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Biostatistics for the Health Sciences
by
R. Clifford Blair; Richard A. Taylor
Publisher: Prentice Hall
Publishing Date: 2007/01/04
eText ISBN-10
0-13-208435-X
eText ISBN-13
978-0-13-208435-2
Print ISBN-10
0-13-117660-9
Print ISBN-13
978-0-13-117660-7
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Biostatistics for the Health Sciences
by
R. Clifford Blair; Richard A. Taylor
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Copyright, ii
Preface, xi
1. Foundations of Biostat...
2. Descriptive Methods, 9
3. Probability, 51
4. Introduction to Infere...
5. Paired Samples Methods...
6. Two Independent Sample...
7. Multi-Sample Methods, ...
8. The Assessment of Rela...
9. Linear Regression, 319
10. Methods Based on the ...
Appendices, 415
Bibliography, 527
Index, 531
Table of Contents
Copyright, ii
Preface, xi
1. Foundations of Biostatistics, 1
1.1. Introduction, 1
1.2. Populations and Samples, 2
1.3. Parameters and Statistics, 3
1.4. Descriptive and Inferential Statistics, 4
1.5. Why Populations and Samples?, 5
1.6. What Happens Now?, 6
Key Words and Phrases, 6
Exercises, 6
2. Descriptive Methods, 9
2.1. Introduction, 9
2.2. Scales of Measurement, 9
2.2.1. The Nominal Scale, 10
2.2.2. The Ordinal Scale, 10
2.2.3. The Interval (or Equal Interval) Scale, 11
2.2.4. The Ratio Scale, 11
2.2.5. Continuous and Discrete Data, 11
2.2.6. Further Comments on Scales, 12
2.3. Summation Notation, 12
2.3.1. Basic Notation, 12
2.3.2. Some Rules of Summation, 13
2.4. Distributions, 15
2.4.1. Frequency Distributions, 15
2.4.2. Relative Frequency Distributions, 15
2.4.3. Cumulative Frequency Distributions, 16
2.4.4. Cumulative Relative Frequency Distributions, 17
2.4.5. Grouped Distributions, 17
2.5. Graphs, 19
2.5.1. Bar Graphs, 19
2.5.2. Histograms, 20
2.5.3. Polygons, 20
2.5.4. Stem-and-leaf Displays, 22
2.6. Numerical Methods, 23
2.6.1. Measures of Central Tendency, 25
2.6.2. Measures of Variability, 32
2.6.3. Measures of Relative Position, 38
2.6.4. Measures of Distribution Shape, 44
2.7. A Re-Orientation, 47
Key Words and Phrases, 48
Exercises, 48
3. Probability, 51
3.1. Introduction, 51
3.2. A Definition of Probability, 51
3.3. Contingency Tables, 52
3.3.1. Sampling from the Population, 52
3.3.2. Frequency Tables, 53
3.3.3. Probability Tables, 55
3.3.4. Independence, 56
3.3.5. Sensitivity, Specificity, and Related Concepts, 57
3.3.6. Risk and Odds Ratios, 59
3.3.7. Bayes Rule, 60
3.4. The Normal Curve, 62
3.4.1. Sampling from the Population, 62
3.4.2. Some Characteristics of the Normal Curve, 62
3.4.3. Finding Areas Under the Normal Curve, 64
3.4.4. Using the Normal Curve to Approximate Probabilities, 68
Key Words and Phrases, 71
Exercises, 71
4. Introduction to Inference and One Sample Methods, 75
4.1. Introduction, 75
4.2. Sampling Distributions, 75
4.2.1. Definition, 75
4.2.2. The Sampling Distribution of
x
̄, 76
4.2.3. Using the Normal Curve to Approximate Probabilities Associated with
x
̄, 77
4.2.4. The Sampling Distribution of
p
, 80
4.2.5. Using the Binomial Distribution to Approximate Probabilities Associated with
p
, 81
4.2.6. Using the Normal Curve to Approximate Probabilities Associated with
p
, 84
4.3. Hypothesis Testing, 86
4.3.1. Introduction, 86
4.3.2. Rationale and Method, 87
