Applying Test Equating Methods: Using R

Abstract

1ST ed. 2017. This book describes how to use test equating methods in practice. The non-commercial software R is used throughout the book to illustrate how to perform different equating methods when scores data are collected under different data collection designs, such as equivalent groups design, single group design, counterbalanced design and non equivalent groups with anchor test design. The R packages equate, kequate and SNSequate, among others, are used to practically illustrate the different methods, while simulated and real data sets illustrate how the methods are conducted with the program R. The book covers traditional equating methods including, mean and linear equating, frequency estimation equating and chain equating, as well as modern equating methods such as kernel equating, local equating and combinations of these. It also offers chapters on observed and true score item response theory equating and discusses recent developments within the equating field. More specifically it covers the issue of including covariates within the equating process, the use of different kernels and ways of selecting bandwidths in kernel equating, and the Bayesian nonparametric estimation of equating functions. It also illustrates how to evaluate equating in practice using simulation and different equating specific measures such as the standard error of equating, percent relative error, different that matters and others. Foreword; References; Preface; References; Contents; Acronyms; List of Symbols; 1 General Equating Theory Background; 1.1 Introduction; 1.1.1 A Conceptual Description of Equating; 1.1.2 A Statistical Model View of Equating; 1.2 Statistical Models; 1.2.1 General Definition, Notation, and Examples; 1.2.2 Types of Statistical Models; 1.2.3 Mathematical Statistics Formulation of the Equating Problem; 1.2.4 Mathematical Form of the Equating Transformation; 1.2.5 Continuization; 1.2.6 Requirements for Comparability of Scores; 1.2.7 Assessing the Uncertainty of Equating Results. 1.3 Collecting Data in Equating1.3.1 Data Collection Designs in Equating; 1.3.1.1 Single Group Design; 1.3.1.2 Equivalent Groups Design; 1.3.1.3 Counterbalanced Design; 1.3.1.4 Non Equivalent Groups with Anchor Test Design; 1.3.1.5 Non Equivalent Groups with Covariates Design; 1.4 Some Examples of Equating Transformations; 1.4.1 The Equipercentile Equating Function; 1.4.2 The Linear Equating Function; 1.4.3 The Kernel Equating Function; 1.5 R Packages That Are Used in This Book; 1.6 Summary and Overview of the Book; References; 2 Preparing Score Distributions; 2.1 Data. 2.1.1 Data from Ch2:kolenbrennan20142.1.2 Data from Ch2:vondavieretal2004; 2.1.3 The ADM Admissions Test Data; 2.1.4 The SEPA Test Data; 2.2 Preparing the Score Data; 2.2.1 Functions to Create Score Frequency Distributions; 2.2.2 Score Data in the EG Design; 2.2.3 Score Data in the SG Design; 2.2.4 Score Data in the NEAT Design; 2.3 Presmoothing the Score Distributions; 2.3.1 Polynomial Log-Linear Models for Presmoothing; 2.3.2 Polynomial Log-Linear Smoothing in equate; 2.3.3 Examples; 2.3.3.1 Smoothing Univariate Distributions; 2.3.3.2 Smoothing a Bivariate Distribution. 2.3.4 Choosing the Best Log-Linear Model2.4 Using Other Arguments, Packages and Functions; 2.5 Summary; References; 3 Traditional Equating Methods; 3.1 Equipercentile, Linear, and Mean Equating Transformations; 3.2 Assumptions in the Different Designs; 3.2.1 Assumptions in EG, SG, and CB Designs; 3.2.2 Assumptions in the NEAT Design; 3.3 Traditional Equating Methods for the EG, SG and CB Designs; 3.4 Traditional Equating Methods for the NEAT Design; 3.4.1 Linear Equating Methods for the NEAT Design; 3.4.1.1 Tucker Equating; 3.4.1.2 Nominal Weights Equating. 3.4.1.3 Levine Observed-Score Equating3.4.1.4 Levine True-Score Equating; 3.4.1.5 Chained Linear Equating; 3.4.2 Equipercentile Equating Methods for the NEAT Design; 3.4.2.1 Frequency Estimation; 3.4.2.2 Chained Equipercentile Equating; 3.4.2.3 Braun-Holland Equating; 3.5 Examples with the equate Function; 3.5.1 The equate Function; 3.5.2 Examples Under the EG and SG Designs; 3.5.3 Examples Under the NEAT Design; 3.5.3.1 Linear Methods; 3.5.3.2 Equipercentile Methods; 3.5.3.3 Comparison Between Linear and Equipercentile Methods; 3.5.4 Examples Using the ADM Data Under the NEAT Design.