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ОбложкаQuinn G.P. Experimental design and data analysis for biologists / G.P.Quinn, M.J.Keough. - Cambridge; New York: Cambridge University Press, 2013. - xvii, 537 p.: ill. - Ref.: p.511-526. - Ind.: p.527-537. - ISBN 978-0-521-00976-8
Шифр: (И/Е-Q62) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
 
Preface ........................................................ xv

1    Introduction ............................................... l
1.1  Scientific method .......................................... 1
     1.1.1  Pattern description ................................. 2
     1.1.2  Models .............................................. 2
     1.1.3  Hypotheses and tests ................................ 3
     1.1.4  Alternatives to falsification ....................... 4
     1.1.5  Role of statistical analysis ........................ 5
1.2  Experiments and other tests ................................ 5
1.3  Data, observations and variables ........................... 7
1.4  Probability ................................................ 7
1.5  Probability distributions .................................. 9
     1.5.1  Distributions for variables ........................ 10
     1.5.2  Distributions for statistics ....................... 12

2    Estimation ................................................ 14
2.1  Samples and populations ................................... 14
2.2  Common parameters and statistics .......................... 15
     2.2.1  Center (location) of distribution .................. 15
     2.2.2  Spread or variability .............................. 16
2.3  Standard errors and confidence intervals for the mean ..... 17
     2.3.1  Normal distributions and the Central Limit
            Theorem ............................................ 17
     2.3.2  Standard error of the sample mean .................. 18
     2.3.3  Confidence intervals for population mean ........... 19
     2.3.4  Interpretation of confidence intervals for
            population mean .................................... 20
     2.3.5  Standard errors for other statistics ............... 20
2.4  Methods for estimating parameters ......................... 23
     2.4.1  Maximum likelihood (ML) ............................ 23
     2.4.2  Ordinary least squares (OLS) ....................... 24
     2.4.3  ML vs OLS estimation ............................... 25
2.5  Resampling methods for estimation ......................... 25
     2.5.1  Bootstrap .......................................... 25
     2.5.2  Jackknife .......................................... 26
2.6  Bayesian inference - estimation ........................... 27
     2.6.1  Bayesian estimation ................................ 27
     2.6.2  Prior knowledge and probability .................... 28
     2.6.3  Likelihood function ................................ 28
     2.6.4  Posterior probability .............................. 28
     2.6.5  Examples ........................................... 29
     2.6.6  Other comments ..................................... 29

3    Hypothesis testing ........................................ 32
3.1  Statistical hypothesis testing ............................ 32
     3.1.1  Classical statistical hypothesis testing ........... 32
     3.1.2  Associated probability and Type I error ............ 34
     3.1.3  Hypothesis tests for a single population ........... 35
     3.1.4  One-and two-tailed tests ........................... 37
     3.1.5  Hypotheses for two populations ..................... 37
     3.1.6  Parametric tests and their assumptions ............. 39
3.2  Decision errors ........................................... 42
     3.2.1  Type I and II errors ............................... 42
     3.2.2  Asymmetry and scalable decision criteria ........... 44
3.3  Other testing methods ..................................... 45
     3.3.1  Robust parametric tests ............................ 45
     3.3.2  Randomization (permutation) tests .................. 45
     3.3.3  Rank-based non-parametric tests .................... 46
3.4  Multiple testing .......................................... 48
     3.4.1  The problem ........................................ 48
     3.4.2  Adjusting significance levels and/or P values ...... 49
     3.5  Combining results from statistical tests ............. 50
     3.5.1  Combining P values ................................. 50
     3.5.2  Meta-analysis ...................................... 50
3.6  Critique of statistical hypothesis testing ................ 51
     3.6.1  Dependence on sample size and stopping rules ....... 51
     3.6.2  Sample space - relevance of data not observed ...... 52
     3.6.3  P values as measure of evidence .................... 53
     3.6.4  Null hypothesis always false ....................... 53
     3.6.5  Arbitrary significance levels ...................... 53
     3.6.6  Alternatives to statistical hypothesis testing ..... 53
3.7  Bayesian hypothesis testing ............................... 54


