Modern statistics for the social and behavioral sciences: a practical introduction
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| Format: | Book |
| Language: | English |
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Boca Raton, Fla. [u.a.]
CRC Press
2012
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| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 840 S. graph. Darst. |
| ISBN: | 9781439834565 1439834563 |
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| 245 | 1 | 0 | |a Modern statistics for the social and behavioral sciences |b a practical introduction |c Rand Wilcox |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b CRC Press |c 2012 | |
| 300 | |a XX, 840 S. |b graph. Darst. | ||
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| adam_text | Titel: Modern statistics for the social and behavioral sciences
Autor: Wilcox, Rand R.
Jahr: 2012
Contents
Preface xix
1 INTRODUCTION 1
1.1 Samples versus Populations................... 2
1.2 Software ............................. 3
1.3 R Basics ............................. 4
1.3.1 Entering Data ...................... 4
1.3.2 R Functions and Packages................ 11
1.3.3 Data Sets......................... 13
1.3.4 Arithmetic Operations.................. 14
2 NUMERICAL AND GRAPHICAL SUMMARIES OF
DATA 17
2.1 Basic Summation Notation ................... 18
2.2 Measures of Location ...................... 19
2.2.1 The Sample Mean.................... 19
2.2.2 R Function Mean..................... 21
2.2.3 The Sample Median................... 22
2.2.4 R Function for the Median............... 24
2.2.5 A Criticism of the Median: It Might Trim Too Many
Values........................... 24
2.2.6 R Function for the Trimmed Mean........... 26
2.2.7 A Winsorized Mean................... 26
2.2.8 R Function winmean................... 27
2.2.9 What Is a Measure of Location?............ 28
2.3 Measures of Variation or Scale ................. 28
2.3.1 Sample Variance and Standard Deviation....... 29
2.3.2 R Functions for the Variance and Standard Deviation 30
2.3.3 The Interquartile Range................. 30
2.3.4 R Function idealf..................... 32
2.3.5 Winsorized Variance................... 32
2.3.6 R Function winvar.................... 32
2.3.7 Median Absolute Deviation............... 32
2.3.8 R Function mad..................... 33
2.3.9 Average Absolute Distance from the Median ..... 33
2.3.10 Other Robust Measures of Variation.......... 34
VI
2.3.11 R Functions bivar, pbvar, tauvar, and tbs....... 35
2.4 Detecting Outliers........................ 36
2.4.1 A Method Based on the Mean and Variance...... 37
2.4.2 A Better Outlier Detection Rule: The MAD-Median
Rule............................ 38
2.4.3 R Function out...................... 39
2.4.4 The Boxplot ....................... 39
2.4.5 R Function boxplot ................... 40
2.4.6 Modifications of the Boxplot Rule for Detecting
Outliers.......................... 41
2.4.7 R Function outbox.................... 42
2.4.8 Other Measures of Location............... 43
2.4.9 R Functions mom and onestep............. 45
2.5 Histograms............................ 46
2.5.1 R Functions hist and splot................ 54
2.6 Kernel Density Estimators ................... 54
2.6.1 R Functions kdplot and akerd.............. 55
2.7 Stem-and-Leaf Displays..................... 57
2.7.1 R Function stem..................... 58
2.8 Skewness............................. 58
2.8.1 Transforming Data.................... 59
2.9 Choosing a Measure of Location ................ 61
2.10 Covariance and Pearson s Correlation ............. 62
2.11 Exercises ............................. 63
3 PROBABILITY AND RELATED CONCEPTS 67
3.1 Basic Probability ........................ 68
3.2 Expected Values......................... 69
3.3 Conditional Probability and Independence .......... 71
3.4 Population Variance....................... 77
3.5 The Binomial Probability Function .............. 79
3.6 Continuous Variables and the Normal Curve ......... 84
3.6.1 Computing Probabilities Associated with Normal
Distributions....................... 87
3.6.2 R Function pnorm.................... 89
