Basic Statistics

271 Pages·2009·12.18 MB·English

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BASIC STATISTICS
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BASIC STATISTICS
A Primer for the Biomedical Sciences
Fourth Edition
OLIVE JEAN DUNN
VIRGINIA A. CLARK
WILEY
A JOHN WILEY &SONS, INC., PUBLICATION
Copyright 0 2009 by John Wiley & Sons, Inc. All rights reserved.
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Library of Congress Cataloging-in-Publication Data:
Dunn, Olive Jean.
Basic statistics: a primer for the biomedical sciences / Olive Jean DUM, Virgina A.
Clark. - 4th ed.
p. ; cm.
Includes bibliographical references and index.
ISBN 978-0-470-24879-9 (cloth)
1. Medical statistics. 2. Biometry. I. Clark, Virginia, 1928- 11. Title.
[DNLM: 1. Biometry. 2. Statistics as Topic. WA 950 D923b 20091
RA409.D87 2009
5 19.5'02461-dc22 2009018425
Printed in the United States of America.
1 0 9 8 7 6 5 4 3 2 1
CONTENTS
Preface to the Fourth Edition xiii
1 Initial Steps 1
1.1 Reasons for Studying Biostatistics
1.2 Initial Steps in Designing a Biomedical Study
1.2.1 Setting Objectives
1.2.2 Making a Conceptual Model of the Disease Process
1.2.3 Estimating the Number of Persons with the Risk Factor
or Disease 4
1.3 Common Types of Biomedical Studies 5
1.3.1 Surveys 6
1.3.2 Experiments 7
1.3.3 Clinical Trials 7
1.3.4 Field Trials 9
1.3.5 Prospective Studies 9
1.3.6 Case/Control Studies 10
1.3.7 Other Types of Studies 10
V
CONTENTS
1.3.8 Rating Studies by the Level of Evidence 11
1.3.9 CONSORT 11
Problems 12
References 12
Populations and Samples 13
2.1 Basic Concepts 13
2.2 Definitions of Types of Samples 15
2.2.1 Simple Random Samples 15
2.2.2 Other Types of Random Samples 15
2.2.3 Reasons for Using Simple Random Samples 17
2.3 Methods of Selecting Simple Random Samples 17
2.3.1 Selection of a Small Simple Random Sample 17
2.3.2 Tables of Random Numbers 17
2.3.3 Sampling With and Without Replacement 19
2.4 Application of Sampling Methods in Biomedical Studies 19
2.4.1 Characteristics of a Good Sampling Plan 19
2.4.2 Samples for Surveys 20
2.4.3 Samples for Experiments 21
2.4.4 Samples for Prospective Studies 23
2.4.5 Samples for Case/Control Studies 23
Problems 25
References 26
Collecting and Entering Data 27
3.1 Initial Steps 27
3.1.1 Decide What Data You Need 28
3.1.2 Deciding How to Collect the Data 29
3.1.3 Testing the Collection Process 30
3.2 DataEntry 31
3.3 Screening the Data 33
3.4 CodeBook 33
Problems 34
References 34
Frequency Tables and Their Graphs 35
4.1 Numerical Methods of Organizing Data 36
4.1.1 An Ordered Array 36
CONTENTS vii
4.1.2 Stem and Leaf Tables 36
4.1.3 The Frequency Table 38
4.1.4 Relative Frequency Tables 40
4.2 Graphs 40
4.2.1 The Histogram: Equal Class Intervals 41
4.2.2 The Histogram: Unequal Class Intervals 41
4.2.3 Areas Under the Histogram 43
4.2.4 The Frequency Polygon 44
4.2.5 Histograms with Small Class Intervals 45
4.2.6 Distribution Curves 45
Problems 47
References 47
5 Measures of Location and Variability 49
5.1 Measures of Location 50
5.1.1 The Arithmetic Mean 50
5.1.2 The Median 51
5.1.3 Other Measures of Location 52
5.2 Measures of Variability 52
5.2.1 The Variance and the Standard Deviation 52
5.2.2 Other Measures of Variability 54
5.3 Sampling Properties of the Mean and Variance 55
5.4 Considerations in Selecting Appropriate Statistics 57
5.4.1 Relating Statistics and Study Objectives 57
5.4.2 Relating Statistics and Data Quality 58
5.4.3 Relating Statistics to the Type of Data 58
5.5 A Common Graphical Method for Displaying Statistics 60
Problems 61
References 62
6 The Normal Distribution 63
6.1 Properties of the Normal Distribution 64
6.2 Areas Under the Normal Curve 65
6.2.1 Computing the Area Under a Normal Curve 66
6.2.2 Linear Interpolation 68
6.2.3 Interpreting Areas as Probabilities 70
6.3 Importance of the Normal Distribution 70
6.4 Examining Data for Normality 72
viii CONTENTS
6.4.1 Using Histograms and Box Plots 72
6.4.2 Using Normal Probability Plots or Quantile-Quantile
Plots 72
6.5 Transformations 75
6.5.1 Finding a Suitable Transformation 76
6.5.2 Assessing the Need for a Transformation 77
Problems 77
References 78
7 Estimation of Population Means: Confidence Intervals 79
7.1 Confidence Intervals 80
7.1.1 An Example 80
7.1.2 Definition of Confidence Interval 81
7.1.3 Choice of Confidence Level 82
7.2 Sample Size Needed for a Desired Confidence Interval 83
7.3 The t Distribution 83
7.4 Confidence Interval for the Mean Using the t Distribution 85
7.5 Estimating the Difference Between Two Means: Unpaired Data 86
7.5.1 The Distribution of - 7, 86
7.5.2 Confidence Intervals for ,LL~ - p2: Known Variance 87
7.5.3 Confidence Intervals for ,LL~- p2: Unknown Variance 88
7.6 Estimating the Difference Between Two Means: Paired
Comparison 89
Problems 91
References 93
8 Tests of Hypotheses on Population Means 95
8.1 Tests of Hypotheses for a Single Mean 96
8.1.1 Test for a Single Mean When u Is Known 96
8.1.2 One-sided Tests When u Is Known 99
8.1.3 Summary of Procedures for Test of Hypotheses 100
8.1.4 Test for a Single Mean When Is Unknown 101
8.2 Tests for Equality of two Means: Unpaired Data 103
8.2.1 Testing for Equality of Means When u Is Known 103
8.2.2 Testing for Equality of Means When 0 Is Unknown 104
8.3 Testing for Equality of Means: Paired Data 107
8.4 Concepts Used in Statistical Testing 108
8.4.1 Decision to Accept or Reject 108