4    Graphical exploration of data ............................. 58
4.1  Exploratory data analysis ................................. 58
     4.1.1 Exploring samples ................................... 58
4.2  Analysis with graphs ...................................... 62
     4.2.1 Assumptions of parametric linear models ............. 62
4.3  Transforming data ......................................... 64
     4.3.1  Transformations and distributional assumptions ..... 65
     4.3.2  Transformations and linearity ...................... 67
     4.3.3  Transformations and additivity ..................... 67
4.4  Standardizations .......................................... 67
4.5  Outliers .................................................. 68
4.6  Censored and missing data ................................. 68
     4.6.1  Missing data ....................................... 68
     4.6.2  Censored (truncated) data .......................... 69
4.7  General issues and hints for analysis ..................... 71
     4.7.1 General issues ...................................... 71

5    Correlation and regression ................................ 72
5.1  Correlation analysis ...................................... 72
     5.1.1  Parametric correlation model ....................... 72
     5.1.2  Robust correlation ................................. 76
     5.1.3  Parametric and non-parametric confidence regions ... 76
5.2  Linear models ............................................. 77
5.3  Linear regression analysis ................................ 78
     5.3.1  Simple (bivariate) linear regression ............... 78
     5.3.2  Linear model for regression ........................ 80
     5.3.3  Estimating model parameters ........................ 85
     5.3.4  Analysis of variance ............................... 88
     5.3.5  Null hypotheses in regression ...................... 89
     5.3.6  Comparing regression models ........................ 90
     5.3.7  Variance explained ................................. 91
     5.3.8  Assumptions of regression analysis ................. 92
     5.3.9  Regression diagnostics ............................. 94
     5.3.10 Diagnostic graphics ................................ 96
     5.3.11 Transformations .................................... 98
     5.3.12 Regression through the origin ...................... 98
     5.3.13 Weighted least squares ............................. 99
     5.3.14 X random (Model II regression) .................... 100
     5.3.15 Robust regression ................................. 104
5.4  Relationship between regression and correlation .......... 106
5.5  Smoothing ................................................ 107
     5.5.1  Running means ..................................... 107
     5.5.2  LO(W)ESS .......................................... 107
     5.5.3  Splines ........................................... 108
     5.5.4  Kernels ........................................... 108
     5.5.5  Other issues ...................................... 109
5.6  Power of tests in correlation and regression ............. 109
5.7  General issues and hints for analysis .................... 110
     5.7.1  General issues .................................... 110
     5.7.2  Hints for analysis ................................ 110

6    Multiple and complex regression .......................... 111
6.1  Multiple linear regression analysis ...................... 111
     6.1.1  Multiple linear regression model .................. 114
     6.1.2  Estimating model parameters ....................... 119
     6.1.3  Analysis of variance .............................. 119
     6.1.4  Null hypotheses and model comparisons ............. 121
     6.1.5  variance explained ................................ 122
6.1.6  Which predictors are important? ........................ 122
     6.1.7  Assumptions of multiple regression ................ 124
     6.1.8  Regression diagnostics ............................ 125
     6.1.9  Diagnostic graphics ............................... 125
     6.1.10 Transformations ................................... 127
     6.1.11 Collinearity ...................................... 127
     6.1.12 Interactions in multiple regression ............... 130
     6.1.13 Polynomial regression ............................. 133
     6.1.14 Indicator (dummy) variables ....................... 135
     6.1.15 Finding the "best" regression model ............... 137
     6.1.16 Hierarchical partitioning ......................... 141
     6.1.17 Other issues in multiple linear regression ........ 142
6.2  Regression trees ......................................... 143
6.3  Path analysis and structural equation modeling ........... 145
6.4  Nonlinear models ......................................... 150
6.5  Smoothing and response surfaces .......................... 152
6.6  General issues and hints for analysis .................... 153
     6.6.1  General issues .................................... 153
     6.6.2  Hints for analysis ................................ 154

