd and with the more commonly used Monte Carlo (MC) simulation approaches

Item nonresponses are prevalent in standardized testing. They happen either when students fail to reach the end of a test due to a time limit or quitting, or when students choose to omit some items strategically. Oftentimes, item nonresponses are nonrandom, and hence, the missing data mechanism needs to be properly modeled. In this paper, we proposed to use an innovative item response time model as

Item Response Theory models with varying thresholds are essential tools to account for unknown types of response tendencies in rating data. However, in order to separate constructs to be measured and response tendencies, specific constraints have to be imposed on varying thresholds and their interrelations. In this article, a multidimensional extension of a Partial Credit Model using a sum‐to‐zero

In this article, it is shown how item text can be represented by (a) 113 features quantifying the text's linguistic characteristics, (b) 16 measures of the extent to which an information‐retrieval‐based automatic question‐answering system finds an item challenging, and (c) through dense word representations (word embeddings). Using a random forests algorithm, these data then are used to train a prediction

In signal detection rater models for constructed response (CR) scoring, it is assumed that raters discriminate equally well between different latent classes defined by the scoring rubric. An extended model that relaxes this assumption is introduced; the model recognizes that a rater may not discriminate equally well between some of the scoring classes. The extension recognizes a different type of rater

A key consideration when giving any computerized adaptive test (CAT) is how much adaptation is present when the test is used in practice. This study introduces a new framework to measure the amount of adaptation of Rasch‐based CATs based on looking at the differences between the selected item locations (Rasch item difficulty parameters) of the administered items and target item locations determined

For assessments that use different forms in different administrations, equating methods are applied to ensure comparability of scores over time. Ideally, a score scale is well maintained throughout the life of a testing program. In reality, instability of a score scale can result from a variety of causes, some are expected while others may be unforeseen. The situation is more challenging for assessments

Although the root‐mean squared deviation (RMSD) is a popular statistical measure for evaluating country‐specific item‐level misfit (i.e., differential item functioning [DIF]) in international large‐scale assessment, this paper shows that its sensitivity to detect misfit may depend strongly on the proficiency distribution of the considered countries. Specifically, items for which most respondents in

Automated test assembly (ATA) is a modern approach to test assembly that applies advanced optimization algorithms on computers to build test forms automatically. ATA greatly improves the efficiency and accuracy of the test assembly. This study investigated the effects of the modeling methods and solvers in the mixed‐integer programming (MIP) approach to ATA in the context of assembling parallel linear

This article presents the pseudo‐equivalent group approach and discusses how it can enhance the quality of linking in the presence of nonequivalent groups. The pseudo‐equivalent group approach allows to achieve pseudo‐equivalence using propensity score reweighting techniques. We use it to perform linking to establish scale concordance between two assessments. The article presents Monte‐Carlo simulations

Multilevel bifactor item response theory (IRT) models are commonly used to account for features of the data that are related to the sampling and measurement processes used to gather those data. These models conventionally make assumptions about the portions of the data structure that represent these features. Unfortunately, when data violate these models' assumptions but these models are used anyway

We make a distinction between the operational practice of using an observed score to assess differential item functioning (DIF) and the concept of departure from measurement invariance (DMI) that conditions on a latent variable. DMI and DIF indices of effect sizes, based on the Mantel‐Haenszel test of common odds ratio, converge under restricted conditions if a simple sum score is used as the matching

Smoothing is designed to yield smoother equating results that can reduce random equating error without introducing very much systematic error. The main objective of this study is to propose a new statistic and to compare its performance to the performance of the Akaike information criterion and likelihood ratio chi‐square difference statistics in selecting the smoothing parameter for polynomial loglinear

Does reviewing previous answers during multiple‐choice exams help examinees increase their final score? This article formalizes the question using a rigorous causal framework, the potential outcomes framework. Viewing examinees’ reviewing status as a treatment and their final score as an outcome, the article first explains the challenges of identifying the causal effect of answer reviewing in regular

One of the methods of controlling test security in adaptive testing is imposing random item‐ineligibility constraints on the selection of the items with probabilities automatically updated to maintain a predetermined upper bound on the exposure rates. Three major improvements of the method are presented. First, a few modifications to improve the initialization of the method and accelerate the impact

The residual gain score has been of historical interest, and its percentile rank has been of interest more recently given its close correspondence to the popular Student Growth Percentile. However, these estimators suffer from low accuracy and systematic bias (bias conditional on prior latent achievement). This article explores three alternatives—using the expected a posterior (EAP), conditioning on

Testing programs are often interested in using a student growth measure. This article presents analytic derivations of the accuracy of common student growth measures on both the raw scale of the test and the percentile rank scale in terms of the proportional reduction in mean squared error and the squared correlation between the estimator and target. The study contrasts the accuracy of the growth measures