3.7 Understanding the Effects of Non-Normality ......... 94
3.7.1 Skewness ......................... 99
3.8 Pearson s Correlation and the Population Covariance .... 101
3.8.1 Computing the Population Covariance and Pearson s
Correlation........................ 102
3.9 Some Rules about Expected Values .............. 104
3.10 Chi-Squared Distributions ................... 105
3.11 Exercises ............................. 106
Vil
4 SAMPLING DISTRIBUTIONS AND CONFIDENCE
INTERVALS 111
4.1 Random Sampling........................ 112
4.2 Sampling Distributions ..................... 112
4.2.1 Sampling Distribution of the Sample Mean...... 114
4.2.2 Computing Probabilities Associated with the Sample
Mean ........................... 117
4.3 A Confidence Interval for the Population Mean........ 121
4.3.1 Known Variance..................... 121
4.3.2 Confidence Intervals When a Is Not Known...... 124
4.3.3 R Functions pt and qt.................. 126
4.3.4 Confidence Interval for the Population Mean Using Stu-
dent s T.......................... 127
4.3.5 R Function t.test..................... 127
4.4 Judging Location Estimators Based on Their Sampling
Distribution ........................... 129
4.4.1 Trimming and Accuracy: Another Perspective .... 134
4.5 An Approach to Non-Normality: The Central Limit Theorem 135
4.6 Student s T and Non-Normality ................ 138
4.7 Confidence Intervals for the Trimmed Mean.......... 147
4.7.1 Estimating the Standard Error of a Trimmed Mean . 147
4.7.2 R Function trimse.................... 153
4.8 A Confidence Interval for the Population Trimmed
Mean ............................... 153
4.8.1 R Function trimci .................... 157
4.9 Transforming Data ....................... 159
4.10 Confidence Interval for the Population Median........ 159
4.10.1 R Function sint...................... 161
4.10.2 Estimating the Standard Error of the Sample Median 162
4.10.3 R Function msmedse................... 162
4.10.4 More Concerns about Tied Values........... 162
4.11 A Rémark About MOM and M-Estimators.......... 164
4.12 Confidence Intervals for the Probability of Success...... 164
4.12.1 R Functions binomci and acbinomci.......... 167
4.13 Exercises ............................. 168
5 HYPOTHESIS TESTING 173
5.1 The Basics of Hypothesis Testing ............... 174
5.1.1 P-Value or Significance Level.............. 180
5.1.2 R Function t.test..................... 182
5.1.3 Criticisms of Two-Sided Hypothesis Testing and
P-Values.......................... 182
5.1.4 Summary and Generalization.............. 184
5.2 Power and Type II Errors.................... 185
5.2.1 Understanding How n, a, and a Are Related to Power 190
5.3 Testing Hypotheses about the Mean When a Is Not Known . 193
5.4 Controlling Power and Determining n ............. 195
5.4.1 Choosing n Prior to Collecting Data.......... 195
5.4.2 R Function power.t.test................. 196
5.4.3 Stein s Method: Judging the Sample Size When Data
Are Available....................... 196
5.4.4 R Functions steinl and stein2.............. 198
5.5 Practical Problems with Student s T Test........... 199
5.6 Hypothesis Testing Based on a Trimmed Mean........ 205
5.6.1 R Function trimci .................... 206
5.6.2 R Functions steinl.tr and stein2.tr........... 208
5.7 Testing Hypotheses about the Population Median ...... 208
5.7.1 R Function sintv2 .................... 208
5.8 Making Decisions about Which Measure of Location to Use . 209
5.9 Exercises ............................. 209
6 REGRESSION AND CORRELATION 213
6.1 The Least Squares Principle .................. 214
6.2 Confidence Intervals and Hypothesis Testing ......... 217
6.2.1 Classic Inferential Techniques.............. 221
6.2.2 Multiple Regression ................... 223
6.2.3 R Functions ols, lm, and olsplot............. 225
6.3 Standardized Regression .................... 228
6.4 Practical Concerns about Least Squares Regression and How
They Might Be Addressed ................... 230
6.4.1 The Effect of Outliers on Least Squares Regression . . 231
6.4.2 Beware of Bad Leverage Points............. 234
6.4.3 Beware of Discarding Outliers among the Y Values . . 236
6.4.4 Do Not Assume Homoscedasticity or That the
