Permutation statistical methods with R:
Gespeichert in:
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| Sprache: | English |
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[2021]
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xxiv, 660 Seiten |
| ISBN: | 9783030743635 9783030743604 |
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| 100 | 1 | |a Berry, Kenneth J. |e Verfasser |0 (DE-588)1105489388 |4 aut | |
| 245 | 1 | 0 | |a Permutation statistical methods with R |c Kenneth J. Berry, Kenneth L. Kvamme, Janis E. Johnston, Paul W. Mielke, Jr. |
| 264 | 1 | |a Cham |b Springer |c [2021] | |
| 300 | |a xxiv, 660 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 700 | 1 | |a Kvamme, Kenneth L. |e Verfasser |0 (DE-588)1147773343 |4 aut | |
| 700 | 1 | |a Johnston, Janis E. |d 1957- |e Verfasser |0 (DE-588)1105494063 |4 aut | |
| 700 | 1 | |a Mielke, Paul W. |e Verfasser |0 (DE-588)1105493067 |4 aut | |
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-030-74361-1 |
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Datensatz im Suchindex
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| adam_text | Contents 1 Introduction................................................................................................ 1.1 Overviews of Chaps. 2-11 ............................................................ 1.2 Chapter 2............................................................................................. 1.3 Chapter 3............................................................................................. 1.4 Chapter 4 . ........................................................................................... 1.5 Chapter 5 . ........................................................................................... 1.6 Chapter 6............................................................................................. 1.7 Chapter 7............................................................................................ 1.8 Chapter 8............................................................................................ 1.9 Chapter 9............................................................................................ 1.10 Chapter 10.......................................................................................... 1.11 Chapter 11.......................................................................................... 1.12 Summary........................................................................................... 1.13 Preview of Chap. 2. ....................................................................... References.................................................................................................... 1 4 5 6 6 7
9 11 12 13 14 16 17 18 18 2 The R Programming Language............................................................... 2.1 R and RStudio, What are They About?........................................ 2.1.1 . What is R?...................... 2.1.2 Using R: Interactive Versus “Batch” Mode.................. 2.1.3 Installing R....................................................................... 2.1.4 RStudio............................................................................... 2.1.5 R Help................................................................................. 2.1.6 R Manuals and Books..................................................... 2.2 Beginning R and RStudio............................................................... 2.2.1 Preliminaries........................................... 2.2.2 R as a Simple Calculator................................................ 2.2.3 Arrow Keys for Using Previous Commands................. 2.2.4 Variables......................................... 2.2.5 The Assignment Operator................................................ 19 19 20 21 21 21 25 26 27 27 27 28 29 29 XV
Contents xvi 2.3 2.4 2.5 2.6 2.7 2.8 2.9 Using Variables in Expressions............... 2.2.6 Removing Variables—Using R Functions 2.2.7 Mathematical Functions........................... 2.2.8 Nesting of Commands............................. 2.2.9 2.2.10 Numerical Representations...................... Vectors Creating Vector Variables...................... 2.3.1 Using Subscripts: Vector Indexing.... 2.3.2 Adding and Removing Vector Elements 2.3.3 Doing Mathematics with Vectors.......... 2.3.4 2.3.5 Missing Values....................................... Random Numbers.................................... 2.3.6 Basic Statistical Functions...................... 2.3.7 Basic R Data Types 2.4.1 Coercion...................................... Numeric Data............................... 2.4.2 2.4.3 Logical Data............................... 2.4.4 Integer Data............................... 2.4.5 Character Data.......................... Learning More About Variables 2.4.6 Matrices 2.5.1 Creating Matrices............................................ 2.5.2 Characteristics of a Matrix........................... 2.5.3 Applying Functions to Query Matrices . . . 2.5.4 Manipulating Matrices.................................. 2.5.5 Naming Rows and Columns................... . . 2.5.6 Adding New Rows or Columns to Matrices Arrays: More Than Two Dimensions........................... Factors 2.7.1 Factor Functions............................................ 2.7.2 Useful Data Manipulations with Factors. . Lists. . 2.8.1 Referencing List Elements 2.8.2 Manipulating Lists.......... 2.8.3 Search Path
Attachment . Data Frames 2.9.1 Viewing and Selecting Data Frame Elements 2.9.2 Computing Statistics......................................... 2.9.3 Sorting Data Frames......................................... 2.9.4 R’s Sorting Functions....................................... 2.9.5 Adding Rows or Columns to Data Frames . . 2.9.6 Creating a New Data Frame........................... 2.9.7 Editing Values in a Data Frame................... 30 30 31 32 33 34 34 37 37 38 38 40 41 42 43 43 43 48 49 51 52 52 54 54 56 57 57 58 60 61 63 64 65 66 67 67 69 71 72 73 75 76 77
Contents Saving Work.................................................................................... 2.10.1 Setting and Getting Folder Pathways............................. 2.10.2 Session History Files....................................................... 2.10.3 R Scripts............................................................................. 2.10.4 Workspace Files................................................................ 2.10.5 Writing External Text Files.............................................. 2.11 Reading External Text Files.......................................................... 2.11.1 Reading Files Holding a SingleVariable....................... 2.11.2 Reading Tables of Data with ManyVariables.............. 2.12 Downloading and Installing Packages......................................... 2.13 Programming Structures in R......................................................... 2.13.1 The Comment.................................................................. 2.13.2 Writing Your Own Functions........................................ 2.13.3 Conditional Statements.................................................... 2.13.4 Loops................................................................................. 2.13.5 Writing Interactive Code.................................................. 2.14 Summary.......................................................................................... 2.15 Preview of Chap. 3..........................................................................
