The Chain and Post‐Stratification Methods for Observed‐Score Equating: Their Relationship to Population Invariance

Alina A. von Davier · Paul W. Holland · Dorothy T. Thayer

80 citations0/0 files storedJournal of Educational Measurement

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Educational Technology and Assessment

Abstract

The Non‐Equivalent‐groups Anchor Test (NEAT) design has been in wide use since at least the early 1940s. It involves two populations of test takers, P and Q, and makes use of an anchor test to link them. Two linking methods used for NEAT designs are those (a) based on chain equating and (b) that use the anchor test to post‐stratify the distributions of the two operational test scores to a common population (i.e., Tucker equating and frequency estimation). We show that, under different sets of assumptions, both methods are observed score equating methods and we give conditions under which the methods give identical results. In addition, we develop analogues of the Dorans and Holland (2000) RMSD measures of population invariance of equating methods for the NEAT design for both chain and post‐stratification equating methods.

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1950Theory of Mental Tests 1952Review of Educational Measurement.2012Test Equating: Methods and Practices 2004The Kernel Method of Test Equating 1995Test Equating 2000Population Invariance and the Equatability of Tests: Basic Theory and The Linear Case 2000Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions 1990What Combination of Sampling and Equating Methods Works Best?

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2008A Comparison of the Frequency Estimation and Chained Equipercentile Methods Under the Common-Item Nonequivalent Groups Design 20066 Equating Test Scores 2013Observed-Score Equating: An Overview 2008Anchor Test Type and Population Invariance: An Exploration Across Subpopulations and Test Administrations 2005A Unified Approach to Linear Equating for the Nonequivalent Groups Design

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