Preface to the Second Edition ................................. vii
Preface to the First Edition ................................... ix
1. Introduction ................................................. 1
2. Description of MRPP ......................................... 11
2.1. General Formulation of MRPP ............................ 14
2.1.1. Univariate Example of MRPP ...................... 15
2.1.2. Bivariate Example of MRPP ....................... 18
2.2. Choice of Weights and Distance Functions ............... 20
2.3. P-Value of an Observed δ ............................... 24
2.3.1. Monte Carlo Resampling Approximation ............ 24
2.3.2. Pearson Type III Approximation .................. 25
2.3.3. Approximation Comparisons ....................... 29
2.3.4. Group Weights ................................... 30
2.3.5. Within-Group Agreement Measure .................. 31
2.4. Exact and Approximate P-Values ......................... 32
2.5. MRPP with an Excess Group .............................. 35
2.6. Detection of Multiple Clumping ......................... 40
2.7. Detection of Evenly Spaced Location Patterns ........... 44
2.8. Dependence of MRPP on v ................................ 45
2.9. Permutation Version of One-Way ANOVA ................... 50
2.10. Euclidean and Hotelling Commensuration ................ 53
2.11. Power Comparisons ..................................... 57
2.11.1. The Normal Probability Distribution ........... 63
2.11.2. The Cauchy Probability Distribution ........... 65
2.11.3. Noncentrality and Power ....................... 66
2.11.4. Synopsis ...................................... 66
2.12. Summary ............................................... 68
3. Additional MRPP Applications ................................ 69
3.1. Autoregrcssive Pattern Detection Methods ............... 69
3.2. Asymmetric Two-Way Contingency Table Analyses .......... 73
3.2.1. Development of the Problem ...................... 75
3.2.2. A Nonasymptotic Solution ........................ 76
3.2.3. Examples ........................................ 78
3.2.4. Null Hypotheses ................................. 81
3.2.5. Extension to Multiple Binary Choices ............ 82
3.3. Measurement of Agreement ............................... 86
3.3.1. Interval Dependent Variables .................... 88
3.3.2. Ordinal Dependent Variables ..................... 91
3.3.3. Nominal Dependent Variables ..................... 92
3.3.4. Mixed Dependent Variables ....................... 93
3.3.5. Relationships with Existing Statistics .......... 95
3.4. Analyses Involving Cyclic Data ......................... 97
3.4.1. Analysis of Circular Data ....................... 98
3.4.2. Analysis of Spherical Data ...................... 99
3.5. Analyses Based on Generalized Runs .................... 103
3.5.1. Wald -Wolfowitz Runs Test ...................... 105
3.5.2. Generalized Runs Test .......................... 106
3.6. Analyses Involving Rank-Order Statistics .............. 108
3.6.1. An Extended Class of Rank Tests ................ 109
3.6.2. Asymptotically Most Powerful Rank Tests
and v .......................................... 111
3.7. Analyses of Metal Contamination and Learning
Achievement ........................................... 116
3.7.1. Methods ........................................ 117
3.7.2. Results ........................................ 119
3.7.3. Alternative Analyses ........................... 121
4. Description of MRBP ........................................ 125
4.1. General Formulation of MRBP ........................... 127
4.2. Permutation Randomized Block Analysis of Variance ..... 131
4.3. Rank and Binary Data .................................. 133
4.3.1. Example 1 ...................................... 137
4.3.2. Example 2 ...................................... 138
4.3.3. Multiple Binary Category Choices ............... 138
4.4. One-Sample and Matched-Pair Designs ................... 141
4.4.1. Comparisons Among Univariate Rank Tests ........ 144
4.4.2. Multivariate Tests ............................. 145
4.5. Measurement of Agreement .............................. 150
4.5.1. Agreement Between Two Observers ................ 151
4.5.2. Multiple Observers ............................. 161
4.5.3. Test of Significance ........................... 164
4.5.4. Two Independent Groups of Observers ............ 166
4.5.5. Agreement With a Standard ...................... 167
5. Regression Analysis, Prediction, and Agreement ............. 171
5.1. Historical Perspective ................................ 172
5.2. OLS and LAD Regressions ............................... 172
5.2.1. Some OLS and LAD Comparisons ................... 174
5.2.2. Distance ....................................... 174
5.2.3. Leverage ....................................... 176
5.2.4. Influence ...................................... 176
5.3. MRPP Regression Analyses of Linear Models ............. 179
5.3.1. Permutation Test ............................... 182
5.3.2. Example ........................................ 183
5.3.3. Discussion ..................................... 186
5.3.4. Examples of MRPP Regression Analyses ........... 187
5.3.5. One-Way Randomized Design ...................... 187
5.3.6. One-Way Randomized Design with a Covariate ..... 188
5.3.7. Factorial Design ............................... 190
5.3.8. One-Way Block Design ........................... 195