References..................................................................................................... 78 78 79 79 80 81 82 83 84 87 89 89 90 91 94 98 98 99 99 Permutation Statistical Methods............................................................. 3.1 Introduction......................................................................................... 3.2 A Brief History of Permutation Methods...................................... 3.2.1 The 1920s.......................................................................... 3.2.2 The 1930s.......................................................................... 3.2.3 The 1940s.......................................................................... 3.2.4 The 1950s.......................................................................... 3.2.5 The 1960s.......................................................................... 3.2.6 The 1970s.......................................................................... 3.2.7 The 1980s.......................................................................... 3.2.8 The 1990s.......................................................................... 3.2.9 The 2000s.......................................................................... 3.2.10 The 2010s.......................................................................... 3.3 The Neyman-Pearson Population Model...................................... 3.4 The Fisher-Pitman Permutation Model........................................... 3.4.1 Exact Permutation Tests................................................... 3.4.2
Monte Carlo Permutation Tests....................................... 3.5 Permutation and Parametric Statistical Tests.................................. 3.5.1 The Assumption of Random Sampling........................... 3.5.2 The Assumption of Normality......................................... 3.6 Advantages of Permutation Methods.............................................. 3.7 Calculation Efficiency........................................................................ 3.7.1 High-SpeedComputing..................................................... 3.7.2 Analysis with Combinations........................................... 101 102 102 103 103 104 105 105 106 107 108 108 109 110 Ill 112 114 115 115 116 116 117 118 118 2.10 3 xvii
Contents xviii 3.7.3 Mathematical Recursion......................... 3.7.4 Variable Components of a Test Statistic 3.7.5 Holding an Array Constant.................... 3.8 Summary................................................................... 3.9 Preview of Chap. 4................................................... References............................................................................ 119 119 120 120 121 121 Central Tendency and Variability............................................................ 4.1 Introduction......................................................................................... 4.2 Data Storage Modes and Structures................................................. 4.3 Statistical Graphics.............................................................................. 4.4 The Sample Mode .............................................................................. 4.4.1 R Script for the Sample Mode......................................... 4.5 The Sample Mean................................................................................. 4.5.1 R Script for the Sample Mean......................................... 4.6 The Sample Median............................................................................ 4.6.1 R Script for the Sample Median..................................... 4.7 The Sample Standard Deviation and Variance............................... 4.7.1 R Script for the Sample Standard Deviation................. 4.8 The Mean Absolute Deviation.......................................................... 4.8.1 R Script for the
Mean Absolute Deviation.................... 4.9 An Alternative Approach to Dispersion Measures........................ 4.9.1 Pairwise Differences: Standard Deviation....................... 4.9.2 R Script for the Sample Standard Deviation.................. 4.10 Summary.............................................................................................. 4.11 Preview of Chap. 5............................................................................. Reference......................................................................................................... 4 5 One-Sample Tests..................... 5.1 Introduction.......................................................................................... 5.2 Student’s One-Sample t Test.............................................................. 5.3 A Permutation Approach..................................................................... 5.4 The Relationship Between Test Statistics tand б.......................... 5.5 Test Statistics t and б.......................................................................... 5.5.1 R Script for Student’s t Test............................................. 5.5.2 R Script for Test Statistic б............................................... 5.5.3 R Script for an Exact Student’s t Test............................ 5.5.4 The Choice Between Test Statistics t and б.................. 5.6 The Measurement of Effect Size....................................................... 5.6.1 R Script for the Expected Value of б............................... 5.7 Detailed Calculations for
Statistics б andμ .................................... 5.7.1 Comparisons of Effect Size Measures............................. 5.7.2 R Script for the 91 Measure of Effect Size..................... 1ZJ 126 12$ 134 135 137 138 140 141 143 144 146 147 149 149 152 153 154 154 155 15 156 152 159 159 161 167 169 172 172 174 176 179 180
Contents xix 5.8 6 Measures of Effect Size........................ 5.8.1 R Script for Measures of Effect Size............................ 5.9 Analyses with v = 2 and v = 1..................................................... 5.9.1 An Exact Analysis with v = 2....................................... 5.9.2 R Script for Test Statistic б............................................ 5.9.3 The Assumption of Normality....................................... 5.9.4 An Exact Analysis with v = 1....................................... 5.10 Exact and Monte Carlo Analyses.................................................. 5.10.1 A Monte Carlo Analysis with v = 2........................ . 5.10.2 R Script for a Monte Carlo Analysis............................. 5.10.3 An Exact Analysis with v = 2........................................ 5.10.4 A Monte Carlo Analysis with v = 1............................. 5.10.5 An Exact Analysis with v = 1........................................ 5.11 Rank-Score Permutation Analyses................................................ 5.11.1 The Wilcoxon Signed-Ranks Test................................. 5.11.2 A Pennutation Approach................................................ 5.11.3 An Example Analysis.................................................... 5.11.4 R Script for Wilcoxon’s Signed-Ranks Test................ 5.11.5 An Exact Analysis with v = 2........................................ 5.11.6 The Relationship Between Statistics T and б............... 5.11.7 R Script for a Monte Carlo ProbabilityValue.............. 5.11.8 An Exact Analysis with v =
