Table Of Content

Statistics in Nutrition and Dietetics Statistics in Nutrition and Dietetics Michael Nelson Emeritus Reader in Public Health Nutrition King’s College London Public Health Nutrition Research Ltd UK This edition first published 2020 © 2020 by John Wiley & Sons Ltd All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions. The right of Michael Nelson to be identified as the author of in this work has been asserted in accordance with law. 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Title: Statistics in nutrition and dietetics / Michael Nelson. Description: Hoboken, NJ : John Wiley & Sons, 2020. | Includes bibliographical references and index. Identifiers: LCCN 2019030279 (print) | ISBN 9781118930649 (paperback) | ISBN 9781118930632 (adobe pdf) | ISBN 9781118930625 (epub) Subjects: MESH: Nutritional Sciences–statistics & numerical data | Statistics as Topic | Research Design Classification: LCC RM217 (print) | LCC RM217 (ebook) | NLM QU 16.1 | DDC 613.2072/7–dc23 LC record available at https://lccn.loc.gov/2019030279 LC ebook record available at https://lccn.loc.gov/2019030280 Cover Design: Laurence Parc | NimbleJack &Partners | www.nimblejack.co.uk Cover Image: © filo/Getty Images; PHN Courtesy of Public Health Nutrition Research Ltd Set in 10.5/13pt STIXTwoText by SPi Global, Pondicherry, India 10 9 8 7 6 5 4 3 2 1 To Stephanie Contents About the Author ix Preface xi Acknowledgements xv About the Companion Website xvii PART 1 Setting the Statistical Scene 1 CHAPTER 1 The Scientific Method 3 CHAPTER 2 Populations and Samples 31 CHAPTER 3 Principles of Measurement 71 CHAPTER 4 Probability and Types of Distribution 95 CHAPTER 5 Confidence Intervals and Significance Testing 115 PART 2 Statistical Tests 131 CHAPTER 6 Two Sample Comparisons for Normal Distributions: The t-test 135 CHAPTER 7 Nonparametric Two-Sample Tests 155 CHAPTER 8 Contingency Tables, Chi-Squared Test, and Fisher’s Exact Test 167 CHAPTER 9 McNemar’s Test 195 CHAPTER 10 Association: Correlation and Regression 205 CHAPTER 11 Analysis of Variance 227 vii viii Contents PART 3 Doing Research 249 CHAPTER 12 Design, Sample Size, and Power 251 CHAPTER 13 Describing Statistical Models and Selecting Appropriate Tests 263 CHAPTER 14 Designing a Research Protocol 267 CHAPTER 15 Presenting Results to Different Audiences 283 PART 4 Solutions to Exercises 299 APPENDIX A1 Probabilities (P) of the Binomial Distribution for n, r, and p (Based on Sample Proportions) or π (Proportion in the Population) 323 APPENDIX A2 Areas in the Tail of the Normal Distribution 341 APPENDIX A3 Areas in the Tail of the t Distribution 343 APPENDIX A4 Wilcoxon U Statistic (Mann–Whitney Test) 345 APPENDIX A5 Wilcoxon T Statistic 347 APPENDIX A6 Sign Test Statistic R 349 APPENDIX A7 Percentages in the Tail of the Chi-Squared Distribution 351 APPENDIX A8 Quantiles of the Spearman Rank Correlation Coefficient 353 APPENDIX A9 Percentages in the Tail of the F Distribution 355 APPENDIX A10 Flow Chart for Selecting Statistical Tests 363 Index 365 About the Author Dr. Michael Nelson is Emeritus Reader in Public Health Nutrition at King’s College London, and for- mer Director of Research and Nutrition at the Children’s Food Trust. He is currently Director of Public Health Nutrition Research Ltd (http://www. phnresearch.org.uk/). His early career with the Medical Research Council sparked a keen interest in nutritional epide- miology, statistics, and measurement validity. Research interests have included the diets of UK school children and links between diet and poverty, cognitive function, behaviour and attainment, and monitoring the impact of standards on school lunch take‐up and consumption. He collaborates nation- ally and internationally to promote a strong evi- dence base for school food policy. He has published over 200 peer‐reviewed articles and other publica- tions in the public domain. January 2020 ix Preface WHY IS THIS BOOK NEEDED? statistics. I did away with exams, and assessed understanding through practical exercises and coursework. Worldwide, there is no basic statistics textbook that This book takes you only to the foothills of provides examples relevant to nutrition and dietet- statistical analysis. A reasonable competence with ics. While it could be argued that general medical arithmetic and a little algebra are required. For the science statistics texts address the needs of nutrition application of more demanding and complex and dietetics students, it is clear that students find it statistical techniques, the help of a statistician will easier to take on board the concepts relating to sta- be needed. Once you have mastered the material in tistical analysis and research if the examples are this book, you may want to attempt a more advanced drawn from their own area of study. Many books course on statistics. also make basic assumptions about students’ back- grounds that may not always be appropriate, and use statistical jargon that can be very off‐putting for stu- AIMS AND SCOPE dents who are coming to statistics for the first time. The aim of this book is to provide clear, uncompli- cated explanations and examples of statistical con- WHO IS THIS BOOK FOR? cepts and techniques for data analysis relevant to learning and research in nutrition and dietetics. The book is aimed at undergraduate and postgradu- There are lots of short, practical exercises to work ate students studying nutrition and dietetics, as well through. These support insight into why various as their tutors and lecturers. In addition, there are tests work. There are also examples of SPSS1 output many researchers in nutrition and dietetics who for each test. This makes it is possible to marry up apply basic statistical techniques in the analysis of the outcomes computed manually with those pro- their data, for whom a basic textbook provides use- duced by the computer. Examples are taken from ful guidance, and which helps to refresh their uni- around the globe relating to all aspects of nutrition, versity learning in this area with examples relevant from biochemical experiments to public health to their own field. nutrition, and from clinical and community practice LEVEL AND PRE-REQUISITE 1SPSS stands for ‘Statistical Package for the Social Sciences’. It was developed at Stamford University in California, and the first manual was authored by Norman Nie, Dale Bent, and The level of the material is basic. It is based on a Hadlai Hull in 1970. The package was bought in 2009 by course that I taught at King’s College London over IBM. The worked examples and syntax in this book are based many years to nutrition and dietetics students, phys- on Version 24 (2016). It has come a long way since its first iotherapists, nurses, and medical students. One