5.3.9. Balanced Two-Way Block Design .................. 196
5.3.10. Unbalanced Two-Way Block Design ............... 201
5.3.11. Latin Square Design ........................... 204
5.3.12. Split-Plot Design ............................. 206
5.4. MRPP, Cade Richards, and OLS Regression Analyses ...... 214
5.4.1. Extension of MRPP Regression Analysis .......... 216
5.4.2. Limitations of MRPP Regression Analysis ........ 218
5.5. MRPP Confidence Intervals for a Regression
Parameter ............................................. 223
5.5.1. The North Dakota Cloud Modification Project .... 224
5.5.2. Crop Hail Insurance Data ....................... 224
5.5.3. Methodology .................................... 225
5.5.4. Analysis Results ............................... 226
5.6. LAD Regression Prediction Models ...................... 227
5.6.1. Prediction and Cross-Validation ................ 229
5.6.2. Application to the Prediction of African
Rainfall ....................................... 255
5.6.3. Linear and Nonlinear Multivariate Regression
Models ......................................... 258
6. Goodness-of-Fit Tests ...................................... 263
6.1. Discrete Data Goodness-of-Fit Tests ................... 263
6.1.1. Fisher's Exact Tests ........................... 264
6.1.2. Exact Test When pi = 1/k for i = 1,..., k ...... 266
6.1.3. Nonasymptotic Tests ............................ 267
6.1.4. Informative Examples ........................... 272
6.2. Continuous Data Goodness-of-Fit Tests ................. 272
6.2.1. Smirnov Matching Test .......................... 273
6.2.2. Kolmogorov Goodness-of-Fit Test ................ 274
6.2.3. Goodness-of-Fit Tests Based on Coverages ....... 275
6.2.4. Power Comparisons of the Kolmogorov and
Kendall-Sherman Tests .......................... 277
7. Contingency Tables ......................................... 283
7.1. Hypergeometric Distribution for r-Way Contingency
Tables ................................................ 283
7.2. Exact Tests ........................................... 285
7.2.1. Analysis of a 2 × 2 Table ...................... 287
7.2.2. Analysis of a 3 × 2 Table ...................... 290
7.2.3. Analysis of a 3 × 3 Table ...................... 292
7.2.4. Analysis of a 2 × 2 × 2 Table .................. 293
7.3. Approximate Nonasymptotic Tests ....................... 296
7.4. Exact, Nonasymptotic, and Asymptotic Comparisons of
the P-Values .......................................... 300
7.5. Log-Linear Analyses of Sparse Contingency Tables ...... 304
7.5.1. Multinomial Analyses ........................... 306
7.5.2. Hypergeometric Analyses ........................ 309
7.5.3. Example ........................................ 310
7.5.4. Discussion ..................................... 316
7.6. Exact Tests For Interaction in 2r Tables .............. 318
7.6.1. Analysis of a 23 Contingency Table ............. 320
7.6.2. Analysis of a 24 Contingency Table ............. 322
7.7. Relationship Between Chi-Square and Goodman-Kruskal
Statistics ............................................ 325
7.8. Summary ............................................... 326
8. Multisample Homogeneity Tests .............................. 329
8.1. Discrete Data Tests ................................... 329
8.1.1. Example Using Incorrect Symmetric Tests ........ 331
8.1.2. Example Using Correct Asymmetric Tests ......... 332
8.2. Continuous Data Tests ................................. 334
8.2.1. Generalized Runs Test .......................... 334
8.2.2. Kolmogorov-Smirnov Test ........................ 334
8.2.3. Empirical Coverage Tests ....................... 335
8.2.4. Examples ....................................... 337
8.3. Summary ............................................... 340
9. Selected Permutation Studies ............................... 341
9.1. A Discrete Method For Combining P-Values .............. 341
9.1.1. Fisher Continuous Method to Combine P-Values ... 342
9.1.2. A Discrete Method For Combining P-Values ....... 342
9.1.3. Three Examples ................................. 346
9.2. Fisher Z Transformation ............................... 358
9.2.1. Distributions .................................. 359
9.2.2. Confidence Intervals ........................... 360
9.2.3. Hypothesis Testing ............................. 369
9.2.4. Discussion ..................................... 375
9.3. Multivariate Similarity Between Two Samples ........... 378
9.3.1. Methodology .................................... 378
9.3.2. Examples ....................................... 381
Appendix A. Computer Programs ................................. 385
A.l. Chapter 2 ............................................. 385
A.2. Chapter 3 ............................................. 386
A.3. Chapter 4 ............................................. 387
A.4. Chapter 5 ............................................. 388
A.5. Chapter 6 ............................................. 388
A.6. Chapter 7 ............................................. 389
A.7. Chapter 8 ............................................. 390
A.8. Chapter 9 ............................................. 391
References .................................................... 393
Author Index .................................................. 423
Subject Index ................................................. 429
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