7    Design and power analysis ................................ 155
7.1  Sampling ................................................. 155
     7.1.1  Sampling designs .................................. 155
     7.1.2  Size of sample .................................... 157
7.2  Experimental design ...................................... 157
     7.2.1  Replication ....................................... 158
     7.2.2  Controls .......................................... 160
     7.2.3  Randomization ..................................... 161
     7.2.4  Independence ...................................... 163
     7.2.5  Reducing unexplained variance ..................... 164
7.3  Power analysis ........................................... 164
     7.3.1  Using power to plan experiments (a priori power
            analysis) ......................................... 166
     7.3.2  Post hoc power calculation ........................ 168
     7.3.3  The effect size ................................... 168
     7.3.4  Using power analyses .............................. 170
7.4  General issues and hints for analysis .................... 171
     7.4.1  General issues .................................... 171
     7.4.2  Hints for analysis ................................ 172

8    Comparing groups or treatments - analysis of variance .... 173
8.1  Single factor (one way) designs .......................... 173
     8.1.1  Types of predictor variables (factors) ............ 176
     8.1.2  Linear model for single factor analyses ........... 178
     8.1.3  Analysis of variance .............................. 184
     8.1.4  Null hypotheses ................................... 186
     8.1.5  Comparing ANOVA models ............................ 187
     8.1.6  Unequal sample sizes (unbalanced designs) ......... 187
8.2  Factor effects ........................................... 188
     8.2.1  Random effects: variance components ............... 188
     8.2.2  Fixed effects ..................................... 190
8.3  Assumptions .............................................. 191
     8.3.1  Normality ......................................... 192
     8.3.2  Variance homogeneity .............................. 193
     8.3.3  Independence ...................................... 193
     8.3.1  ANOVA diagnostics ................................. 194
8.5  Robust ANOVA ............................................. 195
     8.5.1  Tests with heterogeneous variances ................ 195
     8.5.2  Rank-based ("non-parametric") tests ............... 195
     8.5.3  Randomization tests ............................... 196
8.6  Specific comparisons of means ............................ 196
     8.6.1 Planned comparisons or contrasts ................... 197
     8.6.2 Unplanned pairwise comparisons ..................... 199
     8.6.3 Specific contrasts versus unplanned pairwise
           comparisons ........................................ 201
8.7  Tests for trends ......................................... 202
8.8  Testing equality of group variances ...................... 203
8.9  Power of single factor ANOVA ............................. 204
8.10 General issues and hints for analysis .................... 206
     8.10.1 General issues .................................... 206
     8.10.2 Hints for analysis ................................ 206

9    Multifactor analysis of variance ......................... 208
9.1  Nested (hierarchical) designs ............................ 208
     9.1.1  Linear models for nested analyses ................. 210
     9.1.2  Analysis of variance .............................. 214
     9.1.3  Null hypotheses ................................... 215
     9.1.4  Unequal sample sizes (unbalanced designs) ......... 216
     9.1.5  Comparing ANOVA models ............................ 216
     9.1.6  Factor effects in nested models ................... 216
     9.1.7  Assumptions for nested models ..................... 218
     9.1.8  Specific comparisons for nested designs ........... 219
     9.1.9  More complex designs .............................. 219
     9.1.10 Design and power .................................. 219
9.2  Factorial designs ........................................ 221
     9.2.1  Linear models for factorial designs ............... 225
     9.2.2  Analysis of variance .............................. 230
     9.2.3  Null hypotheses ................................... 232
     9.2.4  What are main effects and interactions really
            measuring? ........................................ 237
     9.2.5  Comparing ANOVA models ............................ 241
     9.2.6  Unbalanced designs ................................ 241
     9.2.7  Factor effects .................................... 247
     9.2.8  Assumptions ....................................... 249
     9.2.9  Robust factorial ANOVAs ........................... 250
     9.2.10 Specific comparisons on main effects .............. 250
     9.2.11 Interpreting interactions ......................... 251
     9.2.12 More complex designs .............................. 255
     9.2.13 Power and design in factorial ANOVA ............... 259
9.3  Pooling in multifactor designs ........................... 260
9.4  Relationship between factorial and nested designs ........ 261
9.5  General issues and hints for analysis .................... 261
     9.5.1  General issues .................................... 261
     9.5.2  Hints for analysis ................................ 261