This article considers psychometric properties of composite raw scores and transformed scale scores on mixed‐format tests that consist of a mixture of multiple‐choice and free‐response items. Test scores on several mixed‐format tests are evaluated with respect to conditional and overall standard errors of measurement, score reliability, and classification consistency and accuracy under three item response

The use of computerized adaptive testing algorithms for ranking items (e.g., college preferences, career choices) involves two major challenges: unacceptably high computation times (selecting from a large item pool with many dimensions) and biased results (enhanced preferences or intensified examinee responses because of repeated statements across items). To address these issues, we introduce subpool

A robust body of evidence supports the finding that particular teaching and assessment strategies in the K‐12 classroom can improve student achievement. While experts have identified many effective teaching and learning practices in the assessment for learning literature, teachers’ knowledge and use of “high leverage” formative assessment (FA) practices are difficult to model in novice populations

In equating, smoothing techniques are frequently used to diminish sampling error. There are typically two types of smoothing: presmoothing and postsmoothing. For polynomial log‐linear presmoothing, an optimum smoothing degree can be determined statistically based on the Akaike information criterion or Chi‐square difference criterion. For cubic‐spline postsmoothing, visual inspection has been an important

The literature suggests that simple expert (mathematical) models can improve the quality of decisions, but people are not always eager to accept and endorse such models. We ran three online experiments to test the receptiveness to advice from computerized expert models. Middle‐ and high‐school teachers (N = 435) evaluated student profiles that varied in several personal and task relevant factors. They

An assessment of graphic literacy was developed by articulating and subsequently validating a skills‐based cognitive model intended to substantiate the plausibility of score interpretations. Model validation involved use of multiple sources of evidence derived from large‐scale field testing and cognitive labs studies. Data from large‐scale field testing were evaluated using traditional psychometric

In the logistic regression (LR) procedure for differential item functioning (DIF), the parameters of LR have often been estimated using maximum likelihood (ML) estimation. However, ML estimation suffers from the finite‐sample bias. Furthermore, ML estimation for LR can be substantially biased in the presence of rare event data. The bias of ML estimation due to small samples and rare event data can

An Angoff standard setting study generally yields judgments on a number of items by a number of judges (who may or may not be nested in panels). Variability associated with judges (and possibly panels) contributes error to the resulting cut score. The variability associated with items plays a more complicated role. To the extent that the mean item judgments directly reflect empirical item difficulties

The current study aims to evaluate the performance of three non‐IRT procedures (i.e., normal approximation, Livingston‐Lewis, and compound multinomial) for estimating classification indices when the observed score distribution shows atypical patterns: (a) bimodality, (b) structural (i.e., systematic) bumpiness, or (c) structural zeros (i.e., no frequencies). Under a bimodal distribution, the normal

This study addresses the topic of how anchoring methods for differential item functioning (DIF) analysis can be used in multigroup scenarios. The direct approach would be to combine anchoring methods developed for two‐group scenarios with multigroup DIF‐detection methods. Alternatively, multiple tests could be carried out. The results of these tests need to be aggregated to determine the anchor for

Many large‐scale educational surveys have moved from linear form design to multistage testing (MST) design. One advantage of MST is that it can provide more accurate latent trait (θ) estimates using fewer items than required by linear tests. However, MST generates incomplete response data by design; hence, questions remain as to how to calibrate items using the incomplete data from MST design. Further

When a response pattern does not fit a selected measurement model, one may resort to robust ability estimation. Two popular robust methods are biweight and Huber weight. So far, research on these methods has been quite limited. This article proposes the maximum a posteriori biweight (BMAP) and Huber weight (HMAP) estimation methods. These methods use the Bayesian prior distribution to compensate for

Data‐based decision making (DBDM) is presumed to improve student performance in elementary schools in all subjects. The majority of studies in which DBDM effects have been evaluated have focused on mathematics. A hierarchical multiple single‐subject design was used to measure effects of a 2‐year training, in which entire school teams learned how to implement and sustain DBDM, in 39 elementary schools

The process of setting and evaluating student learning objectives (SLOs) has become increasingly popular as an example where classroom assessment is intended to fulfill the dual purpose use of informing instruction and holding teachers accountable. A concern is that the high‐stakes purpose may lead to distortions in the inferences about students and teachers that SLOs can support. This concern is explored

This article describes an ongoing project to develop a formative, inferential reading comprehension assessment of causal story comprehension. It has three features to enhance classroom use: equated scale scores for progress monitoring within and across grades, a scale score to distinguish among low‐scoring students based on patterns of mistakes, and a reading efficiency index. Instead of two response

Classroom assessment and large‐scale assessment have, for the most part, existed in mutual isolation. Some experts have felt this is for the best and others have been concerned that the schism limits the potential contribution of both forms of assessment. Margaret Heritage has long been a champion of best practices in classroom assessment. Neal Kingston has been involved with the application of psychometrics

If K‐12 students are to be fully integrated as active participants in their own learning, understanding how they interpret formative assessment feedback is needed. The objective of this article is to advance three claims about why teachers and assessment scholars/specialists may have little understanding of students’ interpretation of formative assessment feedback. The three claims are as follows.

