Table Of Content“This edition delivers on many fronts and sets this book apart from the rest. The clear and
conversational style emphasizes the applied and practical without compromising the theo-
retical and conceptual underpinnings. The parallel use of SPSS and R that walks the reader
step-by-step through the procedures coupled with fully annotated interpretation of print-
outs are very appealing to both novice and more seasoned applied researchers. Rather than
treating subjects like power and effect size or verification of assumptions in isolation, the
authors do a fantastic job of blending them with the analyses to make the story behind the
numbers more compelling and complete. The abundance of visuals and APA style write-
ups all contribute to simplify and enhance the learning experience.”
—Devdass Sunnassee, Assistant Clinical Professor,
University of North Carolina, USA
“I have relied on previous versions of this textbook to bring to life statistical concepts in my
beginning and intermediate level graduate classes. I also share this valuable resource with
students who ask questions when working on quantitative projects. This fourth edition
brings enhanced materials, explanations, and examples to aid students in gaining basic pro-
ficiency in foundational statistical concepts. The detailed and numerous practical examples
demonstrate the inner workings of basic statistical methods in the social and behavioural
sciences. I look forward to sharing this enhanced edition with our graduate program”
—Brian F. French, Washington State University, USA
“Combining theory and mathematical accessibility with examples in various fields of
behavioral sciences, SPSS and R applications, APA style write-ups, after-chapter concep-
tual and practice problems for students, online pedagogical aids, this is a valuable book
for introductory statistical courses in behavioral sciences. It has a broad coverage of topics,
and the addition of the new chapter on mediation and moderation adds to its value as a
classroom text or as a reference for applied researchers.”
—Feifei Ye, RAND Corporation, USA
“Anyone familiar with previous editions of Statistical Concepts from Lomax and Hahs-
Vaughn recognize and appreciate the pedigagogically sound treatment of statistical meth-
ods comprising introductory and intermediate topics found in many quantitative methods
graduate programs. In addition to enhancements found in the past versions such as APA-
style write-ups of statistical results and the numerous screen shots depicting both annotated
SPSS input commands and output; the fourth edition begins each chapter with a concrete
research scenario to motivate the particular statistical method. Another new feature that will
resonate with instructors and graduate students are the insightful Stop and Think boxes that
offer moments to reflect and to make connections between statistical ideas, data, and the
software. Clearly, Lomax and Hahs-Vaughn are committed to preparing the next generation
of researchers and practitioners, and the latest edition of Statistical Concepts is a must-have
reference for those seeking this type of comprehensive quantitative methods training.”
—Jeffrey R. Harring, University of Maryland, College Park, USA
“I have required this textbook for my introductory and intermediate-level students through-
out multiple editions, and it has continued to get better and better. This new edition contin-
ues to emphasize the development of statistical understanding while also providing readers
with valuable information on how to perform a variety of procedures using SPSS and R.
The authors have added a terrific new chapter on mediation and moderation that reviews
concepts and procedures that are often not a point of emphasis in traditional (textbook) cov-
erage of multiple regression (but that are crucial for more modern data analysis). This is a
book that not only is a wonderful learning resource for students, but also one they will want
to keep in their personal libraries to reference when carrying out their own future research.”
—H. Michael Crowson, The University of Oklahoma, USA
A Second Course
Statistical Concepts—A Second Course presents the last 10 chapters from An Introduction to
Statistical Concepts, Fourth Edition. Designed for second and upper-level statistics courses,
this book highlights how statistics work and how best to utilize them to aid students in the
analysis of their own data and the interpretation of research results.
In this new edition, Hahs-Vaughn and Lomax discuss sensitivity, specificity, false
positive and false negative errors. Coverage of effect sizes has been expanded upon and
more organizational features (to summarize key concepts) have been included. A final
chapter on mediation and moderation has been added for a more complete presentation
of regression models.
