Coefficient alpha reliability persists as the most common reliability coefficient reported in research. The assumptions for its use are, however, not well-understood. The current paper challenges the commonly used expressions of coefficient alpha and argues that while these expressions are correct when estimating reliability for summed scores,…

The generalized S-X[superscript 2]-test is a test of item fit for items with polytomous responses format. The test is based on a comparison of the observed and expected number of responses in strata defined by the test score. In this article, we make four contributions. We demonstrate that the performance of the generalized S-X[superscript 2]-test…

Examinees with item preknowledge tend to obtain inflated test scores that undermine test score validity. With the availability of process data collected in computer-based assessments, the research on detecting item preknowledge has progressed on using both item scores and response times. Item revisit patterns of examinees can also be utilized as…

A potential negative consequence of high-stakes testing is inappropriate test behaviour involving individuals and/or institutions. Inappropriate test behaviour and test collusion can result in aberrant response patterns and anomalous test scores and invalidate the intended interpretation and use of test results. A variety of statistical techniques…

As a result of the COVID-19 pandemic, at-home testing has become a popular delivery mode in many testing programs. When programs offer at-home testing to expand their service, the score comparability between test takers testing remotely and those testing in a test center is critical. This article summarizes statistical procedures that could be…

Pearson product-moment correlation coefficient between item g and test score X, known as item-test or item-total correlation ("Rit"), and item-rest correlation ("Rir") are two of the most used classical estimators for item discrimination power (IDP). Both "Rit" and "Rir" underestimate IDP caused by the…

The interpretation of psychometric test results is usually based on norm scores. We compared semiparametric continuous norming (SPCN) with conventional norming methods by simulating results for test scales with different item numbers and difficulties via an item response theory approach. Subsequently, we modeled the norm scores based on random…

Forced-choice questionnaires have been proposed to avoid common response biases typically associated with rating scale questionnaires. To overcome ipsativity issues of trait scores obtained from classical scoring approaches of forced-choice items, advanced methods from item response theory (IRT) such as the Thurstonian IRT model have been…

According to Wollack and Schoenig (2018), benefitting from item preknowledge is one of the three broad types of test fraud that occur in educational assessments. We use tools from constrained statistical inference to suggest a new statistic that is based on item scores and response times and can be used to detect the examinees who may have…

The design and psychometric methodology of the National Assessment of Educational Progress (NAEP) is constantly evolving to meet the changing interests and demands stemming from a rapidly shifting educational landscape. NAEP has been built on strong research foundations that include conducting extensive evaluations and comparisons before new…

This study developed an abbreviated form of Barron's (1953) Ego Strength Scale for use in research among college student samples. A version of Barron's scale was administered to 100 undergraduate college students. Using item-total score correlations and internal consistency, the scale was reduced to 18 items (Es18). The Es18 possessed adequate…

Within polytomous items, differential item functioning (DIF) can take on various forms due to the number of response categories. The lack of invariance at this level is referred to as differential step functioning (DSF). The most common DSF methods in the literature are the adjacent category log odds ratio (AC-LOR) estimator and cumulative…

In applications of item response theory (IRT), an estimate of the reliability of the ability estimates or sum scores is often reported. However, analytical expressions for the standard errors of the estimators of the reliability coefficients are not available in the literature and therefore the variability associated with the estimated reliability…

In this article, the authors applied profile analysis to Maths exam data to demonstrate how different exam forms, differing in difficulty and length, can be reported and easily interpreted. The results were presented for different groups of participants and for different institutions in different Maths domains by evaluating the balance. Some…

This study examined the effect of similar vs. dissimilar proficiency distributions on uniform DIF detection on a statewide eighth grade mathematics assessment. Results from the similar- and dissimilar-ability reference groups with an SWD focal group were compared for four models: logistic regression, hierarchical generalized linear model (HGLM),…