Foundational and applied statistics for biologists using R:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, FL
CRC Press
2014
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 555 - 574 |
| Physical Description: | XXI, 596 S. graph. Darst. |
| ISBN: | 9781439873380 |
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Record in the Search Index
| _version_ | 1804151649705394176 |
|---|---|
| adam_text | FOUNDATIONAL
and APPLIED
STATISTICSfor
BIOLOGISTS
USING R
Ken A Aho
IdahoStateUniversity
Pocatello,Idaho,USA
CRC Press
Taylor amp; Francis Croup
Boca Raton London New York
CRC Press is an imprint of the
Taylor amp; Francis Group, an informa business
ACHAPMAN amp;HALLBOOK
Contents
Preface xix
Acknowledgments xxi
Section I Foundations
1 Philosophical and Historical Foundations 3
1 1 Introduction 3
1 2 Nature of Science 3
1 3 Scientific Principles 4
131 Objectivity 4
132 Realism 4
133 Communalism 5
1 4 Scientific Method 5
141A Terse History 6
1411 Experimentation 8
1412 Induction 8
1413 Probability 8
1 5 Scientific Hypotheses 9
151 Falsifiability 9
1 6 Logic 10
161 Induction 10
162 Deduction 11
163 Induction versus Deduction 11
164 Logic and Null Hypothesis Testing 12
1641 Modus Tollens 12
1642 Reductio Ad Absurdum 13
1 7 Variability and Uncertainty in Investigations 14
1 8 Science and Statistics 16
1 9 Statistics and Biology 16
1 10 Summary 18
Exercises 18
2 Introduction to Probability 21
2 1 Introduction: Models for Random Variables 21
211 Set Theory Terminology 23
212 Philosophical Conceptions of Probability 24
2 2 Classical Probability 26
221 Disjoint 28
2211 Boole s Inequality 30
222 Independence 31
2221 Bonferroni s Inequality 31
2 3 Conditional Probability 32
vii
viii Contents
2 4 Odds 34*
241 Odds Ratio and Relative Risk 34
2 5 Combinatorial Analysis 35
251 Multiplication Principle 35
252 Permutations 36
253 Combinations 37
2 6 Bayes Rule 38
2 7 Summary 43
Exercises 43
3 Probability Density Functions 49
3 1 Introduction 49
311 How to Read This Chapter 50
312 So, What Is Density? 50
313 Cumulative Distribution Function 52
3 2 Introductory Examples of pdfs 54
321 Discrete pdfs 55
3211 Bernoulli Distribution 55
3212 Binomial Distribution 55
322 Continuous pdfs 60
3221 Continuous Uniform Distribution 60
3222 Normal Distribution 61
33 Other Important Distributions 65
331 Other Discrete pdfs 66
3311 Poisson Distribution ^ 66
3312 Hypergeometric Distribution 69
3313 Geometric Distribution 71
3314 Negative Binomial Distribution 72
332 Other Continuous pdfs 74
3321 Chi-Squared Distribution 74
3322 f-Distribution 76
3323 F-Distribution 77
3324 Exponential Distribution 79
3325 Beta Distribution 81
3326 Gamma Distribution 82
3327 Weibull Distribution 83
3328 Lognormal Distribution 86
3329 Logistic Distribution 88
3 4 Which pdf to Use? 90
341 Empirical cdfs 90
3 5 Reference Tables 91
3 6 Summary 92
Exercises 95
4 Parameters and Statistics 101
4 1 Introduction 101
411 How to Read This Chapter 102
4 2 Parameters 103
421 Expected Value 103
Contents ix
422 Variance 105
423 Chebyshev Inequality 106
4 3 Statistics 106
431 Important Considerations 106
432 Sampling Error 108
433 Gauging Estimator Effectiveness 108
434 Types of Estimators 108
435 Measures of Location 109
4351 Arithmetic Mean 109
4352 Geometric Mean 110
4353 Harmonic Mean Ill
4354 Mode 113
436 Robust Measures of Location 113
4361 Median 114
4362 Trimmed Mean 115
4363 Winsorized Mean 115
4364 M-Estimators 116
4365 Which Location Estimator to Use? 118
437 Measures of Scale 119
4371 Sample Variance 119
4372 Coefficient of Variation 121
438 Robust Estimators of Scale 122
4381 Interquartile Range 123
4382 Median Absolute Deviation 123
4383 Which Scale Estimator to Use? 124
