Basic Statistics: A Primer for the Biomedical Sciences [4 ed.] 9780470248799, 0470248793

Table of contents :
Basic Statistics......Page 5
CONTENTS......Page 7
Preface to the Fourth Edition......Page 15
1.1 Reasons for Studying Biostatistics......Page 17
1.2.1 Setting Objectives......Page 18
1.2.2 Making a Conceptual Model of the Disease Process......Page 19
1.2.3 Estimating the Number of Persons with the Risk Factor or Disease......Page 20
1.3 Common Types of Biomedical Studies......Page 21
1.3.1 Surveys......Page 22
1.3.3 Clinical Trials......Page 23
1.3.5 Prospective Studies......Page 25
1.3.7 Other Types of Studies......Page 26
1.3.9 CONSORT......Page 27
References......Page 28
2.1 Basic Concepts......Page 29
2.2.2 Other Types of Random Samples......Page 31
2.3.2 Tables of Random Numbers......Page 33
2.4.1 Characteristics of a Good Sampling Plan......Page 35
2.4.2 Samples for Surveys......Page 36
2.4.3 Samples for Experiments......Page 37
2.4.5 Samples for Case/Control Studies......Page 39
Problems......Page 41
References......Page 42
3.1 Initial Steps......Page 43
3.1.1 Decide What Data You Need......Page 44
3.1.2 Deciding How to Collect the Data......Page 45
3.1.3 Testing the Collection Process......Page 46
3.2 Data Entry......Page 47
3.4 Code Book......Page 49
References......Page 50
4 Frequency Tables and Their Graphs......Page 51
4.1.2 Stem and Leaf Tables......Page 52
4.1.3 The Frequency Table......Page 54
4.2 Graphs......Page 56
4.2.2 The Histogram: Unequal Class Intervals......Page 57
4.2.3 Areas Under the Histogram......Page 59
4.2.4 The Frequency Polygon......Page 60
4.2.6 Distribution Curves......Page 61
References......Page 63
5 Measures of Location and Variability......Page 65
5.1.1 The Arithmetic Mean......Page 66
5.1.2 The Median......Page 67
5.2.1 The Variance and the Standard Deviation......Page 68
5.2.2 Other Measures of Variability......Page 70
5.3 Sampling Properties of the Mean and Variance......Page 71
5.4.1 Relating Statistics and Study Objectives......Page 73
5.4.3 Relating Statistics to the Type of Data......Page 74
5.5 A Common Graphical Method for Displaying Statistics......Page 76
Problems......Page 77
References......Page 78
6 The Normal Distribution......Page 79
6.1 Properties of the Normal Distribution......Page 80
6.2 Areas Under the Normal Curve......Page 81
6.2.1 Computing the Area Under a Normal Curve......Page 82
6.2.2 Linear Interpolation......Page 84
6.3 Importance of the Normal Distribution......Page 86
6.4.2 Using Normal Probability Plots or Quantile-Quantile Plots......Page 88
6.5 Transformations......Page 91
6.5.1 Finding a Suitable Transformation......Page 92
Problems......Page 93
References......Page 94
7 Estimation of Population Means: Confidence Intervals......Page 95
7.1.1 An Example......Page 96
7.1.2 Definition of Confidence Interval......Page 97
7.1.3 Choice of Confidence Level......Page 98
7.3 The t Distribution......Page 99
7.4 Confidence Interval for the Mean Using the t Distribution......Page 101
7.5.1 The Distribution of X1 – X2......Page 102
7.5.2 Confidence Intervals for μ1 – μ2: Known Variance......Page 103
7.5.3 Confidence Intervals for μ1 – μ2: Unknown Variance......Page 104
7.6 Estimating the Difference Between Two Means: Paired Comparison......Page 105
Problems......Page 107
References......Page 109
8 Tests of Hypotheses on Population Means......Page 111
8.1.1 Test for a Single Mean When σ Is Known......Page 112
8.1.2 One-sided Tests When σ Is Known......Page 115
8.1.3 Summary of Procedures for Test of Hypotheses......Page 116
8.1.4 Test for a Single Mean When σ Is Unknown......Page 117
8.2.1 Testing for Equality of Means When σ Is Known......Page 119
8.2.2 Testing for Equality of Means When σ Is Unknown......Page 120
8.3 Testing for Equality of Means: Paired Data......Page 123
8.4.1 Decision to Accept or Reject......Page 124
8.4.2 Two Kinds of Error......Page 125
8.4.3 An Illustration of β......Page 126
8.5 Sample Size......Page 127
8.6 Confidence Intervals Versus Tests......Page 129
8.7 Correcting for Multiple Testing......Page 130
Problems......Page 131
References......Page 132
9 Variances: Estimation and Tests......Page 133