10   Randomized blocks and simple repeated measures:
     unreplicated two factor designs .......................... 262
10.1 Unreplicated two factor experimental designs ............. 262
     10.1.1 Randomized complete block (RCB) designs ........... 262
     10.1.2 Repeated measures (RM) designs .................... 265
10.2 Analyzing RCB and RM designs ............................. 268
     10.2.1 Linear models for RCB and RM analyses ............. 268
     10.2.2 Analysis of variance .............................. 272
     10.2.3 Null hypotheses ................................... 273
     10.2.4 Comparing ANOVA models ............................ 274
10.3 Interactions in RCB and RM models ........................ 274
     10.3.1 Importance of treatment by block interactions ..... 274
     10.3.2 Checks for interaction in unreplicated designs .... 277
10.4 Assumptions .............................................. 280
     10.4.1 Normality, independence of errors ................. 280
     10.4.2 Variances and covariances - sphericity ............ 280
     10.4.3 Recommended strategy .............................. 284
10.5 Robust RCB and RM analyses ............................... 284
10.6 Specific comparisons ..................................... 285
10.7 Efficiency of blocking (to block or not to block?) ....... 285
10.8 Time as a blocking factor ................................ 287
10.9 Analysis of unbalanced RCB designs ....................... 287
10.10 Power of RCB or simple RM designs ....................... 289
10.11 More complex block designs .............................. 290
     10.11.1 Factorial randomized block designs ............... 290
     10.11.2 Incomplete block designs ......................... 292
     10.11.3 Latin square designs ............................. 292
     10.11.4 Crossover designs ................................ 296
10.12 Generalized randomized block designs .................... 298
10.13 RCB and RM designs and statistical software ............. 298
10.14 General issues and hints for analysis ................... 299
     10.14.1 General issues ................................... 299
     10.14.2 Hints for analysis ............................... 300

11   Split-plot and repeated measures designs: partly
     nested analyses of variance .............................. 301
11.1 Partly nested designs .................................... 301
     11.1.1 Split-plot designs ................................ 301
     11.1.2 Repeated measures designs ......................... 305
     11.1.3 Reasons for using these designs ................... 309
11.2 Analyzing partly nested designs .......................... 309
     11.2.1 Linear models for partly nested analyses .......... 310
     11.2.2 Analysis of variance .............................. 313
     11.2.3 Null hypotheses ................................... 315
     11.2.4 Comparing ANOVA models ............................ 318
11.3 Assumptions .............................................. 318
     11.3.1 Between plots/subjects ............................ 318
     11.3.2 Within plots/subjects and multisample sphericity .. 318
11.4 Robust partly nested analyses ............................ 320
11.5 Specific comparisons ..................................... 320
     11.5.1 Main effects ...................................... 320
     11.5.2 Interactions ...................................... 321
     11.5.3 Profile (i.e. trend) analysis ..................... 321
11.6 Analysis of unbalanced partly nested designs ............. 322
11.7 Power for partly nested designs .......................... 323
11.8 More complex designs ..................................... 323
     11.8.1 Additional between-plots/subjects factors ......... 324
     11.8.2 Additional within-plots/subjects factors .......... 329
     11.8.3 Additional between-plots/subjects and within-
            plots/subjects factors ............................ 332
     11.8.4 General comments about complex designs ............ 335
11.9 Partly nested designs and statistical software ........... 335
11.10 General issues and hints for analysis ................... 337
     11.10.1 General issues ................................... 337
     11.10.2 Hints for individual analyses .................... 337

