A Practical Approach to Using Statistics in Health Research A Practical Approach to Using Statistics in Health Research From Planning to Reporting Adam Mackridge Philip Rowe This edition first published 2018 © 2018 John Wiley & Sons, Inc. 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 Adam Mackridge and Philip Rowe to be identified as the authors of this work has been asserted in accordance with law. Registered Office John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA Editorial Office 111 River Street, Hoboken, NJ 07030, USA For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com. 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Neither the publisher nor the author shall be liable for any damages arising here from. Library of Congress Cataloguing-in-Publication Data Names: Mackridge, Adam (Adam John), 1979- author. | Rowe, Philip, author. Title: A practical guide to statistics for health research / by Adam Mackridge, Philip Rowe. Description: Hoboken, NJ : Wiley, 2018. | Includes bibliographical references and index. | Identifiers: LCCN 2017055955 (print) | LCCN 2018001635 (ebook) | ISBN 9781119383598 (pdf) | ISBN 9781119383611 (epub) | ISBN 9781119383574 (hardback) Subjects: LCSH: Medical statistics. | Medicine–Research–Statistical methods. | BISAC: MEDICAL / Epidemiology. | MATHEMATICS / Probability & Statistics / General. Classification: LCC R853.S7 (ebook) | LCC R853.S7 M33 2018 (print) | DDC 610.2/1–dc23 LC record available at https://lccn.loc.gov/2017055955 Cover Design: Wiley Cover Image: © Tetra Images/Getty Images Set in 10/12pt WarnockPro by SPi Global, Chennai, India Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 v Contents About the Companion Website xv 1 Introduction 1 1.1 At Whom is This Book Aimed? 1 1.2 At What Scale of Project is This Book Aimed? 2 1.3 Why Might This Book be Useful for You? 2 1.4 How to Use This Book 3 1.5 Computer Based Statistics Packages 4 1.6 Relevant Videos etc. 5 2 Data Types 7 2.1 What Types of Data are There and Why Does it Matter? 7 2.2 Continuous Measured Data 7 2.2.1 Continuous Measured Data – Normal and Non‐Normal Distribution 8 2.2.2 Transforming Non‐Normal Data 13 2.3 Ordinal Data 13 2.4 Categorical Data 14 2.5 Ambiguous Cases 14 2.5.1 A Continuously Varying Measure that has been Divided into a Small Number of Ranges 14 2.5.2 Composite Scores with a Wide Range of Possible Values 15 2.6 Relevant Videos etc. 15 3 Presenting and Summarizing Data 17 3.1 Continuous Measured Data 17 3.1.1 Normally Distributed Data – Using the Mean and Standard Deviation 18 vi Contents 3.1.2 Data With Outliers, e.g. Skewed Data – Using Quartiles and the Median 18 3.1.3 Polymodal Data – Using the Modes 20 3.2 Ordinal Data 21 3.2.1 Ordinal Scales With a Narrow Range of Possible Values 22 3.2.2 Ordinal Scales With a Wide Range of Possible Values 22 3.2.3 Dividing an Ordinal Scale Into a Small Number of Ranges (e.g. Satisfactory/Unsatisfactory or Poor/Acceptable/Good) 22 3.2.4 Summary for Ordinal Data 23 3.3 Categorical Data 23 3.4 Relevant Videos etc. 24 Appendix 1: An Example of the Insensitivity of the Median When Used to Describe Data from an Ordinal Scale With a Narrow Range of Possible Values 25 4 Choosing a Statistical Test 27 4.1 Identify the Factor and Outcome 27 4.2 Identify the Type of Data Used to Record the Relevant Factor 29 4.3 Statistical Methods Where the Factor is Categorical 30 4.3.1 Identify the Type of Data Used to Record the Outcome 30 4.3.2 Is Continuous Measured Outcome Data Normally Distributed or Can It Be Transformed to Normality? 