1....................................... 5.12 Summary....................................................................................... 5.13 Preview of Chap. 6........................................................................ References................................................................................................. 181 182 184 188 189 192 193 195 199 200 204 204 205 206 206 207 207 209 213 214 215 218 22θ 22θ 221 Two-Sample Tests 223 224 224 225 226 228 229 230 235 238 242 245 248 249 252 258 261 262 6.1 6.2 6.3 6.4 6.5 6.6 Introduction...................................................................... Two-Sample Tests........................................................... 6.2.1 Student’s Two-Sample t Test......................... A Permutation Approach.................................................. 6.3.1 The Relationship Between Statistics t and б. . Test Statistics t and б....................................................... 6.4.1 R Script for a Test of Homogeneity R Script for Student’s t Test......... 6.4.2 A Permutation Approach................ 6.4.3 R Script for Test Statistic б........... 6.4.4 Measures of Effect Size..................................... 6.5.1 Comparisons of Effect Size Measures 6.5.2 R Script for Measures of Effect Size . Analyses with v = 2 and v = 1......................... An Exact Analysis with v = 2 6.6.1 Measures of Effect Size .... 6.6.2 An Exact Analysis with v = 1 6.6.3
Contents XX Exact and Monte Carlo Analyses............ .. . · A Monte Carlo Analysis with v = 2 6.7.1 R Script for a Monte Carlo Analysis 6.7.2 Measures of Effect Size................... 6.7.3 A Monte Carlo Analysis with v = 1 6.7.4 Rank-Score Permutation Analyses 6.8 The Wilcoxon-Mann-Whitney Test.......... 6.8.1 R Script for the Wilcoxon Rank-Sum Test 6.8.2 An Exact Analysis with v = 2................... 6.8.3 R Script for an Exact Wilcoxon Test.... 6.8.4 An Exact Analysis with v — 1................... 6.8.5 Summary 6.9 6.10 Preview of Chap. 7 References 6.7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 264 270 272 276 277 279 279 282 285 288 291 293 293 294 7 Matched-Pairs Tests....................... Introduction........................................................................................ Matched-Pairs Tests.......................................................................... 7.2.1 Student’s Matched-Pairs / Test....................................... 297 A Permutation Approach................................................................... 298 7.3.1 The Relationship Between Statistics t and б.................. 299 Test Statistics t and б........................................................................ 299 7.4.1 R Script for Student’s Matched-Pairs t Test.................. 301 7.4.2 An Exact Analysis............................................................. 305 7.4.3 R Script for an Exact Matched-Pairs Test.................... 308 Measures of Effect Size...................................................................... 310 7.5.1 Comparisons of Effect
Size Measures............................ 313 7.5.2 R Script for Measures of Effect Size............................. 314 Analyses with v = 2 and v = 1........................................................ 316 7.6.1 An Exact Analysis with v = 2.......................................... 320 7.6.2 R Script for an Exact Student’s t Test........................... 322 7.6.3 An Exact Analysis with v = 1.......................................... 324 7.6.4 A Comparison of v = 2 and v = 1.................................. 326 Exact and Monte Carlo Analyses..................................................... 327 7.7.1 A Monte Carlo Analysis with v = 2.............................. 330 7.7.2 R Script for a Monte Carlo Analysis.............................. 333 7.7.3 An Exact Analysis with v = 2.......................................... 336 7.7.4 A Monte Carlo Analysis with v = 1.............................. 337 7.7.5 An Exact Analysis with v = 1.......................................... 338 Rank-Score Permutation Analyses................................................... 339 7.8.1 The Wilcoxon Signed-Ranks Test................................... 339 7.8.2 R Script for Wilcoxon’s Signed-Ranks Test.................. 342 7.8.3 An Exact Analysis with v = 2........................................... 347 7.8.4 R Script for an Exact Signed-Ranks Test....................... 349
Contents 8 xxi 7.8.5 The Relationship Between Statistics T and б............... 7.8.6 An Exact Analysis with v = 1......................................... 7.9 Summary............................................................................................. 7.10 Preview of Chap. 8............................................................................. References....................................................................................................... 352 352 354 354 355 Completely-Randomized Designs.............................................................. 8.1 Introduction.......................................................................................... 8.2 Fisher’s F-Ratio Test......................................................................... 8.3 A Permutation Approach................ .. ................................................. 8.4 The Relationship Between Statistics F and б................................ 8.5 Test Statistics F and б....................................................................... 8.5.1 The Bartlett Test for Homogeneity................................. 8.5.2 R Script for Bartlett’s Test of Homogeneity.................. 8.5.3 The Analysis of Variance................................................. 8.5.4 R Script for an Analysis of Variance.............................. 8.5.5 An Alternative to R Function aov()................................ 8.5.6 A Permutation Approach................................................... 8.5.7 R Script for Test Statistic б...............................................
8.6 Measures of Effect Size....................................................................... 8.6.1 Comparisons of Effect Size Measures............................ 8.6.2 R Script for Measures of Effect Size.............................. 8.7 Analyses with v = 2 and v = 1........................................................ 8.7.1 The Analysis of Variance................................................. 8.7.2 A Monte Carlo Analysis with v = 2.............................. 8.7.3 Measures of Effect Size................................................... 8.7.4 A Monte Carlo Analysis with v=l .............................. 8.8 Exact and Monte Carlo Analyses..................................................... 8.8.1 The Analysis of Variance................................................ 8.8.2 A Monte Carlo Analysis with v = 2............................. 8.8.3 Measures of Effect Size................................................... 8.8.4 A Monte Carlo Analysis with v = 1............................. 8.9 Rank-score Permutation Analyses.................................................. 8.9.1 The Kruskal-Wallis Rank-sum Test................................ 8.9.2 R Script for the Kruskal-Wallis Rank-sum Test.......... 8.9.3 A Monte Carlo Analysis with v = 2............................. 8.9.4 R Script for a K-W Probability Value........................... 8.10 Summary.............................................................................................. 8.11 Preview of Chap. 9.............................................................................
