Table Of ContentQuantitative Data Analysis for
Language Assessment Volume I
Quantitative Data Analysis for Language Assessment Volume I: Fundamental
Techniques is a resource book that presents the most fundamental techniques
of quantitative data analysis in the field of language assessment. Each chapter
provides an accessible explanation of the selected technique, a review of language
assessment studies that have used the technique, and finally, an example of an
authentic study that uses the technique. Readers also get a taste of how to apply
each technique through the help of supplementary online resources that include
sample datasets and guided instructions. Language assessment students, test
designers, and researchers should find this a unique reference, as it consolidates
theory and application of quantitative data analysis in language assessment.
Vahid Aryadoust is an Assistant Professor of language assessment literacy at the
National Institute of Education of Nanyang Technological University, Singapore.
He has led a number of language assessment research projects funded by, for
example, the Ministry of Education (Singapore), Michigan Language Assessment
(USA), Pearson Education (UK), and Paragon Testing Enterprises (Canada), and
published his research in, for example, Language Testing, Language Assessment
Quarterly, Assessing Writing, Educational Assessment, Educational Psychology,
and Computer Assisted Language Learning. He has also (co)authored a number
of book chapters and books that have been published by Routledge, Cambridge
University Press, Springer, Cambridge Scholar Publishing, Wiley Blackwell, etc.
He is a member of the Advisory Board of multiple international journals including
Language Testing, Language Assessment Quarterly, Educational Assessment,
Educational Psychology, and Asia Pacific Journal of Education. In addition, he
has been awarded the Intercontinental Academia Fellowship (2018–2019) which
is an advanced research program launched by the University-Based Institutes
for Advanced Studies. Vahid’s areas of interest include theory-building and
quantitative data analysis in language assessment, neuroimaging in language
comprehension, and eye-tracking research.
Michelle Raquel is a Senior Lecturer at the Centre of Applied English Studies,
University of Hong Kong, where she teaches language testing and assessment to
postgraduate students. She has extensive assessment development and management
experience in the Hong Kong education and government sector. In particular,
she has either led or been part of a group that designed and administered large-
scale computer-based language proficiency and diagnostic assessments such as the
Diagnostic English Language Tracking Assessment (DELTA). She specializes in
data analysis, specifically Rasch measurement, and has published several articles
in international journals on this topic as well as academic English, diagnostic
assessment, dynamic assessment of English second-language dramatic skills,
and English for specific purposes (ESP) testing. Michelle’s research areas are
classroom-based assessment, diagnostic assessment, and workplace assessment.
Routledge Research in Language Education
The Routledge Research in Language Education series provides a platform for
established and emerging scholars to present their latest research and discuss key
issues in Language Education. This series welcomes books on all areas of language
teaching and learning, including but not limited to language education policy
and politics, multilingualism, literacy, L1, L2 or foreign language acquisition,
curriculum, classroom practice, pedagogy, teaching materials, and language
teacher education and development. Books in the series are not limited to the
discussion of the teaching and learning of English only.
Books in the series include
Interdisciplinary Research Approaches to Multilingual Education
Edited by Vasilia Kourtis-Kazoullis, Themistoklis Aravossitas,
Eleni Skourtou and Peter Pericles Trifonas
From language skills to literacy
Broadening the scope of English language education through media literacy
Csilla Weninger
Addressing Difficult Situations in Foreign-Language Learning
Confusion, Impoliteness, and Hostility
Gerrard Mugford
Translanguaging in EFL Contexts
A Call for Change
Michael Rabbidge
Quantitative Data Analysis for Language Assessment Volume I
Fundamental Techniques
Edited by Vahid Aryadoust and Michelle Raquel
For more information about the series, please visit www.routledge.com/Routledge-
Research-in-Language-Education/book-series/RRLE
Quantitative Data Analysis
for Language Assessment
Volume I
Fundamental Techniques
Edited by Vahid Aryadoust
and Michelle Raquel
First published 2019
by Routledge
2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN
and by Routledge
52 Vanderbilt Avenue, New York, NY 10017
Routledge is an imprint of the Taylor & Francis Group, an informa business
© 2019 selection and editorial matter, Vahid Aryadoust and
Michelle Raquel; individual chapters, the contributors
The right of Vahid Aryadoust and Michelle Raquel to be identified
as the authors of the editorial material, and of the authors for their
individual chapters, has been asserted in accordance with sections 77
and 78 of the Copyright, Designs and Patents Act 1988.
