The epistemology of statistical science

Book Cover......Page 1
Title Page......Page 3
CONTENTS......Page 6
Preface......Page 8
1.1 Introduction......Page 11
1.2 The discourse of science......Page 13
1.3 Establishing scientific facts......Page 15
1.4 The ultimate words of statistics......Page 16
1.5 Mathematical forms and physical meanings......Page 17
1.6 A few basic statistical ideas......Page 20
1.7 Measuring the quality of fit of an isolated singleton......Page 21
1.8 Measuring the quality of fit of a class characteristic......Page 26
1.9 A word of caution......Page 30
1.11 Alternatives to a hypothesised model......Page 31
1.12 Data analysis, science and sufficiency......Page 35
1.13 Remark on ancillary frames of reference......Page 40
1.15 Definition of a commencement test......Page 41
1.17 The specification of alternatives for a commencement test......Page 47
1.18 Remark on terminology......Page 48
1.19 Definition of co-ordination tests and significance tests......Page 49
1.20 Derivation of co-ordination tests from givensignificance tests......Page 50
1.21 A normative prescription with destructive consequences......Page 51
1.22 Combining independent levels of co-ordination......Page 57
1.23 The sensitivity of a given test to different alternatives......Page 59
1.24 The sensitivity of different tests to a given alternative......Page 72
1.25 The separating characteristics of a co-ordination test......Page 74
1.27 Simultaneous statistical inference......Page 75
1.28 Ordering by modelled frequency – a defective principle......Page 80
1.29 Some formal relations between co-ordination tests andsignificance tests......Page 81
1.30 Predictions, predications and forecasts......Page 82
1.31 Scientific data analysis......Page 86
1.32 Relevant subsidiary models......Page 95
1.33 The notion of ‘critical regions’ as a source of ill-conceivedorderings......Page 99
1.34 Inconceivable orderings......Page 102
1.35 Developing scientific concepts......Page 106
1.36 The role of simulation......Page 108
1.37 Spanning the interface......Page 112
1.38 Beyond the interface......Page 115
1.39 The receding Ideal......Page 116
1.40 The scientific status of randomised designs......Page 117
2.2 Null hypotheses as opposed to hypothesised models......Page 118
2.3 Measuring the quality-of-fit of alternative members ofa class of models......Page 121
2.4 Some definitions......Page 131
2.5 One-to-one transformations of the index......Page 139
2.6 Unilateral and bilateral tests of co-ordination......Page 142
2.7 Some principles of shortfall testing......Page 144
2.8 Shortfall tests vis-à-vis Dunnett’s ‘multiple comparison’procedures......Page 149
2.9 A destructive prescription revisited......Page 153
2.10 On a notion of objectivity......Page 157
2.11 Normative prescriptions as comfortable recipes......Page 158
2.12 Scientific data analysis in case of elimination testing......Page 159
2.13 In the statistical laboratory......Page 165
2.14 The principle of scientific implication......Page 166
2.15 The notion of probability inference......Page 169
3.2 Decision-making under risk as opposed to data analysis......Page 171
3.4 Decision-making under risk in case of different populations......Page 173
3.5 Statistical thinkers versus statistical doers......Page 174
3.6 The Neyman-Pearson lemma for decision-making under risk......Page 175
3.7 The first of two different resolutions of the mixedsampling problem......Page 180
3.9 When separating characteristics are irrelevant......Page 182
3.10 Randomisation and an old enigma of card play......Page 183
3.11 The target problem......Page 184
3.13 Concluding remark on a counter-argument......Page 185
4.1 Introduction......Page 186
4.2 The problem of attaining real-world repetitions......Page 187
4.4 A dilemma......Page 188
4.5 Stereotypic arrays destroy statistical evidence......Page 190
4.6 Stereotypic arrays destroy substantive evidence......Page 191
4.7 Stereotypic arrays involve silly embarrassments......Page 192
4.8 Stereotypic arrays cannot avoid circular reasoning......Page 193
4.10 Different usage of the term ‘paradox’......Page 195
4.11 Pratt’s paradox......Page 196
4.12 Berkson’s paradox......Page 197
4.13 The vacuous-interval paradox......Page 198
4.14 A class of fallacious arguments......Page 200
4.15 When operating characteristics are irrelevant......Page 202
4.16 The data-analytic approach to Welch’s problem......Page 204
4.17 A revealing peripheral case......Page 207
4.19 Neyman’s theory of statistical inference......Page 208
4.20 The incoherence dilemma of frequentist inference......Page 209