30 4.3.3 Identify Whether Your Sets of Outcome Data Are Related or Independent 31 4.3.4 For the Factor, How Many Levels Are Being Studied? 32 4.3.5 Determine the Appropriate Statistical Method for Studies with a Categorical Factor 32 4.4 Correlation and Regression with a Measured Factor 34 4.4.1 What Type of Data Was Used to Record Your Factor and Outcome? 34 4.4.2 When Both the Factor and the Outcome Consist of Continuous Measured Values, Select Between Pearson and Spearman Correlation 34 4.5 Relevant Additional Material 38 Contents vii 5 Multiple Testing 39 5.1 What Is Multiple Testing and Why Does It Matter? 39 5.2 What Can We Do to Avoid an Excessive Risk of False Positives? 40 5.2.1 Use of Omnibus Tests 40 5.2.2 Distinguishing Between Primary and Secondary/ Exploratory Analyses 40 5.2.3 Bonferroni Correction 41 6 Common Issues and Pitfalls 43 6.1 Determining Equality of Standard Deviations 43 6.2 How Do I Know, in Advance, How Large My SD Will Be? 43 6.3 One‐Sided Versus Two‐Sided Testing 44 6.4 Pitfalls That Make Data Look More Meaningful Than It Really Is 45 6.4.1 Too Many Decimal Places 45 6.4.2 Percentages with Small Sample Sizes 47 6.5 Discussion of Statistically Significant Results 47 6.6 Discussion of Non‐Significant Results 50 6.7 Describing Effect Sizes with Non‐Parametric Tests 51 6.8 Confusing Association with a Cause and Effect Relationship 52 7 Contingency Chi‐Square Test 55 7.1 When Is the Test Appropriate? 55 7.2 An Example 55 7.3 Presenting the Data 57 7.3.1 Contingency Tables 57 7.3.2 Clustered or Stacked Bar Charts 57 7.4 Data Requirements 59 7.5 An Outline of the Test 59 7.6 Planning Sample Sizes 59 7.7 Carrying Out the Test 60 7.8 Special Issues 61 7.8.1 Yates Correction 61 7.8.2 Low Expected Frequencies – Fisher’s Exact Test 61 7.9 Describing the Effect Size 61 viii Contents 7.9.1 Absolute Risk Difference (ARD) 62 7.9.2 Number Needed to Treat (NNT) 63 7.9.3 Risk Ratio (RR) 63 7.9.4 Odds Ratio (OR) 64 7.9.5 Case: Control Studies 65 7.10 How to Report the Analysis 65 7.10.1 Methods 65 7.10.2 Results 66 7.10.3 Discussion 67 7.11 Confounding and Logistic Regression 67 7.11.1 Reporting the Detection of Confounding 68 7.12 Larger Tables 69 7.12.1 Collapsing Tables 69 7 12.2 Reducing Tables 70 7.13 Relevant Videos etc. 71 8 Independent Samples (Two‐Sample) T‐Test 73 8.1 When Is the Test Applied? 73 8.2 An Example 73 8.3 Presenting the Data 75 8.3.1 Numerically 75 8.3.2 Graphically 75 8.4 Data Requirements 75 8.4.1 Variables Required 75 8.4.2 Normal Distribution of the Outcome Variable Within the Two Samples 75 8.4.3 Equal Standard Deviations 78 8.4.4 Equal Sample Sizes 78 8.5 An Outline of the Test 78 8.6 Planning Sample Sizes 79 8.7 Carrying Out the Test 79 8.8 Describing the Effect Size 79 8.9 How to Describe the Test, the Statistical and Practical Significance of Your Findings in Your Report 80 8.9.1 Methods Section 80 8.9.2 Results Section 80 8.9.3 Discussion Section 81 8.10 Relevant Videos etc. 81 Contents ix 9 Mann–Whitney Test 83 9.1 When Is the Test Applied? 