All rights reserved. No part of this book may be reprinted or
reproduced or utilised in any form or by any electronic, mechanical,
or other means, now known or hereafter invented, including
photocopying and recording, or in any information storage or
retrieval system, without permission in writing from the publishers.
Trademark notice: Product or corporate names may be trademarks
or registered trademarks, and are used only for identification and
explanation without intent to infringe.
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication Data
A catalog record for this book has been requested
ISBN: 978-1-138-73312-1 (hbk)
ISBN: 978-1-315-18781-5 (ebk)
Typeset in Galliard
by Apex CoVantage, LLC
Visit the eResources: www.routledge.com/9781138733121
Contents
List of figures vii
List of tables ix
Preface xi
Editor and contributor biographies xiii
Introduction 1
VAHID ARYADOUST AND MICHELLE RAQUEL
SECTION I
Test development, reliability, and generalizability 13
1 Item analysis in language assessment 15
RITA GREEN
2 Univariate generalizability theory in language assessment 30
YASUYO SAWAKI AND XIAOMING XI
3 Multivariate generalizability theory in language assessment 54
KIRBY C. GRABOWSKI AND RONGCHAN LIN
SECTION II
Unidimensional Rasch measurement 81
4 Applying Rasch measurement in language assessment:
unidimensionality and local independence 83
JASON FAN AND TREVOR BOND
5 The Rasch measurement approach to differential item
functioning (DIF) analysis in language assessment research 103
MICHELLE RAQUEL
vi Contents
6 Application of the rating scale model and the partial credit
model in language assessment research 132
IKKYU CHOI
7 Many-facet Rasch measurement: implications for
rater-mediated language assessment 153
THOMAS ECKES
SECTION III
Univariate and multivariate statistical analysis 177
8 Analysis of differences between groups: the t-test and
the analysis of variance (ANOVA) in language assessment 179
TUĞBA ELIF TOPRAK
9 Application of ANCOVA and MANCOVA in language
assessment research 198
ZHI LI AND MICHELLE Y. CHEN
10 Application of linear regression in language assessment 219
DAERYONG SEO AND HUSEIN TAHERBHAI
11 Application of exploratory factor analysis in language
assessment 243
LIMEI ZHANG AND WENSHU LUO
Index 262
Figures
1.1 Facility values and distracter analysis 21
1.2 Discrimination indices 22
1.3 Facility values, discrimination, and internal consistency
(reliability) 23
1.4 Task statistics 23
1.5 Distracter problems 24
2.1 A one-facet crossed design example 36
2.2 A two-facet crossed design example 37
2.3 A two-facet partially nested design example 38
3.1 Observed-score variance as conceptualized through CTT 55
3.2 Observed-score variance as conceptualized through G theory 56
4.1 Wright map presenting item and person measures 93
4.2 Standardized residual first contrast plot 96
5.1 ICC of an item with uniform DIF 105
5.2 ICC of an item with non-uniform DIF 106
5.3 Standardized residual plot of 1st contrast 115
5.4 ETS DIF categorization of DIF items based on DIF size
and statistical significance 116
5.5 Sample ICC of item with uniform DIF (positive DIF contrast) 119
5.6 Sample ICC of item with uniform DIF (negative DIF contrast) 119
5.7 Macau high-ability students (M2) vs. HK high-ability
students (H2) sample ICCs of an item with NUDIF
(positive DIF contrast) 121
5.8 Macau high-ability students (M2) vs. HK high-ability
students (H2) sample ICCs of an item with NUDIF
(negative DIF contrast) 121
5.9 Plot diagram of person measures with vs. without DIF items 124
6.1 Illustration of the RSM assumption 136
6.2 Distributions of item responses 140
6.3 Estimated response probabilities for Items 1, 2, and 3 from