References....................................................................................................... 357 357 358 360 362 362 363 365 368 370 374 376 378 382 385 387 390 393 398 401 403 405 408 412 415 417 419 419 422 425 427 431 431 432
Contents xxii 433 9 Randomized-Blocks Designs 433 Introduction.................................................... 9.1 434 9.2 Randomized-Blocks Analysis of Variance . . 435 9.2.1 Fisher’s F-Ratio Test Statistic . . . . 437 A Permutation Approach................................ 9.3 438 9.4 The Relationship Between Statistics F and 5 439 Test Statistics F and б........................................ 9.5 442 R Script for a Randomized-Blocks Analysis 9.5.1 446 An Exact Analysis with v = 2.. . . 9.5.2 450 R Script for a Permutation Analysis 9.5.3 453 9.6 Measures of Effect Size 454 An Example Analysis.................................. 9.6.1 460 R Script for Three Measures of Effect Size 9.6.2 463 Analyses with v = 2 and v = 1................................ 9.7 468 A Monte Carlo Analysis with v = 2 . . . . 9.7.1 470 R Script for a Monte Carlo Analysis .... 9.7.2 473 Measures of Effect Size........................... 9.7.3 475 A Monte Carlo Analysis with v = 1 .... 9.7.4 476 A Larger Monte Carlo Analysis....................... 9.8 481 9.8.1 A Monte Carlo Analysis with v = 2 483 9.8.2 Measures of Effect Size................ . 484 Rank-Score Permutation Analyses ................ 9.9 485 Friedman’s Analysis of Variance for Ranks 9.9.1 486 R Script for Friedman’s Rank-Sum Test . . 9.9.2 489 9.9.3 A Monte Carlo Analysis with v = 2......... 491 9.9.4 R Script for Friedman’s Rank-Sum Test . . 495 9.9.5 A Monte Carlo Analysis with v = 1......... 496 9.10 Summary 497 9.11 Preview of Chap. 10 497 References 10 Correlation and
Association.................................................................. 10.1 Introduction................................................................................... 10.2 Linear Correlation.......................................................................... 10.2.1 A Permutation Approach................................................ 10.3 The Relationship Between Statistics and 5.............................. 10.4 An Example Analysis.................................................................... 10.4.1 R Script for Pearson’s Correlation Coefficient............ 10.4.2 An Exact PermutationAnalysis...................................... 10.4.3 R Script for an Exact Analysis...................................... 10.4.4 R Script for a Monte Carlo Analysis............................. 10.5 A Measure of Effect Size............................................................. 10.5.1 A Monte Carlo Permutation Analysis ......................... ^99 500 501 503 503 504 506 510 512 514 517 521
Contents 10.6 Spearman’s Rank-Order Correlation Coefficient.......................... 10.6.1 The Relationship Between Statistics rs and б............... 10.6.2 R Script for Spearman’s Rank Correlation.................... 10.6.3 A Monte Carlo Permutation Analysis ........................... 10.6.4 R Script for a Monte Carlo Analysis............................. 10.6.5 R Script for an Exact Analysis...................................: . 10.7 Kendall’s τα Measure of Association............................................. 10.7.1 An Example........................................................................ 10.7.2 The Relationship Between Kendall’s S and б............... 10.7.3 R Script for Kendall’s τα Coefficient............................. 10.7.4 A Monte Carlo Permutation Analysis ........................... 10.7.5 R Script for a Monte Carlo Analysis............................. 10.7.6 An Exact Permutation Analysis...................................... 10.7.7 R Script for an Exact Analysis...................................... 10.8 Kendall’s r* Measure of Association............................................. 10.8.1 Example Analysis.............................................................. 10.8.2 R Script for Kendall’s τ₺ Coefficient . ........................... 10.8.3 R Script for a Monte Carlo Analysis............................. 10.8.4 An Exact Permutation Analysis . ..................................... 10.8.5 R Script for an Exact Analysis...................................... 10.9 The Analysis of Contingency
Tables............................................. 10.9.1 R Script for Analyzing a Contingency Table............... 10.10 Spearman’s Footrule Agreement Measure...................................... 10.10.1 The Relationship Between ΊΖ and 5?............................ 10.10.2 A Monte Carlo Analysis.................................................. 10.10.3 R Script for an Exact Analysis...................................... 10.11 The Relationship Between 7^and 5.............................................. 10.12 Summary............................................................................................ 10.13 Preview of Chap. 11......................................................................... References..................................................................................................... 11 Chi-Squared and Related Measures...................................................... 11.1 Introduction....................................................................................... 11.2 Chi-Squared Goodness-of-Fit Tests................................................ 11.2.1 Example........................................................................... 11.2.2 R Script for Pearson’s Goodness-of-Fit Test.................. 11.2.3 A Monte Carlo Permutation Analysis ........................... 11.2.4 R Script for a Monte Carlo Probability Value............. 11.3 Measures of Effect Size.................................................................... 11.3.1 Pearson’s χ2 Measure of Effect Size............................. 11.3.2 R Code for a χ2
Measure of Effect Size........................ 11.3.3 Wilks’ G2 Measure of Effect Size.................................. 11.3.4 R Code for a G2 Measure of Effect Size...................... xxiii 526 529 531 535 536 539 541 543 544 546 550 550 553 554 557 559 561 563 566 566 570 572 575 578 582 585 587 589 590 590 591 591 592 593 596 598 598 601 602 603 605 607
Contents xxiv 11.3.5 A Chance-Corrected Measure of Effect Size.................. 11.3.6 R Code for a Chance-Corrected Measure....................... 11.4 Chi-Squared Test of Independence................................................... 11.4.1 Example............................................................................... 11.4.2 R Script for Pearson’s Test of Independence............... 11.4.3 A Measure of Effect Size.................................................. 11.4.4 R Script for Cramer’s Measure of Effect Size............... 11.5 A Chance-Corrected Measure of Effect Size.................................. 11.5.1 Illustration of a Chance-Coirected Measure................. 11.5.2 A Maximum Chi-Squared Procedure.............................. 11.5.3 R Script for a Measure of Effect Size........................... 11.5.4 A Monte Carlo Probability Value................................... 11.5.5 R Script for a Monte Carlo Probability Value............. 11.6 Fisher’s Exact Probability Test........................................................ 11.6.1 Example Analysis................................................................ 11.6.2 R Script for Fisher’s Exact Probability Test................. 11.6.3 A Recursion Example......................................................... 11.6.4 Recursion with an Arbitrary Origin................................. 11.6.5 R Script for Fisher’s ExactProbability Test.................... 11.7 Summary.............................................................................................. References...................
