Table Of ContentDr. Almonroeder is uniquely qualified to author a text on applied research as it relates
to the rehabilitation professions. As a practicing clinician, researcher, and faculty
member, he has the rare ability to describe the complexities of research and statistics
in a relevant and understandable way to bridge the gap between research and clinical
practice.
Nathan Short, PhD, OTD, OTR/L, CHT, Huntington University, USA
Advanced Statistics for Physical and
Occupational Therapy
Advanced Statistics for Physical and Occupational Therapy explains the basis for statistical
analyses that are commonly used to answer clinical research questions related to physical
and occupational therapy. This textbook provides a resource to help students and faculty
in physical and occupational therapy graduate programs understand the basis for common
statistical analyses and be able to apply these techniques in their own research. This textbook
provides readers with the basis for common statistical analyses, including t-tests, analysis of
variance, regression, and nonparametric tests. Each chapter includes step-by-step tutorials
with corresponding example data sets explaining how to conduct these statistical analyses
using Statistical Package for the Social Sciences (SPSS) software and the Excel Analysis
ToolPak, as well as how to identify and interpret relevant output and report results.
Advanced Statistics for Physical and Occupational Therapy is key reading for students in
physical therapy, occupational therapy, sport performance, and sport rehabilitation gradu
ate programs as well as students in athletic training courses, applied statistics in sport, and
research methods in sport modules.
This new text will also be of interest to practicing clinicians who hope to better understand
the research they are reading and/or are interested in starting to conduct their own clinical
research.
Thomas Gus Almonroeder, PT, DPT, PhD, is an assistant professor in the Department of
Health Professions at the University of Wisconsin – La Crosse, USA.
Advanced Statistics for Physical
and Occupational Therapy
Thomas Gus Almonroeder
Cover image: © kali9 / Getty images
First published 2022
by Routledge
605 Third Avenue, New York, NY 10158
and by Routledge
4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
Routledge is an imprint of the Taylor & Francis Group, an informa business
© 2022 Thomas Gus Almonroeder
The right of Thomas Gus Almonroeder to be identified as 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 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.
Library of Congress Cataloging-in-Publication Data
Names: Almonroeder, Thomas Gus, author.
Title: Advanced statistics for physical and occupational therapy / Thomas
Gus Almonroeder.
Description: First edition. | New York, NY : Routledge, 2022. | Includes bibliographical
references and index.
Identifiers: LCCN 2021061866 (print) | LCCN 2021061867 (ebook) |
ISBN 9781032017129 (hardback) | ISBN 9781032017112 (paperback) |
ISBN 9781003179757 (ebook)
Subjects: LCSH: Physical therapy—Statistical aspects. | Occupational therapy. | Statistics.
Classification: LCC RM695 .A36 2022 (print) | LCC RM695 (ebook) |
DDC 615.8/2—dc23/eng/20211220
LC record available at https://lccn.loc.gov/2021061866
LC ebook record available at https://lccn.loc.gov/2021061867
ISBN: 978-1-032-01712-9 (hbk)
ISBN: 978-1-032-01711-2 (pbk)
ISBN: 978-1-003-17975-7 (ebk)
DOI: 10.4324/9781003179757
Typeset in Times New Roman
by Apex CoVantage, LLC
Access the Support Material: www.routledge.com/9781032017112
Contents
List of Figures ix
List of Tables xii
List of Boxes xiii
Preface xiv
Glossary xvi
1 Introduction to fundamental concepts 1
2 Descriptive statistics 11
3 The normal distribution 31
4 Probability and statistical inference 40
5 t-tests 58
6 Introduction to analysis of variance 77
7 Factorial analysis of variance 98
8 Correlation 112
9 Simple linear regression 131
10 Multiple regression 149
11 Logistic regression 168
12 Non-parametric tests 179
13 Effect sizes and confidence intervals 188
viii Contents
14 Sample size estimation 195
15 Analysis of covariance 201
16 Multivariate analysis of variance 204
Data Sets 207
Appendixes 216
References 234
Index 239
Figures
1.1 Diagram depicting sampling error. 4
1.2 Table highlighting the attributes of nominal, ordinal, interval, and ratio
variables. 8
2.1 Histogram of 6 Minute Walk Test distances for a hypothetical sample of 50
subjects. 14
2.2 Stem-and-leaf plot of resting heart rate values for a hypothetical sample of
40 subjects. 16
2.3 Subplot A includes an example of a unimodal distribution (one peak), while
subplot B includes an example of a bimodal distribution (two peaks). 17
2.4 Subplot A includes an example of a positively skewed distribution (‘tails
off’ to the right), while subplot B includes an example of a negatively
skewed distribution (‘tails off’ to the left). 18
2.5 Examples of a leptokurtic distribution and a platykurtic distribution. 19
2.6 Example of a frequency distribution with the normal distribution curve
superimposed (left side of the figure). 20
2.7 Examples of how the locations of the mean, median, and mode differ for
positively (subplot A) and negatively (subplot B) skewed distributions. 21
2.8 Examples of two distributions of scores with the same means but different
degrees of variability. 23
2.9 Examples of two different distributions of scores. 24
2.10 Resting heart rates for 15 individuals. 25
2.11 Box plot based on the resting heart rate data from Figure 2.10. 25
3.1 Graph of the normal distribution curve. 32
3.2 Standard normal curves with different areas designated. 35
3.3 Standard normal curve highlighting the 68–95–99.7 rule. 36
3.4 Normal distribution curves for birth weights of babies born in the United
States (μ = 7.5 pounds, σ = 1.3 pounds). 37
3.5 Relevant areas of the distributions for Learning Activity 3.1. 39
4.1 Hypothetical distribution of body mass index (BMI) values for adults in the
United States population. 42
4.2 Two superimposed distributions of sample means. 44
4.3 Hypothetical confidence intervals based on 20 random samples of size n. 47
4.4 90%, 95%, and 99% confidence intervals (CIs) based on the hypothetical
hemoglobin data. 48
4.5 Table highlighting each of the four potential scenarios whenever a
hypothesis test is conducted. 50