Regression Line Is Straight............... 237
6.4.5 Violating Assumptions When Testing Hypotheses . . . 239
6.4.6 Dealing with Heteroscedasticity: The HC4 Method . . 241
6.4.7 R Functions olshc4 and hc4test............. 242
6.5 Pearson s Correlation and the Coefficient of Determination . 243
6.5.1 A Closer Look at Interpreting r............. 246
6.6 Testing H0: p = 0 ........................ 250
6.6.1 R Functions cor.test and pwr.t.test........... 251
6.6.2 R Function pwr.r.test .................. 253
6.6.3 Testing Ho - p = 0 When There is Heteroscedasticity . 254
6.6.4 R Function pcorhc4 ................... 254
6.6.5 When Is It Safe to Conclude That Two Variables Are
Independent?....................... 254
6.7 A Regression Method for Estimating the Median of Y and
Other Quantités ......................... 255
6.7.1 R Function rqfit ..................... 257
IX
6.8 Detecting Heteroscedasticity .................. 257
6.8.1 R Function khomreg................... 258
6.9 Concluding Remarks ...................... 259
6.10 Exercises ............................. 259
7 BOOTSTRAP METHODS 265
7.1 Bootstrap-t Method ....................... 265
7.1.1 Symmetric Confidence Intervals............. 271
7.1.2 Exact Nonparametric Confidence Intervals for Means
Are Impossible...................... 273
7.2 The Percentile Bootstrap Method ............... 274
7.3 Inferences about Robust Measures of Location ........ 277
7.3.1 Using the Percentile Method .............. 277
7.3.2 R Functions onesampb, momci, and trimpb...... 278
7.3.3 The Bootstrap-t Method Based on Trimmed Means . 279
7.3.4 R Function trimcibt................... 281
7.4 Estimating Power When Testing Hypotheses about a Trimmed
Mean ............................... 282
7.4.1 R Functions powtlest and powtlan........... 283
7.5 A Bootstrap Estimate of Standard Errors........... 286
7.5.1 R Function bootse.................... 287
7.6 Inferences about Pearson s Correlation: Dealing with
Heteroscedasticity ........................ 287
7.6.1 R Function pcorb..................... 289
7.7 Bootstrap Methods for Least Squares Regression....... 290
7.7.1 R Functions hc4wtest, olswbtest, lsfitci........ 292
7.8 Detecting Associations Even When There Is Curvature . . . 294
7.8.1 R Functions indt and medind.............. 296
7.9 Quantile Regression ....................... 297
7.9.1 R Functions qregci and rqtest.............. 298
7.9.2 A Test for Homoscedasticity Using a Quantile
Regression Approach................... 298
7.9.3 R Function qhomt.................... 300
7.10 Regression: Which Predictors Are Best? ........... 300
7.10.1 R Function regpre.................... 303
7.10.2 Least Angle Regression ................. 305
7.10.3 R Function larsR..................... 306
7.11 Comparing Correlations............... ...... 306
7.11.1 R Functions TWOpov and TWOpNOV........ 308
7.12 Empirical Likelihood ...................... 309
7.13 Exercises ............................. 309
8 COMPARING TWO INDEPENDENT GROUPS 313
8.1 Student s T Test......................... 314
8.1.1 Choosing the Sample Sizes ............... 317
8.1.2 R Function power.t.test................. 317
8.2 Relative Merits of Student s T ................. 318
8.3 Welch s Heteroscedastic Method for Means .......... 322
8.3.1 R Function t.test..................... 324
8.3.2 Tukey s Three-Decision Rule .............. 326
8.3.3 Non-Normality and Welch s Method.......... 327
8.3.4 Three Modern Insights Regarding Methods for
Comparing Means.................... 328
8.4 Methods for Comparing Medians and Trimmed Means .... 329
8.4.1 Yuen s Method for Trimmed Means .......... 329
8.4.2 R Functions yuen and fac21ist.............. 330
8.4.3 Comparing Medians................... 331
8.4.4 R Function msmed.................... 332
8.5 Percentile Bootstrap Methods for Comparing Measures of
Location ............................. 332
8.5.1 Using Other Measures of Location........... 335
8.5.2 Comparing Medians................... 335
8.5.3 R Function medpb2 ................... 335
8.5.4 Some Guidelines on When to Use the Percentile Boot-
strap Method....................... 336
8.5.5 R Functions trimpb2 and pb2gen............ 336