4.3.3. The One Mean Z Test, 89
4.3.4. The One Mean
t
Test, 102
4.3.5. One Sample Tests for a Proportion, 108
4.3.6. Equivalence Tests, 117
4.3.7. Errors and Correct Decisions in Hypothesis Testing, 125
4.4. Confidence Intervals, 137
4.4.1. Introduction, 137
4.4.2. Rationale and Method, 138
4.4.3. A Note of Caution, 141
4.4.4. Confidence Interval for μ When σ Is Known, 142
4.4.5. Confidence Interval for μ When σ Is Not Known, 145
4.4.6. Confidence Interval for π, 148
4.5. Comparison of Hypothesis Tests and Confidence Intervals, 152
4.5.1. Two-Tailed Hypothesis Tests and Two-Sided Confidence Intervals, 152
4.5.2. One-Tailed Hypothesis Tests and One-Sided Confidence Intervals, 154
4.5.3. Some Additional Comments, 155
4.6. A Re-Orientation, 155
Key Words and Phrases, 155
Exercises, 156
5. Paired Samples Methods, 159
5.1. Introduction, 159
5.2. Methods Related to Mean Difference, 160
5.2.1. The Paired Samples (Difference)
t
Test, 160
5.2.2. Establishing Equivalence by Means of Paired Samples
t
Tests, 165
5.2.3. Confidence Interval for Paired Samples Mean Difference, 171
5.2.4. Assumptions, 174
5.3. Methods Related to Proportions, 174
5.3.1. McNemar’s Test of a Paired Samples Proportion, 174
5.3.2. Establishing Equivalence for a Paired Samples Proportion, 180
5.3.3. Confidence Interval for a Paired Samples Proportion, 186
5.3.4. Assumptions, 190
5.4. Methods Related to Paired Samples Risk Ratios, 190
5.4.1. Background, 190
5.4.2. Test of the Hypothesis
RR
= 1 for Paired Samples, 191
5.4.3. Establishing Equivalence by Means of the Paired Samples Risk Ratio, 193
5.4.4. Confidence Interval for a Paired Samples Risk Ratio, 196
5.4.5. Assumptions, 199
5.5. Methods Related to Paired Samples Odds Ratios, 199
5.5.1. Background, 199
5.5.2. Test of the Hypothesis
OR
= 1 for Paired Samples, 201
5.5.3. Establishing Equivalence by Means of the Paired Samples Odds Ratio, 204
5.5.4. Confidence Interval for a Paired Samples Odds Ratio, 208
5.5.5. Assumptions, 212
Key Words and Phrases, 212
Exercises, 212
6. Two Independent Samples Methods, 215
6.1. Introduction, 215
6.2. Methods Related to Differences Between Means, 215
6.2.1. The Independent Samples
t
Test, 215
6.2.2. Establishing Equivalence by Means of Independent Samples
t
Tests, 224
6.2.3. Confidence Interval for the Difference Between Means of Two Independent Samples, 228
6.2.4. Assumptions, 230
6.3. Methods Related to Proportions, 230
6.3.1. An Independent Samples Test for the Difference Between Proportions, 230
6.3.2. Establishing Equivalence by Means of an Independent Samples
Z
Test for the Difference Between Proportions, 234
6.3.3. Confidence Interval for a Difference Between Proportions Based on Two Independent Samples, 236
6.3.4. Assumptions, 238
6.4. Methods Related to Independent Samples Risk Ratios, 238
6.4.1. Background, 238
6.4.2. Test of the Hypothesis RR = 1 for Independent Samples, 239
6.4.3. Establishing Equivalence by Means of the Independent Samples Risk Ratio, 241
6.4.4. Confidence Interval for the Independent Samples Risk Ratio, 244
6.4.5. Assumptions, 246
6.5. Methods Related to Independent Samples Odds Ratios, 247
6.5.1. Background, 247
6.5.2. Test of the Hypothesis OR = 1 for Independent Samples, 249
6.5.3. Establishing Equivalence by Means of the Independent Samples Odds Ratio, 251