12   Analyses of covariance ................................... 339
12.1 Single factor analysis of covariance (ANCOVA) ............ 339
     12.1.1 linear models for analysis of covariance .......... 342
     12.1.2 Analysis of (co)variance .......................... 347
     12.1.3 Null hypotheses ................................... 347
     12.1.4 Comparing ANCOVA models ........................... 348
12.2 Assumptions of ANCOVA .................................... 348
     12.2.1 Linearity ......................................... 348
     12.2.2 Covariate values similar across groups ............ 349
     12.2.3 Fixed covariate (X) ............................... 349
12.3 Homogeneous slopes ....................................... 349
     12.3.1 Testing for homogeneous within-group regression
            slopes 349
     12.3.2 Dealing with heterogeneous within-group
            regression slopes ................................. 350
     12.3.3 Comparing regression lines ........................ 352
12.4 Robust ANCOVA ............................................ 352
12.5 Unequal sample sizes (unbalanced designs) ................ 353
12.6 Specific comparisons of adjusted means ................... 353
     12.6.1 Planned contrasts ................................. 353
     12.6.2 Unplanned comparisons ............................. 353
12.7 More complex designs ..................................... 353
     12.7.1 Designs with two or more covariates ............... 353
     12.7.2 Factorial designs ................................. 354
     12.7.3 Nested designs with one covariate ................. 355
     12.7.4 Partly nested models with one covariate ........... 356
12.8 General issues and hints for analysis .................... 357
     12.8.1 General issues .................................... 357
     12.8.2 Hints for analysis ................................ 358

13   Generalized linear models and logistic regression ........ 359
13.1 Generalized linear models ................................ 359
13.2 Logistic regression ...................................... 360
     13.2.1 Simple logistic regression ........................ 360
     13.2.2 Multiple logistic regression ...................... 365
     13.2.3 Categorical predictors ............................ 368
     13.2.4 Assumptions of logistic regression ................ 368
     13.2.5 Goodness-of-fit and residuals ..................... 368
     13.2.6 Model diagnostics ................................. 370
     13.2.7 Model selection ................................... 370
     13.2.8 Software for logistic regression .................. 371
13.3 Poisson regression ....................................... 371
13.4 Generalized additive models .............................. 372
13.5 Models for correlated data ............................... 375
     13.5.1 Multi-level (random effects) models ............... 376
     13.5.2 Generalized estimating equations .................. 377
13.6 General issues and hints for analysis .................... 378
     13.6.1 General issues .................................... 378
     13.6.2 Hints for analysis ................................ 379

14   Analyzing frequencies .................................... 380
14.1 Single variable goodness-of-fit tests .................... 381
14.2 Contingency tables ....................................... 381
     14.2.1 Two way tables .................................... 381
     14.2.2 Three way tables .................................. 388
14.3 Log-linear models ........................................ 393
     14.3.1 Two way tables .................................... 394
     14.3.2 Log-linear models for three way tables ............ 395
     14.3.3 More complex tables ............................... 400
14.4 General issues and hints for analysis .................... 400
     14.4.1 General issues .................................... 400
     14.4.2 Hints for analysis ................................ 400

15   Introduction to multivariate analyses .................... 401
15.1 Multivariate data ........................................ 401
15.2 Distributions and associations ........................... 402
15.3 Linear combinations, eigenvectors and eigenvalues ........ 405
     15.3.1 Linear combinations of variables .................. 405
     15.3.2 Eigenvalues ....................................... 405
     15.3.3 Eigenvectors ...................................... 406
     15.3.4 Derivation of components .......................... 409
15.4 Multivariate distance and dissimilarity measures ......... 409
     15.4.1 Dissimilarity measures for continuous variables ... 412
     15.4.2 Dissimilarity measures for dichotomous (binary)
            variables ......................................... 413
     15.4.3 General dissimilarity measures for mixed
            variables ......................................... 413
     15.4.4 Comparison of dissimilarity measures .............. 414
15.5 Comparing distance and/or dissimilarity matrices ......... 414
15.6 Data standardization ..................................... 415
15.7 Standardization, association and dissimilarity ........... 417
15.8 Multivariate graphics .................................... 417
15.9 Screening multivariate data sets ......................... 418
     15.9.1 Multivariate outliers ............................. 419
     15.9.2 Missing observations .............................. 419
15.10 General issues and hints for analysis ................... 423
     15.10.1 General issues ................................... 423
     15.10.2 Hints for analysis ............................... 424

