Statistics for Biomedical Engineers and Scientists: How to Visualize and Analyze Data

Cover......Page 1
Statistics for BiomedicalEngineers and Scientists:How to Visualize and Analyze Data......Page 4
Copyright......Page 5
Dedication......Page 6
Quote......Page 7
About the Authors......Page 8
  Aims and Motivation......Page 9
   Learning Objectives......Page 10
   Web Site Resources......Page 11
  Contents and Organization......Page 12
Acknowledgments......Page 14
 1.1 Introduction......Page 15
 1.2 Types of Statistical Data......Page 16
  1.3.1 Dotplot......Page 18
  1.3.2 Histogram......Page 19
  1.3.3 Bar Chart......Page 20
  1.4.2 Median......Page 22
  1.4.4 Which Measure of Central Tendency to Use?......Page 23
  1.5.2 Interquartile Range......Page 24
  1.5.3 Which Measure of Variation to Use?......Page 25
  1.6.2 Visualizing Median and IQR: The Box Plot......Page 26
 1.7 Summary......Page 27
  1.8.1 Visualization of Univariate Data......Page 28
  1.8.3 Calculating Measures of Variation......Page 29
  1.8.4 Visualizing Measures of Variation......Page 30
 1.9 Exercises......Page 31
 2.1 Introduction......Page 36
  2.2.1 Two Categorical Variables......Page 37
  2.2.3 Two Continuous Variables......Page 38
  2.2.4 Which Variable Should Go on Which Axis?......Page 40
  2.2.5 General Comments on Choice of Visualization......Page 41
  2.3.1 Covariance......Page 42
  2.4.1 Pearson's Correlation Coefficient......Page 43
  2.4.2 Spearman's Rank Correlation Coefficient......Page 48
 2.5 Regression Analysis......Page 50
  2.5.1 Using the Best-Fit Line to Make Predictions......Page 52
  2.5.3 Fitting Higher-Order Polynomials......Page 53
 2.6 Bland-Altman Analysis......Page 56
  2.6.1 The Bland-Altman Plot......Page 57
 2.7 Summary......Page 59
  2.8.1 Visualizing Bivariate Data......Page 60
  2.8.2 Covariance......Page 61
  2.8.3 Correlation......Page 62
  2.8.4 Calculating Best-Fit Lines......Page 63
  2.8.5 Bland-Altman Analysis......Page 64
 2.10 Exercises......Page 65
 3.1 Introduction......Page 70
 3.2 Notation......Page 71
  3.2.2 Positive and Negative Predictive Values......Page 72
  3.2.3 Example Calculation of Se, Sp, PPV and NPV......Page 73
 3.3 ROC Curves......Page 74
 3.5 Using MATLAB for ROC Analysis......Page 76
 3.7 Exercises......Page 77
 4.1 Introduction......Page 83
 4.3 Probability......Page 84
  4.3.1 Probabilities of Single Events......Page 85
  4.3.2 Probabilities of Multiple Events......Page 86
  4.4.1 The Normal Distribution......Page 89
 4.5 Why the Normal Distribution Is so Important: The Central Limit Theorem......Page 91
 4.6 Standard Error of the Mean......Page 92
 4.7 Confidence Intervals of the Mean......Page 95
  4.9.1 Probability Distributions......Page 97
  4.9.3 Confidence Interval of the Mean......Page 98
 4.11 Exercises......Page 99
 5.2 Hypothesis Testing......Page 103
 5.3 Types of Data for Hypothesis Tests......Page 105
 5.4 The t-distribution and Student's t-test......Page 106
 5.5 One-Sample Student's t-test......Page 107
 5.6 Confidence Intervals for Small Samples......Page 111
  5.7.1 Paired Data......Page 115
  5.7.2 Unpaired Data......Page 117
 5.8 1-tailed vs. 2-tailed Tests......Page 119
 5.9 Hypothesis Testing with Larger Sample Sizes: The z-test......Page 121
 5.10 Summary......Page 122
  5.11.1 Student's t-test......Page 123
  5.11.3 The t-distribution......Page 124
 5.13 Exercises......Page 125
 6.1 Introduction......Page 130
 6.2 Sign Test......Page 131
 6.3 Wilcoxon Signed-Rank Test......Page 135
 6.4 Mann-Whitney U Test......Page 139
  6.5.1 One-Sample Chi-Square Test......Page 143
  6.5.2 Two-Sample Chi-Square Test for Independence......Page 145
 6.6 Summary......Page 148
  6.7.2 Wilcoxon Signed-Rank Test......Page 149
  6.7.4 Chi-Square Test......Page 150
 6.8 Further Resources......Page 151
 6.9 Exercises......Page 152
 7.1 Introduction......Page 157
  7.2.1 Histograms......Page 158
  7.2.2 Quantile-Quantile Plots......Page 159
  7.3.1 Probability Plot Correlation Coefficient......Page 163
  7.3.3 z-values......Page 164
  7.3.4 Shapiro-Wilk Test......Page 166
  7.3.5 Chi-Square Test for Normality......Page 168
 7.4 Should We Use a Parametric or Nonparametric Test?......Page 171
 7.5 Does It Matter if We Use the Wrong Test?......Page 172
 7.6 Summary......Page 173
  7.7.1 Visual Methods......Page 174
  7.7.2 Numerical Methods......Page 175
 7.9 Exercises......Page 177
 8.1 Introduction......Page 182
  8.2.1 Bonferroni's Correction......Page 183
  8.2.2 Analysis of Variance (ANOVA)......Page 185
   ANOVA With Unequal Sample Sizes......Page 191
 8.3 Multivariate Hypothesis Testing......Page 192
  8.3.1 Hotelling's T2 Test......Page 193
   Two Sample Hotelling's T2 Test......Page 197
  8.3.2 Multivariate Analysis of Variance (MANOVA)......Page 198
 8.4 Which Test Should We Use?......Page 199
  8.6.1 Bonferroni's Correction......Page 201
  8.6.3 Hotelling's T2 Test......Page 202
  8.6.4 MANOVA......Page 204
 8.8 Exercises......Page 205
 9.2 Experimental and Observational Studies......Page 209
  9.2.2 Experimental Studies......Page 210
  9.2.3 Showing Cause-and-Effect......Page 211
 9.3 Random and Systematic Error (Bias)......Page 212
  9.4.2 Blinding......Page 213
  9.4.3 Multiple Measurement......Page 214
  9.4.4 Randomization......Page 215
 9.5 Sample Size and Power Calculations......Page 216
  9.5.1 Illustration of a Power Calculation for a Single Sample t-test......Page 217
  9.5.2 Illustration of a Sample Size Calculation......Page 218
 9.6 Summary......Page 219
  9.7.1 Sample Size Calculations......Page 220
 9.9 Exercises......Page 221
 10.1 Introduction......Page 225
 10.2 SSMs and Dimensionality Reduction......Page 226
  10.3.1 Parameterize the Shape......Page 228
  10.3.3 Compute the Mean Shape Vector......Page 229
  10.3.5 Compute the Eigenvectors and Eigenvalues......Page 230
 10.4 Producing New Shapes From an SSM......Page 231
 10.5 Biomedical Applications of SSMs......Page 232
 10.6 Summary......Page 233
 10.9 Exercises......Page 234
 11.1 Introduction......Page 237
 11.3 Part A: Measuring Myocardium Thickness......Page 238
 11.5 Part C: Sample Analysis......Page 239
 11.6 Summary......Page 240
APPENDIX A. Statistical Tables......Page 242
References......Page 251
Index......Page 252
Back Cover......Page 255