8.6 Bootstrap-t Methods for Comparing Measures of Location . 338
8.6.1 Comparing Means.................... 339
8.6.2 Bootstrap-t Method When Comparing Trimmed Means 339
8.6.3 R Functions yuenbt and yhbt ............. 341
8.6.4 Estimating Power and Judging the Sample Sizes . . . 344
8.6.5 R Functions powest and pow2an............ 344
8.7 Permutation Tests........................ 345
8.7.1 R Function permg.................... 348
8.8 Rank-Based and Nonparametric Methods........... 348
8.8.1 Wilcoxon-Mann-Whitney Test............. 349
8.8.2 R Functions wmw and wilcox.test ........... 351
8.8.3 Handling Tied Values and Heteroscedasticity..... 352
8.8.4 Cliff s Method .................... . 352
8.8.5 R functions cid and cidv2................ 354
8.8.6 The Brunner-Munzel Method.............. 355
8.8.7 R function bmp...................... 358
8.8.8 The Kolmogorov-Smirnov Test............. 359
8.8.9 R Function ks....................... 360
8.8.10 Comparing All Quantiles Simultaneously: An Extension
of the Kolmogorov-Smirnov Test............ 361
8.8.11 R Function sband .................... 361
8.9 Graphical Methods for Comparing Groups .......... 363
8.9.1 Error Bars ........................ 363
8.9.2 R Function ebarplot................... 366
8.9.3 Plotting the Shift Function............... 367
8.9.4 Plotting the Distributions................ 371
8.9.5 R Function sumplot2g.................. 371
8.9.6 Other Approaches.................... 371
8.10 Comparing Measures of Scale.................. 373
8.11 Methods for Comparing Measures of Variation ........ 374
8.11.1 R Function comvar2................... 375
8.11.2 Brown-Forsythe Method................. 375
8.11.3 Comparing Robust Measures of Variation....... 376
8.12 Measuring Effect Size ...................... 377
8.12.1 R Functions yuenv2 and akp.effect............ 385
8.13 Comparing Correlations and Regression Slopes........ 385
8.13.1 R Functions twopcor, twolsreg, and tworegwb..... 387
8.14 Comparing Two Binomials ................... 388
8.14.1 Storer-Kim Method................... 388
8.14.2 Beal s Method ...................... 389
8.14.3 R Functions twobinom, twobici, and power.prop.test . 390
8.15 Making Decisions about Which Method to Use........ 391
8.16 Exercises ............................. 393
COMPARING TWO DEPENDENT GROUPS 399
9.1 The Paired T Test........................ 401
9.1.1 When Does the Paired T Test Perform Well?..... 402
9.1.2 R Function t.test..................... 403
9.2 Comparing Robust Measures of Location ........... 404
9.2.1 R Functions yuend, ydbt, and dmedpb . . ....... 406
9.2.2 Comparing Marginal M-Estimators........... 411
9.2.3 R Function rmmest.................... 412
9.3 Handling Missing Values .................... 412
9.3.1 R Functions rm2miss and rmmismcp.......... 415
9.4 A Different Perspective When Using Robust Measures of
Location ............................. 415
9.4.1 R Functions loc2dif and 12drmci ............ 416
9.5 The Sign Test .......................... 417
9.5.1 R Function signt..................... 417
9.6 Wilcoxon Signed Rank Test................... 418
9.6.1 R Function wilcox.test.................. 420
9.7 Comparing Variances ...................... 420
9.8 Comparing Robust Measures of Scale ............. 421
9.8.1 R Function rmrvar.................... 422
9.9 Comparing All Quantiles .................... 423
9.9.1 R Function lband..................... 423
Xll
9.10 Plots for Dependent Groups .................. 423
9.10.1 R Function g2plotdifxy ................. 425
9.11 Exercises ............................. 425
10 ONE-WAY ANOVA 427
10.1 Analysis of Variance for Independent Groups......... 428
10.1.1 A Conceptual Overview................. 429
10.1.2 ANOVA via Least Squares Regression and Dummy
Coding .......................... 434
10.1.3 R Functions anova, anoval, aov, and fac21ist ..... 435
10.1.4 Controlling Power and Choosing the Sample Sizes . . 439
10.1.5 R Functions power.anova.test and anova.power .... 440
10.2 Dealing with Unequal Variances ................ 441
10.2.1 Welch s Test ....................... 442
10.3 Judging Sample Sizes and Controlling Power When Data Are
