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Library of Congress Cataloging-in-Publication Data

Bowers, David, 1938–

Medical statistics from scratch : an introduction for health professionals / David Bowers. — 2nd ed. p. ; cm.

Includes bibliographical references and index. ISBN 978-0-470-51301-9 (cloth : alk, paper)

1.Medical statistics. 2. Medicine—Research—Statistical methods. I. Title. [DNLM: 1. Biometry. 2. Statistics—methods. WA 950 B786m 2007] RA409.B669 2007

610.72’7—dc22

2007041619

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

ISBN 978-0-470-51301-9

Typeset in 10/12pt Minion by Aptara Inc., New Delhi, India

Printed and bound in Great Britain by Antony Rowe Ltd., Chippenham, Wilts

This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production.

This book is for Susanne

Preface to the 2nd Edition	xi
Preface to the 1st Edition	xiii
Introduction	xv

I Some Fundamental Stuff	1
1 First things ﬁrst – the nature of data	3
Learning Objectives	3
Variables and data	3
The good, the bad, and the ugly – types of variable	4
Categorical variables	4
Metric variables	7
How can I tell what type of variable I am dealing with?	9

II Descriptive Statistics	15
2 Describing data with tables	17
Learning Objectives	17
What is descriptive statistics?	17
The frequency table	18
3 Describing data with charts	29
Learning Objectives	29
Picture it!	29
Charting nominal and ordinal data	30
Charting discrete metric data	34
Charting continuous metric data	35
Charting cumulative data	37
4 Describing data from its shape	43
Learning Objectives	43
The shape of things to come	43

viii CONTENTS

5 Describing data with numeric summary values	51
Learning Objectives	51
Numbers R us	52
Summary measures of location	54
Summary measures of spread	57
Standard deviation and the Normal distribution	65

III Getting the Data	69
6 Doing it right ﬁrst time – designing a study	71
Learning Objectives	71
Hey ho! Hey ho! It’s off to work we go	72
Collecting the data – types of sample	74
Types of study	75
Confounding	81
Matching	81
Comparing cohort and case-control designs	83
Getting stuck in – experimental studies	83

IV From Little to Large – Statistical Inference	91
7 From samples to populations – making inferences	93
Learning Objectives	93
Statistical inference	93
8 Probability, risk and odds	97
Learning Objectives	97
Chance would be a ﬁne thing – the idea of probability	98
Calculating probability	99
Probability and the Normal distribution	100
Risk	100
Odds	101
Why you can’t calculate risk in a case-control study	102
The link between probability and odds	103
The risk ratio	104
The odds ratio	105
Number needed to treat (NNT)	106

V The Informed Guess – Conﬁdence Interval Estimation	109
9 Estimating the value of a single population parameter – the idea of	111
conﬁdence intervals	111
Learning Objectives	111
Conﬁdence interval estimation for a population mean	112
Conﬁdence interval for a population proportion	116
Estimating a conﬁdence interval for the median of a single population	117

CONTENTS	ix
10 Estimating the difference between two population parameters	119
Learning Objectives	119
What’s the difference?	120
Estimating the difference between the means of two independent populations – using
a method based on the two-sample t test	120
Estimating the difference between two matched population means – using a method
based on the matched-pairs t test	125
Estimating the difference between two independent population proportions	126
Estimating the difference between two independent population medians – the
Mann–Whitney rank-sums method	127
Estimating the difference between two matched population medians – Wilcoxon
signed-ranks method	131
11 Estimating the ratio of two population parameters	133
Learning Objectives	133
Estimating ratios of means, risks and odds	133

VI Putting it to the Test	139
12 Testing hypotheses about the difference between two	141
population parameters	141
Learning Objectives	141
The research question and the hypothesis test	142
A brief summary of a few of the commonest tests	144
Some examples of hypothesis tests from practice	146
Conﬁdence intervals versus hypothesis testing	149
Nobody’s perfect – types of error	149
The power of a test	151
Maximising power – calculating sample size	152
Rules of thumb	152
13 Testing hypotheses about the ratio of two population parameters	155
Learning Objectives	155
Testing the risk ratio	155
Testing the odds ratio	158
14 Testing hypotheses about the equality of population proportions:	161
the chi-squared test	161
Learning Objectives	161
Of all the tests in all the world . . . the chi-squared (χ 2) test	162

VII Getting up Close	169
15 Measuring the association between two variables	171
Learning Objectives	171
Association	171
The correlation coefﬁcient	175

x CONTENTS

16 Measuring agreement	181
Learning Objectives	181
To agree or not agree: that is the question	181
Cohen’s kappa	182
Measuring agreement with ordinal data – weighted kappa	184
Measuring the agreement between two metric continuous variables	184

VIII Getting into a Relationship	187
17 Straight line models: linear regression	189
Learning Objectives	189
Health warning!	190
Relationship and association	190
The linear regression model	192
Model building and variable selection	200
18 Curvy models: logistic regression	213
Learning Objectives	213
A second health warning!	213
Binary dependent variables	214
The logistic regression model	215

IX Two More Chapters	225
19 Measuring survival	227
Learning Objectives	227
Introduction	227
Calculating survival probabilities and the proportion surviving: the Kaplan-Meier table	228
The Kaplan-Meier chart	230
Determining median survival time	231
Comparing survival with two groups	232
20 Systematic review and meta-analysis	239
Learning Objectives	239
Introduction	240
Systematic review	240
Publication and other biases	244
The funnel plot	244
Combining the studies	246
Appendix: Table of random numbers	251
Solutions to Exercises	253
References	273
Index	277

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