Assessment of measurement invariance is an essential component of construct validity in psychological measurement. However, the procedure for assessing measurement invariance with dichotomous items partially differs from that of invariance testing with continuous items. However, many studies have focused on invariance testing with continuous items…

The certainty of response index (CRI) measures respondents' confidence level when answering an item. In conjunction with the answers to the items, previous studies have used descriptive statistics and arbitrary thresholds to identify student knowledge profiles with the CRIs. Whereas this approach overlooked the measurement error of the observed…

In this study, the efficiency of various random sampling methods to reduce the number of items rated by judges in an Angoff standard-setting study was examined and the methods were compared with each other. Firstly, the full-length test was formed by combining Placement Test 2012 and 2013 mathematics subsets. After then, simple random sampling…

Multidimensional item response theory (MIRT) models have generated increasing interest in the psychometrics literature. Efficient approaches for estimating MIRT models with dichotomous responses have been developed, but constructing an equally efficient and robust algorithm for polytomous models has received limited attention. To address this gap,…

This study aimed at comparing the effect of two test item formats (multiple-choice and complete) on estimating person's ability, item parameters and the test information function (TIF).To achieve the aim of the study, two format of mathematics(1) test have been created: multiple-choice and complete, In its final format consisted of (31) items. The…

Comparatively little research exists on single-skill math (SSM) curriculum-based measurements (CBMs) for the purpose of monitoring growth, as may be done in practice or when monitoring intervention effectiveness within group or single-case research. Therefore, we examined a common variant of SSM-CBM: 1 digit × 1 digit multiplication. Reflecting…

In low-stakes assessments, some students may not reach the end of the test and leave some items unanswered due to various reasons (e.g., lack of test-taking motivation, poor time management, and test speededness). Not-reached items are often treated as incorrect or not-administered in the scoring process. However, when the proportion of…

This dissertation aims to investigate the effect size measures of differential item functioning (DIF) detection in the context of cognitive diagnostic models (CDMs). A variety of DIF detection techniques have been developed in the context of CDMs. However, most of the DIF detection procedures focus on the null hypothesis significance test. Few…

Item response theory (IRT) has so many advantages than its precedent Classical Test Theory (CTT) such as non-changing item parameters, ability parameter estimations free from the items. However, in order to get these advantages, some assumptions should be met and they are; unidimensionality, normality and local independence. However, it is not…

This report provides evidence of the substantive and structural validity of the Knowledge for Teaching Elementary Fractions Test. Field-test data were gathered with a sample of 241 elementary educators, including teachers, administrators, and instructional support personnel, in spring 2017, as part of a larger study involving a multisite…

The purpose of this research is to first estimate the item and ability parameters and the standard error values related to those parameters obtained from Unidimensional Item Response Theory (UIRT), bifactor (BIF) and Testlet Response Theory models (TRT) in the tests including testlets, when the number of testlets, number of independent items, and…

This simulation study examines the measurement precision, item exposure rates, and the depth of the MAP® Growth™ item pools under various grade-level restrictions. Unlike most summative assessments, MAP Growth allows examinees to see items from any grade level, regardless of the examinee's actual grade level. It does not limit the test to items…

The Early Fractions Test v2.2 is a paper-pencil test designed to measure mathematics achievement of third- and fourth-grade students in the domain of fractions. The purpose, or intended use, of the Early Fractions Test v2.2 is to serve as a measure of student outcomes in a randomized trial designed to estimate the effect of an educational…

Purpose: Studies in the literature have generally demonstrated that the causes of differential item functioning (DIF) are complex and not directly related to defined groups. The purpose of this study is to determine the DIF according to the mixture item response theory (MixIRT) model, based on the latent group approach, as well as the…

The standard error of equating quantifies the variability in the estimation of an equating function. Because common items for deriving equated scores are treated as fixed, the only source of variability typically considered arises from the estimation of common-item parameters from responses of samples of examinees. Use of alternative, equally…