Available ............................. 446
10.3.1 R Functions bdanoval and bdanova2.......... 449
10.4 Trimmed Means ......................... 450
10.4.1 R Functions tlway, tlwayv2, and tlwayF....... 452
10.4.2 Comparing Groups Based on Medians......... 454
10.4.3 R Function medlway................... 455
10.5 Bootstrap Methods ....................... 455
10.5.1 A Bootstrap-t Method.................. 455
10.5.2 R Function tlwaybt................... 456
10.5.3 Two Percentile Bootstrap Methods........... 457
10.5.4 R Functions blway and pbadepth ........... 461
10.5.5 Choosing a Method ................... 462
10.6 Random Effects Model ..................... 462
10.6.1 A Measure of Effect Size................. 466
10.6.2 A Heteroscedastic Method................ 468
10.6.3 A Method Based on Trimmed Means.......... 470
10.6.4 R Function rananova................... 471
10.7 Rank-Based Methods ...................... 472
10.7.1 The Kruskall-Wallis Test................ 473
10.8 R Function kruskal.test ..................... 474
10.8.1 Method BDM....................... 475
10.8.2 R Function bdm..................... 476
10.9 Exercises ............................. 477
11 TWO-WAY AND THREE-WAY DESIGNS 483
11.1 Basics of a Two-Way ANOVA Design ............. 483
11.1.1 Interactions........................ 487
11.1.2 R Functions interaction.plot and interplot....... 494
11.1.3 Interactions When There Are More than Two Levels . 495
11.2 Testing Hypotheses about Main Effects and Interactions . . 497
XIU
11.2.1 R Function anova..................... 501
11.2.2 Inferences about Disordinal Interactions........ 502
11.2.3 The Two-Way ANOVA Model ............. 504
11.3 Heteroscedastic Methods for Trimmed Means, Including
Means............................... 505
11.3.1 R Function t,2way .................... 507
11.4 Bootstrap Methods ....................... 509
11.4.1 R Functions pbad2way and t2waybt.......... 512
11.5 Testing Hypotheses Based on Medians............. 514
11.5.1 R Function m2way.................... 515
11.6 A Rank-Based Method for a Two-Way Design ........ 516
11.6.1 R Function bdm2way .................. 517
11.6.2 The Patel-Hoel Approach to Interactions....... 517
11.7 Three-Way ANOVA....................... 519
11.7.1 R Functions anova and t3way.............. 521
11.8 Exercises ............................. 522
12 COMPARING MORE THAN TWO DEPENDENT
GROUPS 527
12.1 Comparing Means in a One-Way Design............ 527
12.1.1 R Function aov...................... 530
12.2 Comparing Trimmed Means When Dealing with a One-Way
Design .............................. 531
12.2.1 R Functions rmanova and rmdat2mat......... 533
12.2.2 A Bootstrap-t Method for Trimmed Means...... 535
12.2.3 R Function rmanovab.................. 536
12.3 Percentile Bootstrap Methods for a One-Way Design .... 536
12.3.1 Method Based on Marginal Measures of Location . . . 537
12.3.2 R Function bdlway ................... 537
12.3.3 Inferences Based on Difference Scores......... 538
12.3.4 R Function rmdzero................... 541
12.4 Rank-Based Methods for a One-Way Design ......... 541
12.4.1 Friedman s Test ..................... 541
12.4.2 R Function friedman.test ................ 542
12.4.3 Method BPRM...............-....... 543
12.4.4 R Function bprm..................... 544
12.5 Comments on Which Method to Use.............. 544
12.6 Between-by-Within Designs................... 545
12.6.1 Method for Trimmed Means............... 546
12.6.2 R Function bwtrim and bw21ist............. 549
12.6.3 A Bootstrap-t Method.................. 550
12.6.4 R Function tsplitbt.................... 551
12.6.5 Inferences Based on M-estimators and Other Robust
Measures of Location .................. 552
12.6.6 R Functions sppba, sppbb, and sppbi.......... 553
12.6.7 A Rank-Based Test.................... 554
12.6.8 R Function bwrank.................... 559
12.7 Within-by-Within Design.................... 560
12.7.1 R Function wwtrim ................... 561
12.8 Three-Way Designs ....................... 561
12.8.1 R Functions bbwtrim, bwwtrim, and wwwtrim .... 561
12.8.2 Data Management: R Functions bw21ist and bbw21ist 561
12.9 Exercises ............................. 562