................................................................................... 609 610 612 613 614 616 617 618 619 622 625 629 631 634 635 635 638 639 642 644 645 Author Index................................................................................................................ 547 Subject Index.............................................................................. 552
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Contents 1 Introduction. 1.1 Overviews of Chaps. 2-11 . 1.2 Chapter 2. 1.3 Chapter 3. 1.4 Chapter 4 . . 1.5 Chapter 5 . . 1.6 Chapter 6. 1.7 Chapter 7. 1.8 Chapter 8. 1.9 Chapter 9. 1.10 Chapter 10. 1.11 Chapter 11. 1.12 Summary. 1.13 Preview of Chap. 2. . References. 1 4 5 6 6 7
9 11 12 13 14 16 17 18 18 2 The R Programming Language. 2.1 R and RStudio, What are They About?. 2.1.1 . What is R?. 2.1.2 Using R: Interactive Versus “Batch” Mode. 2.1.3 Installing R. 2.1.4 RStudio. 2.1.5 R Help. 2.1.6 R Manuals and Books. 2.2 Beginning R and RStudio. 2.2.1 Preliminaries. 2.2.2 R as a Simple Calculator. 2.2.3 Arrow Keys for Using Previous Commands. 2.2.4 Variables. 2.2.5 The Assignment Operator. 19 19 20 21 21 21 25 26 27 27 27 28 29 29 XV
Contents xvi 2.3 2.4 2.5 2.6 2.7 2.8 2.9 Using Variables in Expressions. 2.2.6 Removing Variables—Using R Functions 2.2.7 Mathematical Functions. 2.2.8 Nesting of Commands. 2.2.9 2.2.10 Numerical Representations. Vectors Creating Vector Variables. 2.3.1 Using Subscripts: Vector Indexing. 2.3.2 Adding and Removing Vector Elements 2.3.3 Doing Mathematics with Vectors. 2.3.4 2.3.5 Missing Values. Random Numbers. 2.3.6 Basic Statistical Functions. 2.3.7 Basic R Data Types 2.4.1 Coercion. Numeric Data. 2.4.2 2.4.3 Logical Data. 2.4.4 Integer Data. 2.4.5 Character Data. Learning More About Variables 2.4.6 Matrices 2.5.1 Creating Matrices. 2.5.2 Characteristics of a Matrix. 2.5.3 Applying Functions to Query Matrices . . . 2.5.4 Manipulating Matrices. 2.5.5 Naming Rows and Columns. . . 2.5.6 Adding New Rows or Columns to Matrices Arrays: More Than Two Dimensions. Factors 2.7.1 Factor Functions. 2.7.2 Useful Data Manipulations with Factors. . Lists. . 2.8.1 Referencing List Elements 2.8.2 Manipulating Lists. 2.8.3 Search Path
Attachment . Data Frames 2.9.1 Viewing and Selecting Data Frame Elements 2.9.2 Computing Statistics. 2.9.3 Sorting Data Frames. 2.9.4 R’s Sorting Functions. 2.9.5 Adding Rows or Columns to Data Frames . . 2.9.6 Creating a New Data Frame. 2.9.7 Editing Values in a Data Frame. 30 30 31 32 33 34 34 37 37 38 38 40 41 42 43 43 43 48 49 51 52 52 54 54 56 57 57 58 60 61 63 64 65 66 67 67 69 71 72 73 75 76 77
Contents Saving Work. 2.10.1 Setting and Getting Folder Pathways. 2.10.2 Session History Files. 2.10.3 R Scripts. 2.10.4 Workspace Files. 2.10.5 Writing External Text Files. 2.11 Reading External Text Files. 2.11.1 Reading Files Holding a SingleVariable. 2.11.2 Reading Tables of Data with ManyVariables. 2.12 Downloading and Installing Packages. 2.13 Programming Structures in R. 2.13.1 The Comment. 2.13.2 Writing Your Own Functions. 2.13.3 Conditional Statements. 2.13.4 Loops. 2.13.5 Writing Interactive Code. 2.14 Summary. 2.15 Preview of Chap. 3.