439 Parameters and Estimators for Distribution Shape 124
4391 Moment Generating Functions 124
4392 Sample Moments and MOM Estimators 126
4 4 OLS and ML Estimators 127
441 Ordinary Least Squares 127
442 Maximum Likelihood 128
4421 So, What Is Likelihood? 132
4422 Likelihood versus Probability 132
443 MOM versus OLS versus ML Estimation 133
4 5 Linear Transformations 134
451 Transformations and Parameters 135
452 Transformations and Statistics 136
4 6 Bayesian Applications 137
461 Priors 138
4611 Noninformative Priors 138
4612 Informative Priors 138
462 Conjugacy 138
4 7 Summary 143
Exercises 143
5 Interval Estimation: Sampling Distributions, Resampling Distributions,
and Simulation Distributions 149
5 1 Introduction 149
511 How to Read This Chapter 149
X Contents
5 2 Sampling Distributions 0 150
521 samp dist 151
522 Sampling Distribution of X 151
5221 Central Limit Theorem 154
523 Sampling Distribution of S2 156
524 Sampling Distribution of t* 156
525 Sampling Distribution of F* 158
5 3 Confidence Intervals 161
531 Confidence Interval for 161
532 Confidence Interval for |o ,o Known 162
5321 Interpreting Confidence Intervals 164
533 Confidence Interval for (x,o Unknown 165
5331 Expressing Precision 165
5332 One-Sided Confidence Intervals 167
534 Confidence Interval for a2 168
535 Confidence Interval for the Population Median 169
536 Confidence Intervals and Sample Size 171
537 Assumptions and Requirements for Confidence Intervals 172
5 4 Resampling Distributions 172
541 Bootstrapping 172
5411 sample 173
5412 Bootstrap Confidence Intervals 174
5413 bootstrap 178
542 Jackknifing 179
5421 pseudo v 181
5 5 Bayesian Applications: Simulation Distributions 182
551 Direct Simulation of the Posterior 183
552 Indirect Simulation: Markov Chain Monte Carlo Approaches 184
5521 Simple Applications 185
5522 Advanced Applications 188
5 6 Summary 192
Exercises 193
6 Hypothesis Testing 197
6 1 Introduction 197
6 2 Parametric Frequentist Null Hypothesis Testing 197
621 Null Hypothesis and Its Motivation 198
622 Significance Testing 199
623 Models for Null Hypothesis Testing 200
6231 Nonsignificant Results 202
6232 Significant Results 203
624 Upper-, Lower-, and Two-Tailed Tests 203
625 Inferences for a Single Population Mean 205
6251 One-Sample z-Test 206
6252 One-Sample i-Test 208
626 Confidence Intervals and Hypothesis Testing 209
627 Inferences for Two Population Means 210
6271 Paired f-Test 211
Contents xi
6272 Pooled Variance t-Test - 214
6273 Welch s Approximate f-Test 217
6 3 Type I and Type II Errors 219
6 4 Power 220
641 Sample Adequacy 223
6411 Power in f-Tests 224
6412 Effect Size in f-Tests 224
6 5 Criticisms of Frequentist Null Hypothesis Testing 225
651A Final Word 227
6 6 Alternatives to Parametric Null Hypothesis Testing 227
661 Permutation Tests 227
662 Rank-Based Permutation Tests 228
6621 Kolmogorov-Smirnov Test 230
6622 Wilcoxon Sign Rank Test 231
6623 Wilcoxon Rank Sum Test 233
663 Robust Estimator Tests 237
6 7 Alternatives to Null Hypothesis Testing 237
671 Bayesian Approaches 237
672 Likelihood-Based Approaches 240
6 8 Summary 240
Exercises 241
7 Sampling Design and Experimental Design 247
7 1 Introduction 247
7 2 Some Terminology 247
721 Variables 247
7211 Explanatory and Response Variables 248
7212 Categorical, Ordinal, and Quantitative Variables 249
7213 Discrete and Continuous Variables 250
7214 Univariate and Multivariate Analysis 250
7215 Lurking Variables and Confounding Variables 251
7 3 The Question Is: What Is the Question? 253
731 Four Types of Questions 253
7 4 Two Important Tenets: Randomization and Replication 254
741 Randomization 254
742 Replication 255
7 5 Sampling Design 256
751 Randomized Designs 256
7511 Simple Random Sampling 256