13 MULTIPLE COMPARISONS 565
13.1 One-Way ANOVA, Independent Groups............ 566
13.1.1 Fisher s Least Significant Difference Method...... 566
13.1.2 The Tukey-Kramer Method............... 568
13.1.3 R Function TukeyHSD.................. 569
13.1.4 Tukey-Kramer and the ANOVA F Test........ 571
13.1.5 A Step-Down Method.................. 571
13.1.6 Dunnett s T3....................... 575
13.1.7 Games-Howell Method.................. 576
13.1.8 Comparing Trimmed Means............... 577
13.1.9 R Function lincon .................... 577
13.1.10 Alternative Methods for Controlling F WE...... 578
13.1.11 Percentile Bootstrap Methods for Comparing Trimmed
Means, Medians, and M-estimators........... 581
13.1.12 R Functions medpb, tmcppb, pbmcp, and mcppb20 . 582
13.1.13 A Bootstrap-t Method ................. 583
13.1.14 R Function linconb................... 584
13.1.15 Rank-Based Methods.................. 584
13.1.16 R Functions cidmul, cidmulv2, and bmpmul..... 585
13.2 Two-Way, between-by-between Design............. 585
13.2.1 Scheffé s Homoscedastic Method............ 588
13.2.2 Heteroscedastic Methods................. 589
13.2.3 Extension of Welch-Sidák and Kaiser-Bowden Methods
to Trimmed Means.................... 592
13.2.4 R Function kbcon .................... 594
13.2.5 R.Function con2way................... 594
13.2.6 Linear Contrasts Based on Medians .......... 597
13.2.7 R Functions msmed and mcp2med........... 598
13.2.8 Bootstrap Methods.................... 598
13.2.9 R Functions linconb, mcp2a, and bbmcppb...... 599
13.2.10 The Patel Hoel Rank-Based Interaction Method ... 600
13.2.11 R Function rimul .................... 600
13.3 Judging Sample Sizes ...................... 600
13.3.1 Tamhane s Procedure.................. 601
13.3.2 R Function tamhane.............. ..... 602
13.3.3 Hochberg s Procedure.................. 603
13.3.4 R Function hochberg................... 605
13.4 Methods for Dependent Groups ................ 605
13.4.1 Linear Contrasts Based on Trimmed Means...... 606
13.4.2 R Function rmmcp.................... 607
13.4.3 Comparing M-estimators ................ 608
13.4.4 R Functions rmmcppb, dmedpb, and dtrimpb..... 608
13.4.5 Bootstrap-t Method................... 609
13.4.6 R Function bptd..................... 609
13.5 Between-by-within Designs ................... 609
13.5.1 R Functions bwmcp, bwamcp, bwbmcp, bwimcp, spm-
cpa, spmcpb, spmcpi, and bwmcppb.......... 612
13.6 Within-by-within Designs.................... 615
13.6.1 Three-Way Designs.................... 616
13.6.2 R Functions con3way, mcp3atm, and rm3mcp..... 616
13.6.3 Bootstrap Methods for Three-Way Designs...... 618
13.6.4 R Functions bbwmcp, bwwmcp, bbbmcppb, bbwmcppb,
bwwmcppb, and wwwmcppb.............. 618
13.7 Exercises ............................. 620
14 SOME MULTIVARIATE METHODS 625
14.1 Location, Scatter, and Detecting Outliers........... 626
14.1.1 Detecting Outliers via Robust Measures of Location and
Scatter .......................... 630
14.1.2 R Functions cov.mve and com.med........... 631
14.1.3 More Measures of Location and Covariance...... 633
14.1.4 R Functions rmba, tbs, and ogk............. 633
14.1.5 R Function out...................... 633
14.1.6 A Projection-Type Outlier Detection Method..... 634
14.1.7 R Functions outpro, outproMC, outproad,
outproadMC, and out3d................. 636
14.1.8 Skipped Estimators of Location............. 638
14.1.9 R Functions smean.................... 638
14.2 One-Sample Hypothesis Testing ................ 638
14.2.1 Comparing Dependent Groups.........: . . . 642
14.2.2 R Functions smeancrv2, hotell, and rmdzeroOP . . . 643
14.3 Two-Sample Case ........................ 645
14.3.1 R Functions smean2, mat2grp, and matsplit...... 645
14.4 MANOVA ............................ 648
14.4.1 R Function manova ................... 649
14.4.2 Robust MANOVA Based on Trimmed Means..... 650
14.4.3 R Functions MULtr.anova and MULAOVp...... 651
14.4.4 A Multivariate Extension of the Wilcoxon-Mann-
Whitney Test....................... 652
14.4.5 Explanatory Measure of Effect Size: A Projection-Type
Generalization ...................... 652
14.4.6 R Function mulwmwv2 ................. 653