6.5.4. Confidence Interval for the Independent Samples Odds Ratio, 254
6.5.5. Assumptions, 256
6.5.6. Estimating Risk of Disease from Case-Control Data, 256
Key Words and Phrases, 258
Exercises, 259
7. Multi-Sample Methods, 263
7.1. Introduction, 263
7.2. The One-way Analysis of Variance (ANOVA) F Test, 264
7.2.1. Hypotheses, 264
7.2.2. Obtained
F
, 264
7.2.3. The Test of Significance, 269
7.2.4. The ANOVA Table, 269
7.2.5. Two Important Characteristics of
MS_b
and
MS_w
, 272
7.2.6. Assumptions, 276
7.3. The 2 by
k
Chi-Square Test, 276
7.3.1. Hypotheses, 276
7.3.2. Obtained χ^2, 277
7.3.3. Assumptions, 282
7.4. Multiple Comparison Procedures, 282
7.4.1. Introduction, 282
7.4.2. Controlling Familywise Errors, 284
7.4.3. Further Comments Regarding Multiple Comparison Procedures, 291
Key Words and Phrases, 292
Exercises, 293
8. The Assessment of Relationships, 295
8.1. Background, 295
8.2. The Pearson Product-Moment Correlation Coefficient, 295
8.2.1. Calculation of the Product-Moment Correlation Coefficient, 295
8.2.2. The Nature of the Relationship, 298
8.2.3. The Strength of the Relationship, 300
8.2.4. Zero Correlation, 307
8.2.5. Cause-Effect Relationships, 308
8.2.6. Test of Hypothesis and Confidence Interval, 309
8.2.7. Assumptions, 312
8.3. The Chi-Square Test for Independence, 312
8.3.1. Assumptions, 315
Key Words and Phrases, 316
Exercises, 316
9. Linear Regression, 319
9.1. Background, 319
9.2. Simple Linear Regression, 320
9.2.1. Calculation of
a
and
b
, 320
9.2.2. The Residual and Regression Sums of Squares and the Coefficients of Determination and Nondetermination, 322
9.2.3. A Note on the Calculation of
SS_res
and
SS_reg
, 324
9.2.4. Further Comments on the Coefficients of Determination and Nondetermination, 325
9.2.5. Inference Regarding
b
and
R
^2, 326
9.2.6. A Logical Inconsistency, 328
9.3. Multiple Linear Regression, 329
9.3.1. The Model, 329
9.3.2. Calculation of the Model, 329
9.3.3. Tests of Significance for
R
^2 and
b
s, 332
9.3.4. The Partial F Test, 333
9.4. Assumptions, 338
9.5. Some Additional Comments Regarding the Utility of MLR, 338
Key Words and Phrases, 339
Exercises, 340
10. Methods Based on the Permutation Principle, 343
10.1. Introduction, 343
10.2. Some Preliminaries, 344
10.2.1. Permutations, 344
10.2.2. Combinations, 345
10.3. Applications, 348
10.3.1. Correlation, 349
10.3.2. Paired Samples Tests, 361
10.3.3. Two Independent Samples, 374
10.3.4. Multiple Independent Samples, 389
10.3.5. Contingency Tables, 399
10.4. Further Comments Regarding Permutation Based Methods, 409
Key Words and Phrases, 411
Exercises, 411
Appendices, 415
Appendix A. Normal Curve Table, 415
Appendix B. Critical Values of Student’s t Distribution, 421
Appendix C. Critical Values of the F Distribution, 427
Appendix D. Critical Values of the Chi-Square Distribution, 447
Appendix E. Critical Values of q for Tukey’s HSD Test, 449
Appendix F. Critical Values of the Rank Correlation Coefficient, 453
Appendix G. Critical Values for Wilcoxon’s Signed-Ranks Test, 457
Appendix H. Critical Values for Wilcoxon’s Rank-Sum Test, 461
Appendix I. Critical Values for the Kruskal-Wallis Test, 463
Appendix J. Case Studies, 469
Appendix K. Answers to Exercises, 479
Bibliography, 527
Index, 531
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