References. 78 78 79 79 80 81 82 83 84 87 89 89 90 91 94 98 98 99 99 Permutation Statistical Methods. 3.1 Introduction. 3.2 A Brief History of Permutation Methods. 3.2.1 The 1920s. 3.2.2 The 1930s. 3.2.3 The 1940s. 3.2.4 The 1950s. 3.2.5 The 1960s. 3.2.6 The 1970s. 3.2.7 The 1980s. 3.2.8 The 1990s. 3.2.9 The 2000s. 3.2.10 The 2010s. 3.3 The Neyman-Pearson Population Model. 3.4 The Fisher-Pitman Permutation Model. 3.4.1 Exact Permutation Tests. 3.4.2
Monte Carlo Permutation Tests. 3.5 Permutation and Parametric Statistical Tests. 3.5.1 The Assumption of Random Sampling. 3.5.2 The Assumption of Normality. 3.6 Advantages of Permutation Methods. 3.7 Calculation Efficiency. 3.7.1 High-SpeedComputing. 3.7.2 Analysis with Combinations. 101 102 102 103 103 104 105 105 106 107 108 108 109 110 Ill 112 114 115 115 116 116 117 118 118 2.10 3 xvii
Contents xviii 3.7.3 Mathematical Recursion. 3.7.4 Variable Components of a Test Statistic 3.7.5 Holding an Array Constant. 3.8 Summary. 3.9 Preview of Chap. 4. References. 119 119 120 120 121 121 Central Tendency and Variability. 4.1 Introduction. 4.2 Data Storage Modes and Structures. 4.3 Statistical Graphics. 4.4 The Sample Mode . 4.4.1 R Script for the Sample Mode. 4.5 The Sample Mean. 4.5.1 R Script for the Sample Mean. 4.6 The Sample Median. 4.6.1 R Script for the Sample Median. 4.7 The Sample Standard Deviation and Variance. 4.7.1 R Script for the Sample Standard Deviation. 4.8 The Mean Absolute Deviation. 4.8.1 R Script for the
Mean Absolute Deviation. 4.9 An Alternative Approach to Dispersion Measures. 4.9.1 Pairwise Differences: Standard Deviation. 4.9.2 R Script for the Sample Standard Deviation. 4.10 Summary. 4.11 Preview of Chap. 5. Reference. 4 5 One-Sample Tests. 5.1 Introduction. 5.2 Student’s One-Sample t Test. 5.3 A Permutation Approach. 5.4 The Relationship Between Test Statistics tand б. 5.5 Test Statistics t and б. 5.5.1 R Script for Student’s t Test. 5.5.2 R Script for Test Statistic б. 5.5.3 R Script for an Exact Student’s t Test. 5.5.4 The Choice Between Test Statistics t and б. 5.6 The Measurement of Effect Size. 5.6.1 R Script for the Expected Value of б. 5.7 Detailed Calculations for
Statistics б andμ . 5.7.1 Comparisons of Effect Size Measures. 5.7.2 R Script for the 91 Measure of Effect Size. 1ZJ 126 12$ 134 135 137 138 140 141 143 144 146 147 149 149 152 153 154 154 155 15 156 152 159 159 161 167 169 172 172 174 176 179 180
Contents xix 5.8 6 Measures of Effect Size. 5.8.1 R Script for Measures of Effect Size. 5.9 Analyses with v = 2 and v = 1. 5.9.1 An Exact Analysis with v = 2. 5.9.2 R Script for Test Statistic б. 5.9.3 The Assumption of Normality. 5.9.4 An Exact Analysis with v = 1. 5.10 Exact and Monte Carlo Analyses. 5.10.1 A Monte Carlo Analysis with v = 2. . 5.10.2 R Script for a Monte Carlo Analysis. 5.10.3 An Exact Analysis with v = 2. 5.10.4 A Monte Carlo Analysis with v = 1. 5.10.5 An Exact Analysis with v = 1. 5.11 Rank-Score Permutation Analyses. 5.11.1 The Wilcoxon Signed-Ranks Test. 5.11.2 A Pennutation Approach. 5.11.3 An Example Analysis. 5.11.4 R Script for Wilcoxon’s Signed-Ranks Test. 5.11.5 An Exact Analysis with v = 2. 5.11.6 The Relationship Between Statistics T and б. 5.11.7 R Script for a Monte Carlo ProbabilityValue. 5.11.8 An Exact Analysis with v =
1. 5.12 Summary. 5.13 Preview of Chap. 6. References. 181 182 184 188 189 192 193 195 199 200 204 204 205 206 206 207 207 209 213 214 215 218 22θ 22θ 221 Two-Sample Tests 223 224 224 225 226 228 229 230 235 238 242 245 248 249 252 258 261 262 6.1 6.2 6.3 6.4 6.5 6.6 Introduction. Two-Sample Tests. 6.2.1 Student’s Two-Sample t Test. A Permutation Approach. 6.3.1 The Relationship Between Statistics t and б. . Test Statistics t and б. 6.4.1 R Script for a Test of Homogeneity R Script for Student’s t Test. 6.4.2 A Permutation Approach. 6.4.3 R Script for Test Statistic б. 6.4.4 Measures of Effect Size. 6.5.1 Comparisons of Effect Size Measures 6.5.2 R Script for Measures of Effect Size . Analyses with v = 2 and v = 1. An Exact Analysis with v = 2 6.6.1 Measures of Effect Size . 6.6.2 An Exact Analysis with v = 1 6.6.3
Contents XX Exact and Monte Carlo Analyses. . . · A Monte Carlo Analysis with v = 2 6.7.1 R Script for a Monte Carlo Analysis 6.7.2 Measures of Effect Size. 6.7.3 A Monte Carlo Analysis with v = 1 6.7.4 Rank-Score Permutation Analyses 6.8 The Wilcoxon-Mann-Whitney Test. 6.8.1 R Script for the Wilcoxon Rank-Sum Test 6.8.2 An Exact Analysis with v = 2. 6.8.3 R Script for an Exact Wilcoxon Test. 6.8.4 An Exact Analysis with v — 1. 6.8.5 Summary 6.9 6.10 Preview of Chap. 7 References 6.7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 264 270 272 276 277 279 279 282 285 288 291 293 293 294 7 Matched-Pairs Tests. Introduction. Matched-Pairs Tests. 7.2.1 Student’s Matched-Pairs / Test. 297 A Permutation Approach. 298 7.3.1 The Relationship Between Statistics t and б. 299 Test Statistics t and б. 299 7.4.1 R Script for Student’s Matched-Pairs t Test. 301 7.4.2 An Exact Analysis. 305 7.4.3 R Script for an Exact Matched-Pairs Test. 308 Measures of Effect Size. 310 7.5.1 Comparisons of Effect