the RSM (dotted lines) and the PCM (solid lines) 143
viii Figures
6.4 Estimated standard errors for person parameters and test
information from the RSM (dotted lines) and the PCM
(solid lines) 145
6.5 Estimated response probabilities for Items 6, 7 and 8 from
the RSM (dotted lines) and the PCM (solid lines),
with observed response proportions (unfilled circles) 146
7.1 The basic structure of rater-mediated assessments 154
7.2 Fictitious dichotomous data: Responses of seven test takers
to five items scored as correct (1) or incorrect (0) 155
7.3 Illustration of a two-facet dichotomous Rasch model
(log odds form) 156
7.4 Fictitious polytomous data: Responses of seven test takers
evaluated by three raters on five criteria using a five-category
rating scale 157
7.5 Illustration of a three-facet rating scale measurement model
(log odds form) 157
7.6 Studying facet interrelations within a MFRM framework 160
7.7 Wright map for the three-facet rating scale analysis of the sample
data (FACETS output, Table 6.0: All facet vertical “rulers”) 162
7.8 Illustration of the MFRM score adjustment procedure 167
9.1 An example of boxplots 202
9.2 Temporal distribution of ANCOVA/MANCOVA-based
publications in four language assessment journals 204
9.3 A matrix of scatter plots 212
10.1 Plot of regression line graphed on a two-dimensional chart
representing X and Y axes 221
10.2 Plot of residuals vs. predicted Y scores where the assumption
of linearity holds for the distribution of random errors 224
10.3 Plot of residuals vs. predicted Y scores where the assumption
of linearity does not hold 224
10.4 Plot of standardized residuals vs. predicted values of the
dependent variable that depicts a violation of homoscedasticity 227
10.5 Histogram of residuals 237
10.6 Plot of predicted values vs. residuals 238
11.1 Steps in running EFA 245
11.2 Scatter plots to illustrate relationships between variables 247
11.3 Scree plot for the ReTSUQ data 256
Tables
2.1 Key Steps for Conducting a G Theory Analysis 34
2.2 Data Setup for the p × i Study Example With 30 Items (n = 35) 42
2.3 Expected Mean Square (EMS) Equations (the p × i Study Design) 42
2.4 G-study Results (the p × i Study Design) 43
2.5 D-study Results (the p × I Study Design) 44
2.6 Rating Design for the Sample Application 47
2.7 G- and D-study Variance Component Estimates for the p × r ′
Design (Rating Method) 48
2.8 G- and D-study Variance Component Estimates for the p × r
Design (Subdividing Method) 49
3.1 Areas of Investigation and Associated Research Questions 59
3.2 Research Questions and Relevant Output to Examine 63
3.3 Variance Component Estimates for the Four Subscales
(p• × T• × R• Design; 2 Tasks and 2 Raters) 69
3.4 Variance and Covariance Component Estimates for the Four
Subscales (p• × T• × R• Design; 2 Tasks and 2 Raters) 72
3.5 G Coefficients for the Four Subscales (p• × T• × R• Design) 73
3.6 Universe-Score Correlations Between the Four Subscales
(p• × T• × R• Design) 74
3.7 Effective Weights of Each Subscale to the Composite
Universe-Score Variance (p• × T• × R• Design) 74
3.8 Generalizability Coefficients for the Subscales When Varying
the Number of Tasks (p• × T• × R• Design) 75
4.1 Structure of the FET Listening Test 90
4.2 Summary Statistics for the Rasch Analysis 92
4.3 Rasch Item Measures and Fit Statistics (N = 106) 94
4.4 Standardized Residual Variance 96
4.5 Largest Standardized Residual Correlations 98
5.1 Selected Language-Related DIF Studies 109
5.2 Listening Sub-skills in the DELTA Listening Test 112
5.3 Rasch Analysis Summary Statistics (N = 2,524) 113
5.4 Principal Component Analysis of Residuals 114
5.5 Approximate Relationships Between the Person Measures
in PCAR Analysis 115
