A conceptualization of multiple-choice exams in terms of signal detection theory (SDT) leads to simple measures of item difficulty and item discrimination that are closely related to, but also distinct from, those used in classical item analysis (CIA). The theory defines a "true split," depending on whether or not examinees know an item,…

This simulation study examines the characteristics of the Explanatory Item Response Model (EIRM) when estimating treatment effects when compared to classical test theory (CTT) sum and mean scores and item response theory (IRT)-based theta scores. Results show that the EIRM and IRT theta scores provide generally equivalent bias and false positive…

The aim of this simulation study, determine the relationship between true latent scores and estimated latent scores by including various control variables and different statistical models. The study also aimed to compare the statistical models and determine the effects of different distribution types, response formats and sample sizes on latent…

There is a need for developmentally appropriate Computational Thinking (CT) assessments that can be implemented in early childhood classrooms. We developed a new instrument called "TechCheck" for assessing CT skills in young children that does not require prior knowledge of computer programming. "TechCheck" is based on…

A classic topic in the fields of psychometrics and measurement has been the impact of the number of scale categories on test score reliability. This study builds on previous research by further articulating the relationship between item response theory (IRT) and classical test theory (CTT). Equations are presented for comparing the reliability and…

Professional standards for educational testing recommend that both the overall standard error of measurement and the conditional standard error of measurement (CSEM) be computed on the score scale used to report scores to examinees. Several methods have been developed to compute scale score CSEMs. This paper compares three methods, based on…

It has been argued that item response theory trait estimates should be used in analyses rather than number right (NR) or summated scale (SS) scores. Thissen and Orlando postulated that IRT scaling tends to produce trait estimates that are linearly related to the underlying trait being measured. Therefore, IRT trait estimates can be more useful…

Will subscores provide additional information than what is provided by the total score? Is there a method that can estimate more trustworthy subscores than observed subscores? To answer the first question, this study evaluated whether the true subscore was more accurately predicted by the observed subscore or total score. To answer the second…

Within a response to intervention model, educators increasingly use progress monitoring (PM) to support medium- to high-stakes decisions for individual students. For PM to serve these more demanding decisions requires more careful consideration of measurement error. That error should be calculated within a fixed linear regression model rather than…

The purpose of this study was to develop general outcome measures (GOM) in mathematics so that teachers could focus their instruction on needed prerequisite skills. We describe in detail, the manner in which content-related evidence was established and then present a number of statistical analyses conducted to evaluate the technical adequacy of…

In educational tests, subscores are often generated from a portion of the items in a larger test. Guidelines based on mean-squared error are proposed to indicate whether subscores are worth reporting. Alternatives considered are direct reports of subscores, estimates of subscores based on total score, combined estimates based on subscores and…