Categorical and Nonparametric Data Analysis: Choosing the Best Statistical Technique

526 Pages·2014·5.862 MB·English

by  E. Michael Nussbaum

CATEGORICAL AND NONPARAMETRIC
DATA ANALYSIS
Featuring in-depth coverage of categorical and nonparametric statistics, this book pro-
vides a conceptual framework for choosing the most appropriate type of test in various
research scenarios. Class tested at the University of Nevada, the book’s clear explanations
of the underlying assumptions, computer simulations, and Exploring the Concept boxes
help reduce reader anxiety. Problems inspired by actual studies provide meaningful illus-
trations of the techniques. The underlying assumptions of each test and the factors that
impact validity and statistical power are reviewed so readers can explain their assump-
tions and how tests work in future publications. Numerous examples from psychology,
education, and other social sciences demonstrate varied applications of the material. Basic
statistics and probability are reviewed for those who need a refresher. Mathematical deri-
vations are placed in optional appendices for those interested in this detailed coverage.
Highlights include the following:
• Unique coverage of categorical and nonparametric statistics better prepares readers to se-
lect the best technique for their particular research project; however, some chapters
can be omitted entirely if preferred.
• Step-by-step examples of each test help readers see how the material is applied in a
variety of disciplines.
• Although the book can be used with any program, examples of how to use the tests in SPSS
and Excel foster conceptual understanding.
• Exploring the Concept boxes integrated throughout prompt students to review key
material and draw links between the concepts to deepen understanding.
• Problems in each chapter help readers test their understanding of the material.
• Emphasis on selecting tests that maximize power helps readers avoid “marginally”
significant results.
• Website (www.routledge.com/9781138787827) features datasets for the book’s exam-
ples and problems, and for the instructor, PowerPoint slides, sample syllabi, answers
to the even-numbered problems, and Excel data sets for lecture purposes.
Intended for individual or combined graduate or advanced undergraduate courses
in categorical and nonparametric data analysis, cross-classified data analysis, advanced
statistics and/or quantitative techniques taught in psychology, education, human devel-
opment, sociology, political science, and other social and life sciences, the book also
appeals to researchers in these disciplines. The nonparametric chapters can be deleted if
preferred. Prerequisites include knowledge of t tests and ANOVA.
E. Michael Nussbaum is a professor of educational psychology at the University of
Nevada, Las Vegas.
CATEGORICAL AND
NONPARAMETRIC DATA
ANALYSIS
Choosing the Best Statistical Technique
E. Michael Nussbaum
First published 2015
by Routledge
711 Third Avenue, New York, NY 10017
and by Routledge
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Routledge is an imprint of the Taylor & Francis Group, an informa business
© 2015 Taylor & Francis
The right of E. Michael Nussbaum to be identified as the author of
this work has been asserted by him 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
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Trademark notice: Product or corporate names may be trademarks
or registered trademarks, and are used only for identification and
explanation without intent to infringe.
Library of Congress Cataloging in Publication Data
A catalog record for this book has been requested
ISBN: 978-1-84872-603-1 (hbk)
ISBN: 978-1-138-78782-7 (pbk)
ISBN: 978-0-203-12286-0 (ebk)
Typeset in Stone Serif
by Apex CoVantage, LLC
This book is dedicated to my mentors who taught me secrets of
statistics: Edward H. Haertel, Henry E. Brady, and David R. Rogosa.
It is also dedicated to my ever patient wife, Lorraine.
CATEGORICAL AND NONPARAMETRIC
DATA ANALYSIS
BRIEF CONTENTS
Preface xv
About the Author xix
CHAPTER 1 Levels of Measurement, Probability, and
the Binomial Formula 1
CHAPTER 2 Estimation and Hypothesis Testing 25
CHAPTER 3 Random Variables and Probability Distributions 57
CHAPTER 4 Contingency Tables: The Chi-Square Test and
Associated Effect Sizes 81
CHAPTER 5 Contingency Tables: Special Situations 99
CHAPTER 6 Basic Nonparametric Tests for Ordinal Data 129
CHAPTER 7 Nonparametric Tests for Multiple or Related Samples 177
CHAPTER 8 Advanced Rank Tests (for Interactions and Robust ANOVA) 215
CHAPTER 9 Linear Regression and Generalized Linear Models 257
CHAPTER 10 Binary Logistic Regression 285
CHAPTER 11 Multinomial Logistic, Ordinal, and Poisson Regression 335
CHAPTER 12 Log-Linear Analysis 377
CHAPTER 13 General Estimating Equations 407
CHAPTER 14 Estimation Procedures 431
CHAPTER 15 Choosing the Best Statistical Technique 469
Answers to Odd-Numbered Problems 473
Index 497
CATEGORICAL AND NONPARAMETRIC
DATA ANALYSIS
CONTENTS
Preface xv
About the Author xix
CHAPTER 1 Levels of Measurement, Probability,
and the Binomial Formula 1
Levels of Measurement 1
Probability 3
The Binomial Formula 10
Problems 21
Appendix 1.1: Logic Behind Combination Formula (Eq. 1.9) 23
CHAPTER 2 Estimation and Hypothesis Testing 25
Estimation 25
Hypothesis Testing 35
The Binomial Test 39
Summary 51
Problems 51
Technical Notes 52
Appendix 2.1: Derivation of the Mean and Standard Error of
the Sampling Distribution for P 54
CHAPTER 3 Random Variables and Probability
Distributions 57
Random Variables 57
Testing the Shape of a Distribution 68
x Contents
Problems 73
Technical Notes 78
Appendix 3.1: Linear Combination of Two Random Variables 79
CHAPTER 4 Contingency Tables: The Chi-Square
Test and Associated Effect Sizes 81
The Contingency Table 81
Effect Sizes 88
Measures of Association 92
Using SPSS 93
Summary 94
Problems 95
Technical Note 97
CHAPTER 5 Contingency Tables: Special Situations 99
The Small Sample Case: Fisher’s Exact Test 99
McNemar Test (for Related Samples) 106
Controlling for a Third Variable: The Mantel-Haenszel Test 112
Summary 118
Problems 118
Technical Notes 122
Appendix 5.1: Understanding the Hypergeometric Distribution 123
Appendix 5.2: Understanding the Mantel-Haenszel Formula 125
CHAPTER 6 Basic Nonparametric Tests for
Ordinal Data 129
Introduction to Nonparametric Statistics 130
Analysis of Association or Trend 137
Comparing Two Groups 149
Robust Methods for Detecting Outliers 160
Summary 163
Problems 163
Technical Notes 169
Appendix 6.1: Computational Formula for τˆ 172
b
Appendix 6.2: Sum of Consecutive Integers 173