4.21 The scientific status of proof by dilemma......Page 215
4.22 The randomised test paradox......Page 216
4.24 A liaison between ‘knowledge’ and its ‘knower'......Page 219
4.25 A persuasive diversion......Page 221
4.26 The knower is not needed......Page 224
4.28 Neyman’s ‘knowing subject’......Page 225
4.29 Stereotypic arrays and decision-making under risk......Page 226
4.30 How is frequentist inference sustained despite its obviousdefects?......Page 227
5.2 Significance levels as measurements of quality of fit......Page 228
5.3 Concluding remark......Page 232
6.2 A pair of non-equivalent definitions......Page 233
6.3 R.A. Fisher’s usage of the term ‘significance level’......Page 236
6.4 Proof of an inadvertent confounding......Page 240
6.5 Another proof......Page 242
6.6 A watershed......Page 248
6.7 Fisher’s ‘knowing subject’......Page 251
6.8 Further confounding......Page 259
6.9 A further development of the F test......Page 264
6.11 The Studentised range test......Page 265
6.13 Simulation of a disagreement......Page 266
6.14 A source of confusion peculiar to statistics......Page 269
6.15 Concluding remark......Page 271
7.1 Introduction......Page 272
7.2 The Neyman-Pearson lemma for data analysis......Page 274
7.3 Likelihood ratio tests in relation to commencement tests......Page 277
7.4 Likelihood ratio rounding......Page 282
7.5 Exhaustively continuous test statistics......Page 289
7.6 Monotone likelihood ratios......Page 290
7.7 Unbiased hypothesis testing......Page 293
7.9 Concluding remarks......Page 296
8.2 A proposal of Kempthorne and Folks......Page 299
8.3 An epistemological consideration......Page 300
8.4 Consonance regions and dissonance regions......Page 301
8.5 An unneeded embellishment......Page 305
8.6 The notion of ‘interval estimation’ in general......Page 309
9.1 Introduction......Page 310
9.2 A proposal that fails......Page 312
9.3 Conditional models that are ‘performable’, even‘performed’, yet vacuous......Page 315
9.4 Another proposal that fails......Page 316
9.5 Yet another proposal that fails......Page 321
9.7 Subsidiary models that are not performable yet are notsubstantively vacuous......Page 326
9.8 Every-day examples of conditioning on ancillary statistics......Page 329
9.9 Conclusion......Page 333
10.2 The basic ideas......Page 334
10.5 ‘Likelihood’: What does it mean?......Page 338
10.6 Physical (bodily) norms of discrepancy......Page 340
10.7 Statistically vacuous likelihood ratios......Page 341
10.8 A vicious circle......Page 346
10.9 Another vicious circle......Page 349
10.11 Absolute quality of fit as opposed to relative qualityof fit......Page 355
10.12 Can odds-ratio testing usefully supplement othermethods of data analysis?......Page 359
10.14 A definition of statistical inference......Page 361
11.2 An explanatory example......Page 363
11.3 Some general forms......Page 365
11.4 Bayes’s Theorem in decision-making under risk......Page 367
11.5 Bayes’s theorem in data analysis......Page 370
11.6 Of how much practical use is Bayes’s theorem?......Page 372
12.2 Personal probabilities......Page 373
12.3 A metaphysical view......Page 375
12.5 A ramshackle foundation......Page 378
12.6 A doubly incoherent discourse......Page 383
12.7 A vicious circle......Page 389
12.8 On a method of commencement testing......Page 392
12.9 There cannot be ‘a parametric commencement’......Page 393
12.10 An unrealistic outlook......Page 394
12.12 Subjective versus objective – a silly dispute......Page 395
13.1 Introduction......Page 396
13.2 Student’s knowing subject......Page 398
13.3 Example of a simultaneous-confidence-interval procedure......Page 400
13.5 Two properties shared by all simultaneous-confidence region procedures......Page 403
13.7 Scheffé’s knowing subject......Page 405
13.8 Tukey’s knowing subject......Page 407
13.9 Dunnet’s knowing subject......Page 409
13.10 One question many answers?......Page 410
13.11 Mean separation procedures......Page 411
13.12 On ‘scientific coherence’ as opposed to ‘numericalcoherence’......Page 416
13.13 Lindley’s ‘knowing subject’......Page 417
13.14 Cox’s ‘knowing subject’......Page 423
13.15 A stupid question......Page 426
13.16 The multiple-comparison ‘lore’ on factorials......Page 427
13.18 A fundamental error......Page 428
13.19 A profession in denial......Page 429
14.2 The basic idea......Page 432
14.3 A concrete example......Page 433
14.4 The shortcomings of fiducial inference......Page 435
14.5 Probability inference......Page 437
15. Epilogue: Challenging the statistical profession......Page 438
References......Page 439