7512 Stratified Random Sampling 256
7513 Cluster Sampling 256
752 Other Designs 256
753 Comparison of Designs 257
754 Adjustments to Estimators to Accounting for Sampling 258
7541 Finite Population Correction 258
7542 Adjustments for Sampling Design 259
755 Lack of Independence in Samples 262
7551 Time Series Models 262
7552 Psuedoreplication 263
xii Contents
O
756 Other General Sampling Concerns 265
7561 Outliers 265
7562 Measurement Error and Precision 266
7563 Bias 266
7564 Missing Data and Nonresponse Bias 266
7565 Transforming Data 267
7566 Altering Datasets 269
7 6 Experimental Design 269
761 General Approaches 269
7611 Manipulative Experiments versus Observational Studies 269
7612 Randomized versus Nonrandomized Experiments 270
7613 Controls 271
7614 Measuring Appropriate Covariates 272
7615 Prospective and Retrospective Studies 272
762 Summary: Inference in the Context of Both Experimental
and Sampling Design 273
763 Classification of Experimental Designs 273
7631 General Linear Models 274
7632 Generalized Linear Models 274
764 Regression Designs 275
7641 Simple Linear Regression 275
i7642 Multiple Regression 275
765 ANOVA Designs 276
7651 ANOVA Terminology 276
7652 Fixed and Random Effects 277
7653A Compendium of ANOVA Designs 278
766 Tabular Designs 286
7661 Three Tabular Designs 287
7 7 Summary 287
Exercises 288
Section II Applications
8 Correlation 295
8 1 Introduction 295
8 2 Pearson s Correlation 296
821 Association and Independence 297
822 Bivariate Normal Distribution 299
823 Estimation of p 300
824 Hypothesis Tests for p 302
825 Confidence Interval for p 306
826 Power, Sample Size, and Effect Size 307
8 3 Robust Correlation 308
831 Rank-Based Permutation Approaches 308
8311 Spearman s ps 308
8312 Kendall s t 312
832 Robust Estimator Approaches 315
8321 Winsorized Correlation 315
Contents xiii
8322 Percentage Bend Criterion, and Sample Biweight
Midvariance 315
8 4 Comparisons of Correlation Procedures 316
8 5 Summary 318
Exercises 318
9 Regression 321
9 1 Introduction 321
911 How to Read This Chapter 321
9 2 Linear Regression Model 322
9 3 General Linear Models 323
931 lm 324
9 4 Simple Linear Regression 324
941 Parameter Estimation 325
942 Hypothesis Testing 329
943 An ANOVA Approach 331
9 5 Multiple Regression 333
951 Parameter Estimation 333
952 Hypothesis Testing 337
9521 Tests Concerning Regression Parameters 337
9522 Combined Effect of X on Y 338
953 An ANOVA Approach 339
9 6 Fitted and Predicted Values 341
9 7 Confidence and Prediction Intervals 343
971 Confidence Interval for (3j 343
972 Confidence Intervals for True Fitted Values and Prediction
Intervals for Predicted Values 344
9 8 Coefficient of Determination and Important Variants 346
9 9 Power, Sample Size, and Effect Size 348
9 10 Assumptions and Diagnostics for Linear Regression 348
9 10 1 Independence of Error Terms 350
9 10 2 Normality of Error Terms 352
9 10 3 Constancy of Error Variance 353
9 10 4 The Relationship between X and Y Is Linear 353
9 10 5 Outliers 354
9 10 6 Multicollinearity 355
9 11 Transformation in the Context of Linear Models 359
9 11 1 Optimal Transformation 361
9 11 1 1 Box-Tidwell 361
9 11 1 2 Box-Cox 361
9 12 Fixing the Y-Intercept 364
9 13 Weighted Least Squares 364
9 14 Polynomial Regression 365
9 15 Comparing Model Slopes 368
9 16 Likelihood and General Linear Models 369
9 17 Model Selection 371
9 17 1 Model Selection Approaches 372
9 17 1 1 AIC 372
9 17 1 2 AICc 374
xiv Contents
9 17 1 3 BIC 374
9 17 1 4 Mallows Cp 9 374
9 17 1 5 PRESS 375
9 17 1 6 Comparison of Selection Criteria 375
9 17 2 Stepwise and All Possible Subset Procedures 377
9 17 2 1 Data Dredging 378
9 18 Robust Regression 378
9 18 1 Bootstrapping Methods 378