14.5 Rank-Based Multivariate Methods............... 656
14.5.1 The Munzel-Brunner Method.............. 656
14.5.2 R Function mulrank................... 657
14.5.3 The Choi-Marden Multivariate Rank Test....... 658
14.5.4 R Function cmanova................... 660
14.6 Multivariate Regression..................... 661
14.6.1 Multivariate Regression Using R............ 662
14.6.2 Robust Multivariate Regression............. 662
14.6.3 R Function mlrreg and mopreg............. 663
14.7 Principal Components...................... 664
14.7.1 R Functions prcomp and regpca ............ 666
14.7.2 Robust Principal Components.............. 671
14.7.3 R Functions outpca, robpca, robpcaS, Ppca, and
Ppca.summary...................... 671
14.8 Exercises ............................. 674
15 ROBUST REGRESSION AND MEASURES OF
ASSOCIATION 677
15.1 Robust Regression Estimators .................. 677
15.1.1 The Theil-Sen Estimator................ 678
15.1.2 R Functions tsreg and regplot.............. 679
15.1.3 Least Median of Squares................. 680
15.1.4 Least Trimmed Squares and Least Trimmed Absolute
Value Estimators..................... 680
15.1.5 R Functions lmsreg, ltsreg, and ltareg......... 681
15.1.6 M-Estimators....................... 681
15.1.7 R Function chreg..................... 682
15.1.8 Deepest Regression Line................. 682
15.1.9 R Function mdepreg................... 682
15.1.10 Skipped Estimators................... 683
15.1.11 R Functions opreg and opregMC............ 683
15.1.12 S-estimators and an E-Type Estimator........ 683
15.1.13 R Function tsts..................... 683
15.2 Comments on Choosing a Regression Estimator ....... 684
15.3 Testing Hypotheses When Using Robust Regression
Estimators ............................ 686
15.3.1 R Functions regtest, regtestMC, regci, and regciMC . 687
15.3.2 Comparing Measures of Location via Dummy Coding 689
15.4 Dealing with Curvature: Smoothers .............. 691
15.4.1 Cleveland s Smoother.................. 691
15.4.2 R Functions lowess and lplot.............. 693
15.4.3 Smoothers Based on Robust Measures of Location . . 696
15.4.4 R Functions rplot and rplotsm............. 697
15.4.5 More Smoothers..................... 697
XVll
15.4.6 R Functions kerreg, runpd, and qsmcobs........ 697
15.4.7 Prediction When X Is Discrete:
The R Function rundis.................. 698
15.4.8 Seeing Curvature with More than Two Predictors . . 698
15.4.9 R Function prplot .................... 699
15.4.10 Some Alternative Methods............... 701
15.5 Some Robust Correlations and Tests of Independence .... 701
15.5.1 Kendall s tau....................... 702
15.5.2 Spearman s rho...................... 703
15.5.3 Winsorized Correlation ................. 703
15.5.4 R. Function wincor.................... 704
15.5.5 OP Correlation . . .................... 704
15.5.6 R Function scor...................... 705
15.5.7 Inferences about Robust Correlations: Dealing with Het-
eroscedasticity...................... 706
15.5.8 R Function corb ..................... 706
15.6 Measuring the Strength of an Association Based on a Robust
Fit ................................ 706
15.7 Comparing the Slopes of Two Independent Groups...... 708
15.7.1 R Functions reg2ci, runmean2g, and 12plot ...... 708
15.8 Tests for Linearity........................ 709
15.8.1 R Functions lintest, lintestMC, and linchk....... 712
15.9 Identifying the Best Predictors................. 713
15.9.1 R Functions regpord, ts2str, and sm2strv7....... 716
15-lODetecting Interactions and Moderator Analysis........ 717
15.10.1 R Functions adtest ................... 720
15.10.2 Graphical Methods for Assessing Interactions..... 720
15.10.3 R Functions kercon, runsm2g, regi, ois.plot.inter,
and reg.plot.inter..................... 722
15.11ANCOVA............................. 725
15.11.1 Classic ANCOVA..................... 725
15.11.2 Some Modern ANCOVA Methods ........... 727
15.11.3R Functions ancsm, Qancsm, ancova, ancpb, ancbbpb,
and ancboot ....................... 729
15.12 Exercises............................. 732
16 BASIC METHODS FOR ANALYZING CATEGORICAL
DATA 735
16.1 Goodness of Fit ......................... 736