The van Hiele theory and van Hiele Geometry Test have been extensively used in mathematics assessments across countries. The purpose of this study is to use classical test theory (CTT) and cognitive diagnostic modeling (CDM) frameworks to examine psychometric properties of the van Hiele Geometry Test and to compare how various classification criteria assign van Hiele levels to students. The findings

In educational practice, test results are used for several purposes. However, validity research is especially focused on the validity of summative assessment. This article aimed to provide a general framework for validating formative assessment. The authors applied the argument‐based approach to validation to the context of formative assessment. This resulted in a proposed interpretation and use argument

Although much attention has been given to rater effects in rater‐mediated assessment contexts, little research has examined the overall stability of leniency and severity effects over time. This study examined longitudinal scoring data collected during three consecutive administrations of a large‐scale, multi‐state summative assessment program. Multilevel models were used to assess the overall extent

The purpose of this study was to build a Random Forest supervised machine learning model in order to predict musical rater‐type classifications based upon a Rasch analysis of raters’ differential severity/leniency related to item use. Raw scores (N = 1,704) from 142 raters across nine high school solo and ensemble festivals (grades 9–12) were collected using a 29‐item Likert‐type rating scale embedded

New items are often evaluated prior to their operational use to obtain item response theory (IRT) item parameter estimates for quality control purposes. Fixed parameter calibration is one linking method that is widely used to estimate parameters for new items and place them on the desired scale. This article provides detailed descriptions of two fixed parameter calibration methods for the bifactor

Many large‐scale assessments are designed to yield two or more scores for an individual by administering multiple sections measuring different but related skills. Multidimensional tests, or more specifically, simple structured tests, such as these rely on multiple multiple‐choice and/or constructed responses sections of items to generate multiple scores. In the current article, we propose an extension

To capitalize on professional expertise in educational assessment, it is desirable to develop and test methods of rater‐mediated assessment that enable classroom teachers to make reliable and informative judgments. Accordingly, this article investigates the reliability of a two‐stage method used by classroom teachers to assess primary school students’ persuasive writing. Stage 1 involves pairwise comparisons

Rater‐mediated assessments require the evaluation of the accuracy and consistency of the inferences made by the raters to ensure the validity of score interpretations and uses. Modeling rater response processes allows for a better understanding of how raters map their representations of the examinee performance to their representation of the scoring criteria. Validity of score meaning is affected by

Rater‐mediated assessments exhibit scoring challenges due to the involvement of human raters. The quality of human ratings largely determines the reliability, validity, and fairness of the assessment process. Our research recommends that the evaluation of ratings should be based on two aspects: a theoretical model of human judgment and an appropriate measurement model for evaluating these judgments

Numerous researchers have proposed methods for evaluating the quality of rater‐mediated assessments using nonparametric methods (e.g., kappa coefficients) and parametric methods (e.g., the many‐facet Rasch model). Generally speaking, popular nonparametric methods for evaluating rating quality are not based on a particular measurement theory. On the other hand, popular parametric methods for evaluating

Rater‐mediated assessments are a common methodology for measuring persons, investigating rater behavior, and/or defining latent constructs. The purpose of this article is to provide a pedagogical framework for examining rater variability in the context of rater‐mediated assessments using three distinct models. The first model is the observation model, which includes ecological/environmental considerations

In educational and psychological measurement, a person‐fit statistic (PFS) is designed to identify aberrant response patterns. For parametric PFSs, valid inference depends on several assumptions, one of which is that the item response theory (IRT) model is correctly specified. Previous studies have used empirical data sets to explore the effects of model misspecification on PFSs. We further this line

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

Scores estimated from multidimensional item response theory (IRT) models are not necessarily comparable across dimensions. In this article, the concept of aligned dimensions is formalized in the context of Rasch models, and two methods are described—delta dimensional alignment (DDA) and logistic regression alignment (LRA)—to transform estimated item parameters so that dimensions are aligned. Both the

Allowance for multiple chances to answer constructed response questions is a prevalent feature in computer‐based homework and exams. We consider the use of item response theory in the estimation of item characteristics and student ability when multiple attempts are allowed but no explicit penalty is deducted for extra tries. This is common practice in online formative assessments, where the number

Ensuring postsecondary readiness is a goal of K‐12 education, but it is unclear whether high school students should get different messages about the required levels of academic preparation depending on their postsecondary trajectories. This study estimated readiness benchmark scores on a college admissions test predictive of earning good grades in majors associated with middle‐skills occupations at