9 18 2 Robust Estimators 379
9 19 Model II Regression (X Not Fixed) 381
9 19 1 MA Regression 382
9 19 2 SMA Regression 383
9 19 3 RMA regression 384
9 19 4 Assumptions and Additional Comments 385
9 20 Generalized Linear Models 386
9 20 1 Model Estimation 387
9 20 2 glm 387
9 20 3 Binomial GLMs 387
9 20 4 Deviance 389
9 20 5 GLM Inferential Methods 391
9 20 5 1 Wald Test 391
9 20 5 2 Likelihood Ratio Test 391
9 20 5 3 ROC and AUC 392
9 20 5 4 Measures of Explained Variance 394
9 20 5 5 Information-Theoretic Criteria 394
9 20 6 Poisson GLMs 395
9 20 7 Assumptions and Diagnostics 396
9 20 7 1 GLM Residuals 396
9 20 7 2 Model Goodness of Fit 397
9 20 7 3 Dispersion, Overdispersion, and Quasi-Likelihood 399
9 20 7 4 Fitted Probabilities Numerically 0 or 1 400
9 21 Nonlinear Models 400
9 21 1 nls 401
9 21 2 Model Examples 401
9 21 3 Assumptions and Additional Comments 402
9 22 Smoother Approaches to Association and Regression 403
9 22 1 LOWESS 404
9 22 2 Kernel-Based Approaches 404
9 22 3 Splines 405
9 22 4 Generalized Additive Models 408
9 22 4 1 gam 409
9 22 4 2 Assumptions and Additional Comments 410
9 23 Bayesian Approaches to Regression 411
9 24 Summary 413
Exercises 414
10 ANOVA 421
10 1 Introduction 421
10 1 1 How to Read This Chapter 422
Contents xv
10 1 2 Notation 422
10 2 One-Way ANOVA 423
10 2 1 lm Revisited 426
10 3 Inferences for Factor Levels 429
10 3 1 Introduction to Contrasts 429
10 3 2 Orthogonality 431
10 3 3 lm contrast 432
10 331 Treatment Contrasts 432
10 332 Helmert Contrasts 433
10 333 Sum Contrasts 435
10 3 4 Issues with Multiple Comparisons 436
10 3 5 Simultaneous Inference Procedures 436
10 351 Bonferroni Correction 437
10 352 Least Significant Difference 437
10 353 Scheffe s Procedure 437
10 354 Tukey-Kramer Method 438
10 355 Dunnett s Method 439
10 356 Comparing Simultaneous Inference Procedures 439
10 3 6 General Methods for P-Value Adjustment 441
10 3 7 Depicting Factor-Level Comparisons 442
10 4 ANOVA as a General Linear Model 442
10 5 Random Effects 445
10 5 1 Variance Components 447
10 5 2 Hypothesis Testing 449
10 521 Likelihood Ratio Test 449
10 5 3 lme and lmer 450
10 6 Power, Sample Size, and Effect Size 453
10 7 ANOVA Diagnostics and Assumptions 454
10 7 1 Independence of Error Terms 454
10 7 2 Normality of Error Terms 456
10 7 3 Constancy of Error Variance 456
10 7 4 Outliers 457
10 7 5 Random and Mixed Effect Models 457
10 8 Two-Way Factorial Design 459
10 8 1 Random Effects 463
10 9 Randomized Block Design 466
10 9 1 Random Block Effects 469
10 10 Nested Design 471
10 11 Split-Plot Design 474
10 11 1 aov 475
10 12 Repeated Measures Design 478
10 12 1 Analysis of Contrasts 479
10 12 2 Modern Mixed-Model Approaches 482
10 13 ANCOVA 483
10 14 Unbalanced Designs 488
10 14 1 Type II and III Sums of Squares 488
10 15 Robust ANOVA 492
10 15 1 Permutation Tests 493
10 15 2 Rank-Based Permutation Tests 493
xvi Contents
10 15 3 Robust Estimator Tests 493
10 15 4 One-Way ANOVA 0 493
10 15 4 1 Permutation Tests 493
10 15 4 2 Rank-Based Permutation Tests 493
10 15 4 3 Robust Estimator Tests 494
10 15 5 Multiway ANOVA 494
10 15 5 1 Permutation Tests 494
10 15 5 2 Rank-Based Permutation Tests 494
10 15 5 3 Robust Estimator Tests 495
10 16 Bayesian Approaches to ANOVA 495
10 17 Summary 496
Exercises 497
11 Tabular Analyses 503
11 1 Introduction 503
11 1 1 How to Read This Chapter 503
11 2 Probability Distributions for Tabular Analyses 504
11 3 One-Way Formats 506
11 3 1 Score Test 507
11 311 Tests for n = n0 507
11 312 Tests for All Jt,- = nj0 508
11 313 Tests for 7ij = 7i2 = • • • = 7tc (Includes Two-Proportion
Test: it, = n2) 508
11 3 2 Wald Test 509
11 321 Tests for ti= n0 509
11 322 Tests for Ttj = tt2 (Two-Proportion Test) 510