Size Measures. 313 7.5.2 R Script for Measures of Effect Size. 314 Analyses with v = 2 and v = 1. 316 7.6.1 An Exact Analysis with v = 2. 320 7.6.2 R Script for an Exact Student’s t Test. 322 7.6.3 An Exact Analysis with v = 1. 324 7.6.4 A Comparison of v = 2 and v = 1. 326 Exact and Monte Carlo Analyses. 327 7.7.1 A Monte Carlo Analysis with v = 2. 330 7.7.2 R Script for a Monte Carlo Analysis. 333 7.7.3 An Exact Analysis with v = 2. 336 7.7.4 A Monte Carlo Analysis with v = 1. 337 7.7.5 An Exact Analysis with v = 1. 338 Rank-Score Permutation Analyses. 339 7.8.1 The Wilcoxon Signed-Ranks Test. 339 7.8.2 R Script for Wilcoxon’s Signed-Ranks Test. 342 7.8.3 An Exact Analysis with v = 2. 347 7.8.4 R Script for an Exact Signed-Ranks Test. 349
Contents 8 xxi 7.8.5 The Relationship Between Statistics T and б. 7.8.6 An Exact Analysis with v = 1. 7.9 Summary. 7.10 Preview of Chap. 8. References. 352 352 354 354 355 Completely-Randomized Designs. 8.1 Introduction. 8.2 Fisher’s F-Ratio Test. 8.3 A Permutation Approach. . . 8.4 The Relationship Between Statistics F and б. 8.5 Test Statistics F and б. 8.5.1 The Bartlett Test for Homogeneity. 8.5.2 R Script for Bartlett’s Test of Homogeneity. 8.5.3 The Analysis of Variance. 8.5.4 R Script for an Analysis of Variance. 8.5.5 An Alternative to R Function aov(). 8.5.6 A Permutation Approach. 8.5.7 R Script for Test Statistic б.
8.6 Measures of Effect Size. 8.6.1 Comparisons of Effect Size Measures. 8.6.2 R Script for Measures of Effect Size. 8.7 Analyses with v = 2 and v = 1. 8.7.1 The Analysis of Variance. 8.7.2 A Monte Carlo Analysis with v = 2. 8.7.3 Measures of Effect Size. 8.7.4 A Monte Carlo Analysis with v=l . 8.8 Exact and Monte Carlo Analyses. 8.8.1 The Analysis of Variance. 8.8.2 A Monte Carlo Analysis with v = 2. 8.8.3 Measures of Effect Size. 8.8.4 A Monte Carlo Analysis with v = 1. 8.9 Rank-score Permutation Analyses. 8.9.1 The Kruskal-Wallis Rank-sum Test. 8.9.2 R Script for the Kruskal-Wallis Rank-sum Test. 8.9.3 A Monte Carlo Analysis with v = 2. 8.9.4 R Script for a K-W Probability Value. 8.10 Summary. 8.11 Preview of Chap. 9.
References. 357 357 358 360 362 362 363 365 368 370 374 376 378 382 385 387 390 393 398 401 403 405 408 412 415 417 419 419 422 425 427 431 431 432
Contents xxii 433 9 Randomized-Blocks Designs 433 Introduction. 9.1 434 9.2 Randomized-Blocks Analysis of Variance . . 435 9.2.1 Fisher’s F-Ratio Test Statistic . . . . 437 A Permutation Approach. 9.3 438 9.4 The Relationship Between Statistics F and 5 439 Test Statistics F and б. 9.5 442 R Script for a Randomized-Blocks Analysis 9.5.1 446 An Exact Analysis with v = 2. . . 9.5.2 450 R Script for a Permutation Analysis 9.5.3 453 9.6 Measures of Effect Size 454 An Example Analysis. 9.6.1 460 R Script for Three Measures of Effect Size 9.6.2 463 Analyses with v = 2 and v = 1. 9.7 468 A Monte Carlo Analysis with v = 2 . . . . 9.7.1 470 R Script for a Monte Carlo Analysis . 9.7.2 473 Measures of Effect Size. 9.7.3 475 A Monte Carlo Analysis with v = 1 . 9.7.4 476 A Larger Monte Carlo Analysis. 9.8 481 9.8.1 A Monte Carlo Analysis with v = 2 483 9.8.2 Measures of Effect Size. . 484 Rank-Score Permutation Analyses . 9.9 485 Friedman’s Analysis of Variance for Ranks 9.9.1 486 R Script for Friedman’s Rank-Sum Test . . 9.9.2 489 9.9.3 A Monte Carlo Analysis with v = 2. 491 9.9.4 R Script for Friedman’s Rank-Sum Test . . 495 9.9.5 A Monte Carlo Analysis with v = 1. 496 9.10 Summary 497 9.11 Preview of Chap. 10 497 References 10 Correlation and
Association. 10.1 Introduction. 10.2 Linear Correlation. 10.2.1 A Permutation Approach. 10.3 The Relationship Between Statistics and 5. 10.4 An Example Analysis. 10.4.1 R Script for Pearson’s Correlation Coefficient. 10.4.2 An Exact PermutationAnalysis. 10.4.3 R Script for an Exact Analysis. 10.4.4 R Script for a Monte Carlo Analysis. 10.5 A Measure of Effect Size. 10.5.1 A Monte Carlo Permutation Analysis . ^99 500 501 503 503 504 506 510 512 514 517 521
