 | Wilcox R.R. Applying contemporary statistical techniques. - San Diego; London; Burlington: Academic Press, 2003. - xii, 608, A-5, B-26, C-6, R-12, I-4 p.: ill. - Incl. bibl. ref. and index. - ISBN 0-12-751541-0
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Preface ........................................................ xi
1 Introduction ................................................ 1
1.1 Software .............................................. 5
1.2 R and S-PLUS Functions Written for This Book
2 Probability and Related Concepts ........................... 17
2.1 Basic Probability .................................... 17
2.2 Expected Values ...................................... 19
2.3 Conditional Probability and Independence ............. 20
2.4 Population Variance .................................. 25
2.5 The Binomial Probability Function .................... 28
2.6 Continuous Variables and the Normal Curve ............ 32
2.7 Understanding the Effects of Nonnormality ............ 39
2.8 Pearson's Correlation ................................ 44
2.9 Some Rules About Expected Values ..................... 47
2.10 Chi-Squared Distributions ............................ 49
2.11 Exercises ............................................ 49
3 Summarizing Data ........................................... 55
3.1 Basic Summation Notation ............................. 55
3.2 Measures of Location ................................. 56
3.3 Measures of Variation or Scale ....................... 69
3.4 Detecting Outliers ................................... 76
3.5 Computing an M-Estimator of Location ................. 81
3.6 Histograms ........................................... 84
3.7 Kernel Density Estimators ............................ 85
3.8 Stem-and-Leaf Displays ............................... 88
3.9 Exercises ............................................ 89
4 Sampling Distributions and Confidence Intervals ............ 93
4.1 Basics ............................................... 93
4.2 Random Sampling ...................................... 95
4.3 Approximating the Sampling Distribution of  ......... 98
4.4 The Sample Mean versus MOM, the Median, Trimmed
Mean, and M-Estimator ............................... 101
4.5 A Confidence Interval for the Population Mean ....... 106
4.6 An Approach to Nonnormality: The Central Limit
Theorem ............................................. 109
4.7 Confidence Intervals when a Is Unknown .............. 115
4.8 Student's T and Nonnormality ........................ 118
4.9 Confidence Intervals for the Trimmed Mean ........... 124
4.10 Transforming Data ................................... 132
4.11 Confidence Interval for the Population Median ....... 132
4.12 A Remark About MOM and M-Estimators ................. 134
4.13 Confidence Intervals for the Probability of
Success ............................................. 134
4.14 Exercises ........................................... 137
5 Hypothesis Testing ........................................ 141
5.1 The Basics of Hypothesis Testing .................... 141
5.2 Power and Type II Errors ............................ 151
5.3 Testing Hypotheses About the Mean When σ Is Not
Known ............................................... 157
5.4 Controlling Power and Determining n ................. 159
5.5 Practical Problems with Student's T ................. 163
5.6 Hypothesis Testing Based on a Trimmed Mean .......... 167
5.7 Exercises ........................................... 170
6 Least Squares Regression and Pearson's Correlation ........ 173
6.1 Fitting a Straight Line to Data: The Least Squares
Principle ........................................... 173
6.2 The Standard Least Squares Model .................... 178
6.3 Hypothesis Testing and Confidence Intervals ......... 186
6.4 Pearson's Correlation ............................... 194
6.5 Testing H0 : ρ = 0 .................................. 199
6.6 Concluding Remarks .................................. 202
6.7 Exercises ........................................... 202
7 Basic Bootstrap Methods ................................... 207
7.1 The Percentile Method ............................... 207
7.2 The Bootstrap-t Interval ............................ 212
7.3 A Modified Percentile Method for Least Squares
Regression and Pearson's Correlation ................ 216
7.4 More About the Population Mean ...................... 219
7.5 Inferences About a Trimmed Mean ..................... 221
7.6 Estimating Power When Testing Hypotheses About
a Trimmed Mean ...................................... 225
7.7 Inferences Based on MOM and M-Estimators ............ 228
7.8 Detecting Nonlinear Associations .................... 229
7.9 Exercises ........................................... 233
8 Comparing Two Independent Croups .......................... 237
8.1 Student's T ......................................... 238
8.2 Relative Merits of Student's T ...................... 240
8.3 Welch's Heteroscedastic Method for Means ............ 243
8.4 Comparing Groups with Individual Confidence
Intervals: An Example of What Not to Do ............. 246
8.5 A Bootstrap Method for Comparing Means .............. 248
8.6 A Permutation Test Based on Means ................... 249
8.7 Yuen's Method for Comparing Trimmed Means ........... 251
8.8 Bootstrap Methods for Comparing Trimmed Means ....... 253
8.9 Comparing MOM-Estimators, M-Estimators, and Other