11 3 3 Likelihood Ratio Test 511
11 331 Tests for n = rc0 511
11 332 Tests for All jt, = niQ (Includes Two-Proportion Test) 512
11 3 4 Comparisons of Methods and Requirements for Valid Inference 512
11 341 Tests for jt = n0 512
11 342 Tests for All it,- = 7t,0 513
11 343 Tests for = n2 (Two-Proportion Test) 513
11 4 Confidence Intervals for 7t 513
11 4 1 Wald Method 513
11 4 2 Score Method 514
11 4 3 Agresti-Coull Method 514
11 4 4 Clopper-Pearson Exact Method 514
11 4 5 Likelihood Ratio Method 514
11 4:6 Comparison of Methods and Requirements for Valid Inference 516
11 4 7 Inference for the Ratio of Two Binomial Proportions 516
11 4 8 Inference for Odds Ratios and Relative Risk 517
11 481 Odds Ratio 517
11 482 Relative Risk 518
11 5 Contingency Tables 519
11 6 Two-Way Tables 520
11 6 1 Chi-Squared (Score) Test 521
11 6 2 Likelihood Ratio Test 521
11 6 3 Fisher s Exact Test 522
Contents xvii
11 6 4 Comparison of Methods and Requirements for Valid Inference 524
11 7 Ordinal Variables 525
11 8 Power, Sample Size, and Effect Size 526
11 9 Three-Way Tables 527
11 9 1 Comparison of Methods and Requirements for Valid Inference 530
11 10 Generalized Linear Models 531
11 10 1 Binomial GLMs 531
11 10 2 Log-Linear Models 532
11 10 2 1 Two-Way Tables 533
11 10 2 2 Three-Way Tables 533
11 10 2 3 Four-Way Tables 537
11 10 3 Comparison of Methods and Requirements for Valid Inference 537
11 11 Summary 537
Exercises 538
Appendix 541
References 555
Index 575
|
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| indexdate | 2024-07-10T00:58:11Z |
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| language | English |
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| publisher | CRC Press |
| record_format | marc |
| spelling | Aho, Ken A. Verfasser (DE-588)1047029081 aut Foundational and applied statistics for biologists using R Ken A. Aho Boca Raton, FL CRC Press 2014 XXI, 596 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 555 - 574 Statistik (DE-588)4056995-0 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf Biostatistik (DE-588)4729990-3 gnd rswk-swf Biologie (DE-588)4006851-1 gnd rswk-swf R Programm (DE-588)4705956-4 s Biologie (DE-588)4006851-1 s Statistik (DE-588)4056995-0 s Biostatistik (DE-588)4729990-3 s DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026990744&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aho, Ken A. Foundational and applied statistics for biologists using R Statistik (DE-588)4056995-0 gnd R Programm (DE-588)4705956-4 gnd Biostatistik (DE-588)4729990-3 gnd Biologie (DE-588)4006851-1 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4705956-4 (DE-588)4729990-3 (DE-588)4006851-1 |
| title | Foundational and applied statistics for biologists using R |
| title_auth | Foundational and applied statistics for biologists using R |
| title_exact_search | Foundational and applied statistics for biologists using R |
| title_full | Foundational and applied statistics for biologists using R Ken A. Aho |
| title_fullStr | Foundational and applied statistics for biologists using R Ken A. Aho |
| title_full_unstemmed | Foundational and applied statistics for biologists using R Ken A. Aho |
| title_short | Foundational and applied statistics for biologists using R |
| title_sort | foundational and applied statistics for biologists using r |
| topic | Statistik (DE-588)4056995-0 gnd R Programm (DE-588)4705956-4 gnd Biostatistik (DE-588)4729990-3 gnd Biologie (DE-588)4006851-1 gnd |
| topic_facet | Statistik R Programm Biostatistik Biologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026990744&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ahokena foundationalandappliedstatisticsforbiologistsusingr |