The rationale of all forms of ANOVA is explained with simple mathematics<
Table of Contents
Preface xi
1 Populations and Samples 1
1.1 The Object of Biostatistics 1
1.2 Scales of Measurement 3
1.3 Central Tendency Measures 5
1.4 Sampling 8
1.5 Inferences from Samples 11
1.6 Measures of Location and Dispersion 14
1.7 The Standard Deviation 15
1.8 The n − 1 Divisor 16
1.9 Degrees of Freedom 18
1.10 Variance of Binary Variables 19
1.11 Properties of Means and Variances 20
1.12 Descriptive Statistics 22
1.13 Sampling Variation 25
1.14 The Normal Distribution 27
1.15 The Central Limit Theorem 29
1.16 Properties of the Normal Distribution 30
1.17 Probability Distribution of Sample Means 32
1.18 The Standard Error of the Mean 33
1.19 The Value of the Standard Error 35
1.20 Distribution of Sample Proportions 37
1.21 Convergence of Binomial to Normal Distribution 39
2 Descriptive Studies 41
2.1 Designing a Research 41
2.2 Study Design 42
2.3 Classification of Descriptive Studies 44
2.4 Cross-sectional Studies 45
2.5 Inferences from Means 47
2.6 Confidence Intervals 48
2.7 Statistical Tables 49
2.8 The Case of Small Samples 51
2.9 Student’s t Distribution 54
2.10 Statistical Tables of the t Distribution 56
2.11 Inferences from Proportions 58
2.12 Statistical Tables of the Binomial Distribution 60
2.13 Sample Size Requirements 61
2.14 Longitudinal Studies 63
2.15 Incidence Studies 65
2.16 Cohort Studies 66
2.17 Inference from Incidence Studies 70
2.18 Standardization 72
2.19 Time-to-Event Cohort Studies 75
2.20 The Actuarial Method 76
2.21 The Kaplan–Meier Method 79
2.22 Probability Sampling 82
2.23 Simple Random Sampling 84
2.24 Replacement in Sampling 85
2.25 Stratified Sampling 87
2.26 Multistage Sampling 92
3 Analytical Studies 97
3.1 Objectives of Analytical Studies 97
3.2 Measures of Association 98
3.3 Odds, Logits, and Odds Ratios 99
3.4 Attributable Risk 101
3.5 Classification of Analytical Studies 103
3.6 Uncontrolled Analytical Studies 104
3.7 Comparative Analytical Studies 105
3.8 Hybrid Analytical Studies 109
3.9 Non-probability Sampling in Analytical Studies 111
3.10 Comparison of Two Means 111
3.11 Comparison of Two Means from Small Samples 114
3.12 Comparison of Two Proportions 116
4 Statistical Tests 121
4.1 The Null and Alternative Hypotheses 121
4.2 The z-Test 122
4.3 The p-Value 125
4.4 Student’s t-Test 126
4.5 The Binomial Test 128
4.6 The Chi-Square Test 130
4.7 The Table of the Chi-Square Distribution 134
4.8 Analysis of Variance 135
4.9 Partitioning the Sum of Squares 139
4.10 Statistical Tables of the F Distribution 142
4.11 The ANOVA Table 143
5 Aspects of Statistical Tests 145
5.1 One-Sided Tests 145
5.2 Power of a Statistical Test 149
5.3 Sample Size Estimation 150
5.4 Multiple Comparisons 153
5.5 Scale Transformation 155
5.6 Non-parametric Tests 156
6 Cross-sectional Studies 161
6.1 Linear Regression 161
6.2 The Least Squares Method 163
6.3 Linear Regression Estimates 166
6.4 Regression and Correlation 171
6.5 The F-Test in Linear Regression 173
6.6 Interpretation of Regression Analysis Results 176
6.7 Multiple Regression 177
6.8 Regression Diagnostics 180
6.9 Selection of Predictor Variables 184
6.10 Independent Nominal Variables 185
6.11 Interaction 188
6.12 Nonlinear Regression 190
7 Case–Control Studies 193
7.1 Analysis of Case–Control Studies 193
7.2 Logistic Regression 194
7.3 The Method of Maximum Likelihood 196
7.4 Estimation of the Logistic Regression Model 198
7.5 The Likelihood Ratio Test 201
7.6 Interpreting the Results of Logistic Regression 202
7.7 Regression Coefficients and Odds Ratios 203
7.8 Applications of Logistic Regression 204