9.2 Testing Whether Two Variances Are Equal: F Test......Page 134
9.3 Approximate t Test......Page 137
9.4 Other Tests......Page 138
References......Page 139
10 Categorical Data: Proportions......Page 141
10.1.1 Graphical Displays of Proportions......Page 142
10.2 Samples from Categorical Data......Page 144
10.3.1 Use of the Normal Approximation to the Binomial......Page 145
10.4 Confidence Intervals for a Single Population Proportion......Page 146
10.5 Confidence Intervals for the Difference in Two Proportions......Page 147
10.6.1 Tests of Hypothesis for a Single Population Proportion......Page 149
10.6.2 Testing the Equality of Two Population Proportions......Page 150
10.7 Sample Size for Testing Two Proportions......Page 152
10.8 Data Entry and Analysis Using Statistical Programs......Page 153
Problems......Page 154
References......Page 155
11 Categorical Data: Analysis of Two-way Frequency Tables......Page 157
11.1.1 Tables Based on a Single Sample......Page 158
11.1.2 Tables Based on Two Samples......Page 159
11.1.3 Tables Based on Matched or Paired Samples......Page 160
11.1.4 Relationship Between Type of Study Design and Type of Table......Page 161
11.2.1 Relative Risk......Page 162
11.2.2 Odds Ratios......Page 163
11.3.1 Chi-Square Test for a Single Sample: Two-by-Two Tables......Page 166
11.3.2 Chi-Square Test for Two Samples: Two-by-Two Tables......Page 170
11.3.3 Chi-Square Test for Matched Samples: Two-by-Two Tables......Page 171
11.3.5 Necessary Sample Size: Two-by-Two Tables......Page 172
11.3.6 The Continuity Correction: Two-by-Two Tables......Page 173
11.4.1 Chi-Square for Larger Tables: Single Sample......Page 174
11.4.2 Interpreting a Significant Test......Page 175
11.4.4 Necessary Sample Size for Large Tables......Page 177
Problems......Page 178
References......Page 180
12 Regression and Correlation......Page 181
12.1 The Scatter Diagram: Single Sample......Page 182
12.2.1 Least-Squares Regression Line......Page 184
12.2.4 The Meaning of the Least-Squares Line......Page 186
12.2.5 The Variance of the Residuals......Page 187
12.2.6 Model Underlying Single-Sample Linear Regression......Page 188
12.2.7 Confidence Intervals in Single-Sample Linear Regression......Page 190
12.2.8 Tests of Hypotheses for Regression Line from a Single Samde......Page 192
12.3.2 The Meaning of the Correlation Coefficient......Page 193
12.3.5 Test of Hypothesis That p = 0......Page 195
12.4 Linear Regression Assuming the Fixed-X Model......Page 196
12.4.2 Linear Regression Using the Fixed-X Model......Page 197
12.5.1 Use of Transformations in Linear Regression......Page 199
Problems......Page 200
References......Page 203
13 Nonparametric Statistics......Page 205
13.1.1 Sign Test for Large Samples......Page 206
13.1.2 Sign Test When the Sample Size Is Small......Page 207
13.2.1 Wilcoxon Signed Ranks Test for Large Samples......Page 208
13.2.2 Wilcoxon Signed Ranks Test for Small Samples......Page 210
13.3.1 Wilcoxon Rank Sum Test for Large Samples......Page 211
13.3.2 Wilcoxon Rank Sum Test for Small Samples......Page 213
13.4 Spearman’s Rank Correlation......Page 214
References......Page 215
14 Introduction to Survival Analysis......Page 217
14.1.2 Example of Measuring Time to an Event......Page 218
14.2.1 The Death Density Function......Page 220
14.2.2 The Cumulative Death Distribution Function......Page 221
14.2.3 The Survival Function......Page 222
14.2.4 The Hazard Function......Page 223
14.3 Computing Estimates of f(t), S(t), and h(t)......Page 224
14.3.1 Clinical Life Tables......Page 225
14.3.2 Kaplan-Meier Estimate......Page 228
14.4 Comparison of Clinical Life Tables and the Kaplan-Meier Method......Page 230
14.5.1 Comparing the Equality of Survival Functions......Page 231
References......Page 232
Appendix A: Statistical Tables......Page 235
Appendix B: Answers to Selected Problems......Page 251
C.1 Computer Systems for Biomedical Education and Research......Page 259
C.2 A Brief Indication of Statistics Computer Program Advances and Some Relevant Publications Since 2000......Page 260
C.3 Choices of Computer Statistical Software......Page 264
Bibliography......Page 265
Index......Page 269