of incarnation, in terms of ease of use, error trapping, and out- the aims was to take the fear and boredom out of put. Be grateful. xi xii Preface in dietetics. All of this is complemented by material • lots of worked examples and exercises that online, including data sets ready for analysis, so that show how to compute the relevant outcome students can begin to understand how to generate measures for each test, both by hand and and interpret SPSS output more clearly. using SPSS The book focuses on quantitative analysis. • real examples from the nutrition and dietetics Qualitative analysis is highly valuable, but uses dif- literature, including biochemical, clinical, ferent approaches to data collection, analysis, and and population‐based examples interpretation. There is an element of overlap, for • principles of research design, transforma- example when quantitative statistical approaches tions, the relevance of sample size, and the are used to assess opinion data collected using ques- concept and calculation of Power tionnaires. But the two approaches have different All of the exercises have worked solutions. underlying principles regarding data collection and Some students say, ‘Why do we have to do the analysis. They complement one another, but cannot exercises by hand when the computer can do the replace one another. same computations in a fraction of a second?’ The Two things this book is not. First, it is not a answer is: computers are stupid. The old adage ‘gar- ‘cookbook’ with formulas. Learning to plug num- bage in, garbage out’ means that if you don’t have bers in to formulas by rote does not provide insight insight into why certain tests work the way they do, into why and how statistical tests work. Such books a computer will generate output that might be mean- are good for reminding readers of the formulas ingless, but it won’t tell you that you’ve made a mis- which underlie the tests, but useless at conveying take, or ask ‘Is this really what you wanted to do?’ the necessary understanding to analyze data prop- So, the purpose of the textbook and supporting erly or read the scientific literature intelligently. learning materials is to help ensure that when you Second, it is not a course in SPSS or Excel. While do use a computer, what goes in isn’t garbage, and SPSS and Excel are used to provide examples of what comes out is correct and provides meaningful output (with some supporting syntax for clarity), it answers to your research questions that you can is no substitute for a proper course in computer‐ interpret intelligently. based statistical analysis. Finally, it is worth saying that some students will find this textbook providing welcome explana- Scope tions about why things work the way they do. Others will find it annoyingly slow and detailed, with too The book provides: much explanation for concepts and applications that seem readily apparent. If you are in the first • a basic introduction to the scientific method group, I hope you enjoy the care with which expla- • an understanding of populations and sam- nations and examples are presented and that it helps ples, principles of measurement, and confi- to demystify what may at first seem a difficult topic. dence intervals If you are in the second group, read quickly to get to • an understanding of the basic theory underly- the heart of the matter, and look for other references ing basic statistical tests, including ‘paramet- and resources for material that you feel is better ric’ tests (those intended for use with data that suited to what you want to achieve. However hard or follow mathematically defined distributions easy the text seems, students in both groups should such as the so‐called ‘normal’ distribution); seek to make friends with a local statistician or tutor and ‘non‐parametric’ tests, for use with data experienced in statistical analysis and not try and distributions that are not parametric do it alone. Preface xiii Unique features and practical examples are worked through, complemented by interpretation of SPSS output. There are many unique features in this textbook and supporting material: Part 3: Doing research • Examples specific to nutrition and dietetics Most undergraduate and postgraduate courses • Clear simple language for students unfamiliar require students to collect data and/or interpret with statistical terms and approaches. For existing data sets. This section places the concepts in many students, the study of statistics is seen Part 1 and the learning in Part 2 into a framework to as either a burden or irrelevant to their deci- help you design studies, and determine sample size sion to study nutrition and/or dietetics. But and the strength of a study to test your hypothesis they will be required to pass a statistics mod- (‘Power’). A Flow Chart helps you select the appro- ule as part of their course. The aim is to make priate statistical test for a given study design. this as engaging and painless as possible. The last chapter explores briefly how to present • Lots of worked examples, with examples of findings to different audiences – what you say to a SPSS output to help students with the inter- group of parents in a school should differ in lan- pretation of their analyses in the future. guage and visual aids from a presentation to a • Putting statistics into context so that it is rele- conference of your peers. vant to many undergraduate and postgraduate research projects. • A website that provides complementary exer- Part 4: Solutions to exercises cises, data sets, and learning and teaching tools and resources for both students and tutors. It would be desperately unfair of me to set exercises at the end of each chapter and not provide the solutions. Sometimes the solutions are obvious. Other CONTENTS times, you will find a commentary about why the solution is what it is, and not something else. This textbook is based on over 20 years of teaching experience. There are four parts: ONLINE Part 1: Setting the statistical scene No textbook is complete these days without online resources that students and tutors can access. For This introduces concepts related to the scientific this textbook, the online elements include: method and approaches to research; populations and samples; principles of measurement; probabil- • Teaching tools ity and types of distribution of observations; and the Teaching notes ○ notion of statistical testing. PowerPoint slides for each chapter ○ SPSS data, syntax, and output files ○ Part 2: Statistical tests • Learning resources: Links to online software and websites that ○ This covers the basic statistical tests for data analysis. support learning about statistics and use of For each test, the underlying theory is explained, statistical software