16.1.1 R Functions chisq.test and pwr.chisq.test ....... 737
16.2 A Test of Independence..................... 739
16.2.1 R Function chi.test.ind.................. 741
16.3 Detecting Differences in the Marginal Probabilities...... 742
16.3.1 R Functions confab and mcnemar.test......... 745
16.4 Measures of Association..................... 746
XVlll
16.4.1 The Proportion of Agreement.............. 749
16.4.2 Kappa........................... 750
16.4.3 Weighted Kappa..................... 751
16.4.4 R Function Ckappa ................... 751
16.5 Logistic Regression ....................... 752
16.5.1 R Functions glm and logreg............... 753
16.5.2 A Confidence Interval for the Odds Ratio....... 755
16.5.3 R Function ODDSR.CI ................. 755
16.5.4 Smoothers for Logistic Regression ........... 756
16.5.5 R Functions logrsm, rplot.bin, and logSM....... 757
16.6 Exercises ............................. 758
Appendix A ANSWERS TO SELECTED EXERCISES 761
Appendix B TABLES 767
Appendix C BASIC MATRIX ALGEBRA 795
Appendix D REFERENCES 803
Index 831
|
| any_adam_object | 1 |
| author | Wilcox, Rand R. |
| author_GND | (DE-588)141426241 |
| author_facet | Wilcox, Rand R. |
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| author_sort | Wilcox, Rand R. |
| author_variant | r r w rr rrw |
| building | Verbundindex |
| bvnumber | BV037381985 |
| classification_rvk | MR 2100 |
| classification_tum | SOZ 720f |
| ctrlnum | (OCoLC)462925907 (DE-599)BVBBV037381985 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Soziologie Mathematik |
| format | Book |
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| id | DE-604.BV037381985 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:23:06Z |
| institution | BVB |
| isbn | 9781439834565 1439834563 |
| language | English |
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| physical | XX, 840 S. graph. Darst. |
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| publisher | CRC Press |
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| spelling | Wilcox, Rand R. Verfasser (DE-588)141426241 aut Modern statistics for the social and behavioral sciences a practical introduction Rand Wilcox Boca Raton, Fla. [u.a.] CRC Press 2012 XX, 840 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Datenanalyse (DE-588)4123037-1 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Sozialwissenschaften (DE-588)4055916-6 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Statistik (DE-588)4056995-0 s Datenanalyse (DE-588)4123037-1 s Sozialwissenschaften (DE-588)4055916-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022535086&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wilcox, Rand R. Modern statistics for the social and behavioral sciences a practical introduction Datenanalyse (DE-588)4123037-1 gnd Statistik (DE-588)4056995-0 gnd Sozialwissenschaften (DE-588)4055916-6 gnd |
| subject_GND | (DE-588)4123037-1 (DE-588)4056995-0 (DE-588)4055916-6 (DE-588)4151278-9 |
| title | Modern statistics for the social and behavioral sciences a practical introduction |
| title_auth | Modern statistics for the social and behavioral sciences a practical introduction |
| title_exact_search | Modern statistics for the social and behavioral sciences a practical introduction |
| title_full | Modern statistics for the social and behavioral sciences a practical introduction Rand Wilcox |
| title_fullStr | Modern statistics for the social and behavioral sciences a practical introduction Rand Wilcox |
| title_full_unstemmed | Modern statistics for the social and behavioral sciences a practical introduction Rand Wilcox |
| title_short | Modern statistics for the social and behavioral sciences |
| title_sort | modern statistics for the social and behavioral sciences a practical introduction |
| title_sub | a practical introduction |
| topic | Datenanalyse (DE-588)4123037-1 gnd Statistik (DE-588)4056995-0 gnd Sozialwissenschaften (DE-588)4055916-6 gnd |
| topic_facet | Datenanalyse Statistik Sozialwissenschaften Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022535086&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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