16   Multivariate analysis of variance and discriminant
     analysis ................................................. 425
16.1 Multivariate analysis of variance (MANOVA) ............... 425
     16.1.1 Single factor MANOVA .............................. 426
     16.1.2 Specific comparisons .............................. 432
     16.1.3 Relative importance of each response variable ..... 432
     16.1.4 Assumptions of MANOVA ............................. 433
     16.1.5 Robust MANOVA ..................................... 434
     16.1.6 More complex designs .............................. 434
16.2 Discriminant function analysis ........................... 435
     16.2.1 Description and hypothesis testing ................ 437
     16.22 Classification and prediction ...................... 439
     16.2.3 Assumptions of discriminant function analysis ..... 441
     16.2.4 More complex designs .............................. 441
16.3 MANOVA vs discriminant function analysis ................. 441
16.4 General issues and hints for analysis .................... 441
     16.4.1 General issues .................................... 441
     16.4.2 Hints for analysis ................................ 441

17   Principal components and correspondence analysis ......... 443
17.1 Principal components analysis ............................ 443
     17.1.1 Deriving components ............................... 447
     17.1.2 Which association matrix to use? .................. 450
     17.1.3 Interpreting the components ....................... 451
     17.1.4 Rotation of components ............................ 451
     17.1.5 How many components to retain? .................... 452
     17.1.6 Assumptions ....................................... 453
     17.1.7 Robust PCA ........................................ 454
     17.1.8 Graphical representations ......................... 454
     17.1.9 Other uses of components .......................... 456
17.2 Factor analysis .......................................... 458
17.3 Correspondence analysis .................................. 459
     17.3.1 Mechanics ......................................... 459
     17.3.2 Scaling and joint plots ........................... 461
     17.3.3 Reciprocal averaging .............................. 462
     17.3.4 Use of CA with ecological data .................... 462
     17.3.5 Detrending ........................................ 463
17.4 Canonical correlation analysis ........................... 463
17.5 Redundancy analysis ...................................... 466
17.6 Canonical correspondence analysis ........................ 467
17.7 Constrained and partial "ordination" ..................... 468
17.8 General issues and hints for analysis .................... 471
     17.8.1 General issues .................................... 471
     17.8.2 Hints for analysis ................................ 471

18   Multidimensional scaling and cluster analysis ............ 473
18.1 Multidimensional scaling ................................. 473
     18.1.1 Classical scaling - principal coordinates
            analysis (PCoA) ................................... 474
     18.1.2 Enhanced multidimensional scaling ................. 476
     18.1.3 Dissimilarities and testing hypotheses about
            groups of objects ................................. 482
     18.1.4 Relating MDS to original variables ................ 487
     18.1.5 Relating MDS to covariates ........................ 487
18.2 Classification ........................................... 488
     18.2.1 Cluster analysis .................................. 488
18.3 Scaling (ordination) and clustering for biological data .. 491
18.4 General issues and hints for analysis .................... 493
     18.4.1 General issues .................................... 493
     18.4.2 Hints for analysis ................................ 493

19   Presentation of results .................................. 494
19.1 Presentation of analyses ................................. 494
     19.1.1 Linear models ..................................... 494
     19.1.2 Other analyses .................................... 497
     19.2 Layout of tables .................................... 497
19.3 Displaying summaries of the data ......................... 498
     19.3.1 Bar graph ......................................... 500
     19.3.2 Line graph (category plot) ........................ 502
     19.3.3 Scatterplots ...................................... 502
     19.3.4 Pie charts ........................................ 503
19.4 Error bars ............................................... 504
     19.4.1 Alternative approaches ............................ 506
19.5 Oral presentations ....................................... 507
     19.5.1 Slides, computers, or overheads? .................. 507
     19.5.2 Graphics packages ................................. 508
     19.5.3 Working with color ................................ 508
     19.5.4 Scanned images .................................... 509
     19.5.5 Information content ............................... 509
     19.6 General issues and hints ............................ 510

References .................................................... 511
Index ......................................................... 527

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