This book acts as a clear and accessible instructional tool to help readers fully understand
statistical concepts and how to apply them to data. It is an invaluable resource for students
undertaking a course in statistics in any number of social science and behavioral science
disciplines.
Debbie L. Hahs-Vaughn is Professor of Methodology, Measurement, and Analysis at the
University of Central Florida, US. Her research primarily relates to methodological issues
when analyzing, and applied research using, complex sample data.
Richard G. Lomax is Professor Emeritus of Educational and Human Ecology at The Ohio
State University, US, and former Associate Dean for Research and Administration. His
research primarily focuses on early literacy and statistics.
A Second Course
Fifth Edition
Debbie L. Hahs-Vaughn
University of Central Florida
Richard G. Lomax
The Ohio State University
Fifth edition published 2020
by Routledge
52 Vanderbilt Avenue, New York, NY 10017
and by Routledge
2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
Routledge is an imprint of the Taylor & Francis Group, an informa business
© 2020 Taylor & Francis
The right of Debbie L. Hahs-Vaughn and Richard G. Lomax to be identified as authors of this work has been asserted by
them 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.
First edition published by Longman Publishing Group 1992
Fourth edition published by Routledge 2012
Library of Congress Cataloging-in-Publication Data
A catalog record for this book has been requested
ISBN: 978-0-367-20404-4 (hbk)
ISBN: 978-0-367-20409-9 (pbk)
ISBN: 978-0-429-27782-5 (ebk)
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Visit the companion website: www.routledge.com/cw/hahs-vaughn
This book is dedicated to our families and to all our former students.
You are statistically significant.
Contents
Preface ...........................................................................................................................................xiii
Acknowledgments .....................................................................................................................xvii
1. One-Factor Analysis of Variance—Fixed-Effects Model .................................................1
1.1 What One-Factor Analysis of Variance Is and How It Works ................................2
1.2 Computing Parametric and Nonparametric Models Using SPSS ........................30
1.3 Computing Parametric and Nonparametric Models Using R ..............................44
1.4 Data Screening .............................................................................................................54
1.5 Power Using G*Power ................................................................................................73
1.6 Research Question Template and Example Write-Up ...........................................77
1.7 Additional Resources .................................................................................................78
Problems ..................................................................................................................................78
2. Multiple Comparison Procedures .....................................................................................85
2.1 What Multiple Comparison Procedures Are and How They Work ....................86
2.2 Computing Multiple Comparison Procedures Using SPSS ................................112
2.3 Computing Multiple Comparison Procedures Using R ......................................116
2.4 Research Question Template and Example Write-Up .........................................120
Problems ................................................................................................................................121
3. Factorial Analysis of Variance—Fixed-Effects Model .................................................129
3.1 What Two-Factor ANOVA Is and How It Works .................................................130
3.2 What Three-Factor and Higher-Order ANOVA Models Are
and How They Work ................................................................................................154
3.3 What the Factorial ANOVA With Unequal n’s Is and How It Works ................157
3.4 Computing Factorial ANOVA Using SPSS ............................................................158
3.5 Computing Factorial ANOVA Using R ..................................................................171
3.6 Data Screening ...........................................................................................................178
3.7 Power Using G*Power ..............................................................................................197
3.8 Research Question Template and Example Write-Up .........................................202
3.9 Additional Resources ...............................................................................................204
Problems ................................................................................................................................204
4. Introduction to Analysis of Covariance: The One-Factor Fixed-Effects
Model With a Single Covariate ........................................................................................215
4.1 What ANCOVA Is and How It Works ....................................................................216
4.2 Computing ANCOVA Using SPSS .........................................................................235
4.3 Computing ANCOVA Using R ...............................................................................245
4.4 Data Screening ...........................................................................................................248
4.5 Power Using G*Power ..............................................................................................271
4.6 Research Question Template and Example Write-Up .........................................276
4.7 Additional Resources ...............................................................................................278
Problems ................................................................................................................................279
ix