7.9 The ROC Curve 205
7.10 Model Validation 208
8 Cohort Studies 213
8.1 Repeated Measurements 213
8.2 The Paired t-Test 213
8.3 McNemar’s Test 215
8.4 Generalized Linear Models 216
8.5 The Logrank Test 219
8.6 The Adjusted Logrank Test 222
8.7 The Incidence Rate Ratio 224
8.8 The Cox Proportional Hazards Model 225
8.9 Assumptions of the Cox Model 229
8.10 Interpretation of Cox Regression 230
9 Measurement 233
9.1 Construction of Clinical Questionnaires 233
9.2 Factor Analysis 234
9.3 Interpretation of Factor Analysis 237
9.4 Factor Rotation 239
9.5 Factor Scores 241
9.6 Reliability 242
9.7 Concordance 248
9.8 Validity 253
9.9 Validation of Diagnostic Tests 255
10 Experimental Studies 257
10.1 Main Design Features and Classification 257
10.2 Experimental Controls 260
10.3 Replicates 261
10.4 Classification of Experimental Designs 262
10.5 Completely Randomized Design 263
10.6 Interaction 268
10.7 Full Factorial Design 269
10.8 The Random Effects Model 274
10.9 Components of Variance 275
10.10 ANOVA Model II and Model III 278
10.11 Rules for the Definition of the Error Terms 282
10.12 ANOVA on Ranks 284
11 Blocking 285
11.1 Randomized Block Design 285
11.2 Generalized Randomized Block Design 288
11.3 Incomplete Block Design 291
11.4 Factorial Design with Randomized Blocks 292
11.5 Latin and Greco-Latin Square Design 293
12 Simultaneous Inference 297
12.1 Multiple Comparisons 297
12.2 Generalist Methods 298
12.3 Multiple Comparisons of Group Means 303
12.4 Pairwise Comparison of Means 304
12.5 Different Variances 312
12.6 Comparison to a Control 313
12.7 Comparison of post hoc Tests 315
12.8 Complex Comparisons 316
12.9 Tests of Multiple Contrasts 320
12.10 A posteriori Contrasts 324
12.11 The Size of an Experiment 326
13 Factorial ANOVA 329
13.1 The n-Way ANOVA 329
13.2 The 2k Factorial Design 331
13.3 The 2k Factorial Design with Blocking 335
13.4 The Fractional Factorial Design 337
14 Nested Designs 339
14.1 Split–Plot Design 339
14.2 Nested (Hierarchical) Design 343
14.3 Mixed Model Nested ANOVA 345
14.4 Mixed Model Nested ANOVA with Three Sublevels 349
14.5 Pure Model II Nested ANOVA 352
15 Repeated Measures 355
15.1 Repeated Measures ANOVA 355
15.2 Repeated Measures ANOVA with Two Factors 359
15.3 ANOVA with Several Repeated Measures 361
15.4 Multivariate Tests 362
16 Clinical Trials 363
16.1 Classification of Clinical Trials 363
16.2 The Clinical Trial Population 365
16.3 The Efficacy Criteria 366
16.4 Controlled Clinical Trials 367
16.5 The Control Group 369
16.6 Blinding 370
16.7 Randomization 371
16.8 Non-comparative Clinical Trials 375
16.9 Regression Toward the Mean 378
16.10 Non-randomized Controlled Clinical Trials 379
16.11 Classical Randomized Clinical Trial Designs 381
16.12 Alternative Clinical Trial Designs 385
16.13 Pragmatic Clinical Trials 387
16.14 Cluster Randomized Trials 389
16.15 The Size of a Clinical Trial 393
16.16 Non-inferiority Clinical Trials 398
16.17 Adaptive Clinical Trials 403
16.18 Group Sequential Plans 405
16.19 The Alpha Spending Function 407
16.20 The Clinical Trial Protocol 409
16.21 The Data Record 411
17 Analysis of Clinical Trials 413
17.1 General Analysis Plan 413
17.2 Data Preparation 414
17.3 Study Populations 415
17.4 Primary Efficacy Analysis 418
17.5 Analysis of Multiple Endpoints 420
17.6 Secondary Analyses 423
17.7 Safety Analysis 424
18 Meta-analysis 427
18.1 Purpose of Meta-analysis 427
18.2 Measures of Effect 428
18.3 The Inverse Variance Method 429
18.4 The Random Effects Model 435
18.5 Heterogeneity 439
18.6 Publication Bias 442
18.7 The Forest Plot 444
References 447
Index 455