83 9.2 An Example 83 9.3 Presenting the Data 85 9.3.1 Numerically 85 9.3.2 Graphically 85 9.3.3 Divide the Outcomes into Low and High Ranges 85 9.4 Data Requirements 86 9.4.1 Variables Required 86 9.4.2 Normal Distributions and Equality of Standard Deviations 87 9.4.3 Equal Sample Sizes 87 9.5 An Outline of the Test 87 9.6 Statistical Significance 87 9.7 Planning Sample Sizes 87 9.8 Carrying Out the Test 88 9.9 Describing the Effect Size 88 9.10 How to Report the Test 89 9.10.1 Methods Section 89 9.10.2 Results Section 89 9.10.3 Discussion Section 90 9.11 Relevant Videos etc. 91 10 One‐Way Analysis of Variance (ANOVA) – Including Dunnett’s and Tukey’s Follow Up Tests 93 10.1 When Is the Test Applied? 93 10.2 An Example 93 10.3 Presenting the Data 94 10.3.1 Numerically 94 10.3.2 Graphically 94 10.4 Data Requirements 94 10.4.1 Variables Required 94 10.4.2 Normality of Distribution for the Outcome Variable Within the Three Samples 95 10.4.3 Standard Deviations 96 10.4.4 Sample Sizes 98 10.5 An Outline of the Test 98 10.6 Follow Up Tests 98 10.7 Planning Sample Sizes 99 x Contents 10.8 Carrying Out the Test 100 10.9 Describing the Effect Size 101 10.10 How to Report the Test 101 10.10.1 Methods 101 10.10.2 Results Section 102 10.10.3 Discussion Section 102 10.11 Relevant Videos etc. 103 11 Kruskal–Wallis 105 11.1 When Is the Test Applied? 105 11.2 An Example 105 11.3 Presenting the Data 106 11.3.1 Numerically 106 11.3.2 Graphically 107 11.4 Data Requirements 109 11.4.1 Variables Required 109 11.4.2 Normal Distributions and Standard Deviations 109 11.4.3 Equal Sample Sizes 110 11.5 An Outline of the Test 110 11.6 Planning Sample Sizes 110 11.7 Carrying Out the Test 110 11.8 Describing the Effect Size 111 11.9 Determining Which Group Differs from Which Other 111 11.10 How to Report the Test 111 11.10.1 Methods Section 111 11.10.2 Results Section 112 11.10.3 Discussion Section 113 11.11 Relevant Videos etc. 114 12 McNemar’s Test 115 12.1 When Is the Test Applied? 115 12.2 An Example 115 12.3 Presenting the Data 116 12.4 Data Requirements 116 12.5 An Outline of the Test 118 12.6 Planning Sample Sizes 118 12.7 Carrying Out the Test 119 12.8 Describing the Effect Size 119 12.9 How to Report the Test 119 Contents xi 12.9.1 Methods Section 119 12.9.2 Results Section 120 12.9.3 Discussion Section 120 12.10 Relevant Videos etc. 121 13 Paired T‐Test 123 13.1 When Is the Test Applied? 123 13.2 An Example 125 13.3 Presenting the Data 125 13.3.1 Numerically 125 13.3.2 Graphically 125 13.4 Data Requirements 126 13.4.1 Variables Required 126 13.4.2 Normal Distribution of the Outcome Data 126 13.4.3 Equal Standard Deviations 128 13.4.4 Equal Sample Sizes 128 13.5 A n Outline of the Test 128 13.6 Planning Sample Sizes 129 13.7 Carrying Out the Test 129 13.8 Describing the Effect Size 129 13.9 How to Report the Test 130 13.9.1 Methods Section 130 13.9.2 Results Section 130 13.9.3 Discussion Section 131 13.10 Relevant Videos etc. 131 14 Wilcoxon Signed Rank Test 133 14.1 When Is the Test Applied? 133 14.2 An Example 134 14.3 Presenting the Data 134 14.3.1 Numerically 134 14.3.2 Graphically 136 14.4 Data Requirements 136 14.4.1 Variables Required 136 14.4.2 Normal Distributions and Equal Standard Deviations 137 14.4.3 Equal Sample Sizes 137 14.5 A n Outline of the Test 137 14.6 Planning Sample Sizes 138 14.7 Carrying Out the Test 139