Measures of Location ................................ 261
8.10 Comparing Variances or Other Measures of Scale ...... 264
8.11 Measuring Effect Size ............................... 269
8.12 Comparing Correlations and Regression Slopes ........ 277
8.13 Comparing Two Binomials ............................. 279
8.14 Exercises ........................................... 282
9 One-Way ANOVA ............................................. 285
9.1 Analysis of Variance (ANOVA) for Independent
Groups .............................................. 287
9.2 Dealing with Unequal Variances ...................... 298
9.3 Judging Sample Sizes and Controlling Power When
Comparing Means ..................................... 302
9.4 Trimmed Means ....................................... 305
9.5 Bootstrap Methods ................................... 309
9.6 Random Effects Model ................................ 314
9.7 Exercises ........................................... 324
10 Two-Way ANOVA ............................................. 329
10.1 The Basics of a Two-Way ANOVA Design ................ 329
10.2 Testing Hypotheses About Main Effects and
Interactions ........................................ 337
10.3 Heteroscedastic Methods for Trimmed Means ........... 344
10.4 Bootstrap Methods ................................... 350
10.5 Testing Hypotheses Based on Medians ................. 353
10.6 Exercises ........................................... 356
11 Comparing Dependent Croups ................................ 361
11.1 The Paired T-Test for Means ......................... 363
11.2 Comparing Trimmed Means ............................. 366
11.3 Bootstrap Methods ................................... 371
11.4 Measuring Effect Size ............................... 379
11.5 Comparing Variances ................................. 381
11.6 Comparing More Than Two Groups ...................... 383
11.7 Percentile Bootstrap Methods for Other Robust
Measures of Location ................................ 389
11.8 Comments on Which Method to Use ..................... 395
11.9 Between-by-Within, or Split-Plot, Designs ........... 397
11.10 Exercises ........................................... 404
12 Multiple Comparisons ...................................... 407
12.1 Homoscedastic Methods for the Means of Independent
Groups .............................................. 408
12.2 ANOVA F Versus Multiple Comparisons ................. 414
12.3 Heteroscedastic Methods for the Means of
Independent Groups .................................. 416
12.4 Linear Contrasts .................................... 420
12.5 Judging Sample Sizes ................................ 427
12.6 Methods for Trimmed Means ........................... 432
12.7 Bootstrap Methods ................................... 437
12.8 Methods for Dependent Groups ........................ 443
12.9 Analyzing Between-by-Within Designs ................. 449
12.10 Exercises ........................................... 454
13 Robust and Exploratory Regression ......................... 457
13.1 Detecting Outliers in Multivariate Data ............. 457
13.2 Some Robust Regression Methods ...................... 476
13.3 More Regression Estimators .......................... 482
13.4 Comments on Choosing a Regression Estimator ......... 488
13.5 Hypothesis Testing and Confidence Intervals ......... 495
13.6 Robust Measures of Correlation ...................... 501
13.7 Exercises ........................................... 511
14 More Regression Methods ................................... 517
14.1 Smoothers ........................................... 517
14.2 Smooths Based on Robust Measures of Location ........ 521
14.3 Comparing the Slopes of Two Independent Groups ...... 527
14.4 Tests for Linearity ................................. 530
14.5 Inferential Methods with Multiple Predictors ........ 533
14.6 Identifying the Best Predictors ..................... 538
14.7 Detecting Interactions .............................. 542
14.8 ANCOVA .............................................. 549
14.9 Exercises ........................................... 553
15 Rank-Based and Nonparametric Methods ...................... 557
15.1 Comparing Two Independent Groups .................... 557
15.2 Comparing More Than Two Groups ...................... 567
15.3 Multiple Comparisons Among Independent Groups ....... 571
15.4 Two-Way Designs ..................................... 572
15.5 Multiple Comparisons in a Two-Way Design ............ 575
15.6 Comparing Two Dependent Groups ...................... 578
15.7 Comparing Multiple Dependent Groups ................. 582
15.8 One-Way Multivariate Methods ........................ 585
15.9 Between-by-Within Designs ........................... 589
15.10 Rank-Based Correlations ............................. 597
15.11 Comparing Rank-Based Correlations ................... 601
15.12 Rank-Based Regression ............................... 601
15.13 The Rank-Transform Method ........................... 604
15.14 Exercises ........................................... 604
Appendix A Solutions to Selected Exercises ................... A-l
Appendix В Tables ............................................ B-l
Appendix С Basic Matrix Algebra .............................. C-l
References .................................................... R-l
Index ......................................................... 1-1
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