Contents 10.6 Spearman’s Rank-Order Correlation Coefficient. 10.6.1 The Relationship Between Statistics rs and б. 10.6.2 R Script for Spearman’s Rank Correlation. 10.6.3 A Monte Carlo Permutation Analysis . 10.6.4 R Script for a Monte Carlo Analysis. 10.6.5 R Script for an Exact Analysis.: . 10.7 Kendall’s τα Measure of Association. 10.7.1 An Example. 10.7.2 The Relationship Between Kendall’s S and б. 10.7.3 R Script for Kendall’s τα Coefficient. 10.7.4 A Monte Carlo Permutation Analysis . 10.7.5 R Script for a Monte Carlo Analysis. 10.7.6 An Exact Permutation Analysis. 10.7.7 R Script for an Exact Analysis. 10.8 Kendall’s r* Measure of Association. 10.8.1 Example Analysis. 10.8.2 R Script for Kendall’s τ₺ Coefficient . . 10.8.3 R Script for a Monte Carlo Analysis. 10.8.4 An Exact Permutation Analysis . . 10.8.5 R Script for an Exact Analysis. 10.9 The Analysis of Contingency
Tables. 10.9.1 R Script for Analyzing a Contingency Table. 10.10 Spearman’s Footrule Agreement Measure. 10.10.1 The Relationship Between ΊΖ and 5?. 10.10.2 A Monte Carlo Analysis. 10.10.3 R Script for an Exact Analysis. 10.11 The Relationship Between 7^and 5. 10.12 Summary. 10.13 Preview of Chap. 11. References. 11 Chi-Squared and Related Measures. 11.1 Introduction. 11.2 Chi-Squared Goodness-of-Fit Tests. 11.2.1 Example. 11.2.2 R Script for Pearson’s Goodness-of-Fit Test. 11.2.3 A Monte Carlo Permutation Analysis . 11.2.4 R Script for a Monte Carlo Probability Value. 11.3 Measures of Effect Size. 11.3.1 Pearson’s χ2 Measure of Effect Size. 11.3.2 R Code for a χ2
Measure of Effect Size. 11.3.3 Wilks’ G2 Measure of Effect Size. 11.3.4 R Code for a G2 Measure of Effect Size. xxiii 526 529 531 535 536 539 541 543 544 546 550 550 553 554 557 559 561 563 566 566 570 572 575 578 582 585 587 589 590 590 591 591 592 593 596 598 598 601 602 603 605 607
Contents xxiv 11.3.5 A Chance-Corrected Measure of Effect Size. 11.3.6 R Code for a Chance-Corrected Measure. 11.4 Chi-Squared Test of Independence. 11.4.1 Example. 11.4.2 R Script for Pearson’s Test of Independence. 11.4.3 A Measure of Effect Size. 11.4.4 R Script for Cramer’s Measure of Effect Size. 11.5 A Chance-Corrected Measure of Effect Size. 11.5.1 Illustration of a Chance-Coirected Measure. 11.5.2 A Maximum Chi-Squared Procedure. 11.5.3 R Script for a Measure of Effect Size. 11.5.4 A Monte Carlo Probability Value. 11.5.5 R Script for a Monte Carlo Probability Value. 11.6 Fisher’s Exact Probability Test. 11.6.1 Example Analysis. 11.6.2 R Script for Fisher’s Exact Probability Test. 11.6.3 A Recursion Example. 11.6.4 Recursion with an Arbitrary Origin. 11.6.5 R Script for Fisher’s ExactProbability Test. 11.7 Summary. References.
. 609 610 612 613 614 616 617 618 619 622 625 629 631 634 635 635 638 639 642 644 645 Author Index. 547 Subject Index. 552 |
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| author | Berry, Kenneth J. Kvamme, Kenneth L. Johnston, Janis E. 1957- Mielke, Paul W. |
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| index_date | 2024-07-03T18:21:18Z |
| indexdate | 2024-07-10T09:14:03Z |
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| spelling | Berry, Kenneth J. Verfasser (DE-588)1105489388 aut Permutation statistical methods with R Kenneth J. Berry, Kenneth L. Kvamme, Janis E. Johnston, Paul W. Mielke, Jr. Cham Springer [2021] xxiv, 660 Seiten txt rdacontent n rdamedia nc rdacarrier Kvamme, Kenneth L. Verfasser (DE-588)1147773343 aut Johnston, Janis E. 1957- Verfasser (DE-588)1105494063 aut Mielke, Paul W. Verfasser (DE-588)1105493067 aut Springer International Publishing (DE-588)1064344704 pbl Erscheint auch als Online-Ausgabe 978-3-030-74361-1 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032909939&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berry, Kenneth J. Kvamme, Kenneth L. Johnston, Janis E. 1957- Mielke, Paul W. Permutation statistical methods with R |
| title | Permutation statistical methods with R |
| title_auth | Permutation statistical methods with R |
| title_exact_search | Permutation statistical methods with R |
| title_exact_search_txtP | Permutation statistical methods with R |
| title_full | Permutation statistical methods with R Kenneth J. Berry, Kenneth L. Kvamme, Janis E. Johnston, Paul W. Mielke, Jr. |
| title_fullStr | Permutation statistical methods with R Kenneth J. Berry, Kenneth L. Kvamme, Janis E. Johnston, Paul W. Mielke, Jr. |
| title_full_unstemmed | Permutation statistical methods with R Kenneth J. Berry, Kenneth L. Kvamme, Janis E. Johnston, Paul W. Mielke, Jr. |
| title_short | Permutation statistical methods with R |
| title_sort | permutation statistical methods with r |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032909939&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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