Purpose: The present study aims to evaluate how the reliabilities computed using a, Stratified a, Angoff-Feldt, and Feldt-Raju estimators may differ when sample size (500, 1000, and 2000) and item type ratio of dichotomous to polytomous items (2:1; 1:1, 1:2) included in the scale are varied. Research Methods: In this study, Cronbach's a,…

Purpose: Based on the general formula, which depends on the length and difficulty of the test, the number of respondents and the number of ability levels, this study aims to provide a closed formula for the adaptive tests with medium difficulty (probability of solution is p = 1/2) to determine the accuracy of the parameters for each item and in…

Although content validity--how well each item of an instrument represents the construct being measured--is foundational in the development of an instrument, statistical validity is also important to the decisions that are made based on the instrument. The primary purpose of this study is to demonstrate how simulation studies can be used to assist…

This study examines the effect of differential item functioning (DIF) items on test equating through multilevel item response models (MIRMs) and traditional IRMs. The performances of three different equating models were investigated under 24 different simulation conditions, and the variables whose effects were examined included sample size, test…

The purpose of this study was to evaluate the combined effects of reduced equating sample size and shortened anchor test length on item response theory (IRT)-based linking and equating results. Data from two independent operational forms of a large-scale testing program were used to establish the baseline results for evaluating the results from…

Small sample equating remains a largely unexplored area of research. This study attempts to fill in some of the research gaps via a large-scale, IRT-based simulation study that evaluates the performance of seven small-sample equating methods under various test characteristic and sampling conditions. The equating methods considered are typically…

A simulation study was performed to determine whether a group's average percent correct in a content domain could be accurately estimated for groups taking a single test form and not the entire domain of items. Six Item Response Theory (IRT) -based domain score estimation methods were evaluated, under conditions of few items per content area per…

A new index for assessing the dimensionality underlying a set of test items was investigated. The incremental fit index (IFI) is based on the sum of squares of the residual covariances. Purposes of the study were to: (1) examine the distribution of the IFI in the null situation, with truly unidimensional data; (2) examine the rejection rate of the…