|
1 Synopsis, by Way of Autobiography |
|
|
1 | (32) |
|
1.1 The Problem as I Originally Confronted it |
|
|
4 | (8) |
|
1.1.1 The Place of Statistics in the Social Sciences |
|
|
4 | (3) |
|
1.1.2 Statistical Inference and its Misconceptions |
|
|
7 | (2) |
|
1.1.3 The Root of the Problem in the Dualistic Concept of Probability |
|
|
9 | (3) |
|
1.2 How this Book Came about |
|
|
12 | (2) |
|
1.3 Some Qualifications, Objections, and Implications |
|
|
14 | (14) |
|
1.3.1 Intervening Developments |
|
|
18 | (2) |
|
1.3.2 Some Qualifications Regarding the Historical Argument |
|
|
20 | (3) |
|
1.3.3 An Ad Hominem Ipsum |
|
|
23 | (5) |
|
|
28 | (5) |
|
2 The Philosophical and Cultural Context for the Emergence of Probability and Statistical Inference |
|
|
33 | (46) |
|
2.1 Brief Excursus on Historical Cognitive Change |
|
|
35 | (6) |
|
|
35 | (2) |
|
|
37 | (2) |
|
2.1.3 General Observations |
|
|
39 | (2) |
|
2.2 The Concept of Skeuomorphosis |
|
|
41 | (6) |
|
2.2.1 Early Technologies of Distance |
|
|
42 | (1) |
|
2.2.2 The Emergence of the Market Economy |
|
|
43 | (1) |
|
2.2.3 Mathematical, Mechanistic, and Relativistic Thinking |
|
|
44 | (2) |
|
2.2.4 Scientific Objectivity |
|
|
46 | (1) |
|
2.3 Some Consequences for Epistemology |
|
|
47 | (11) |
|
2.3.1 The Concept of Sign |
|
|
47 | (2) |
|
2.3.2 The Combinatorics of Language and Thought |
|
|
49 | (2) |
|
|
51 | (4) |
|
|
55 | (3) |
|
2.4 Some Psychological and Cultural Considerations |
|
|
58 | (14) |
|
2.4.1 The Emergence of Self-Consciousness |
|
|
58 | (2) |
|
2.4.2 Polarizations, Alignments, and Projections |
|
|
60 | (12) |
|
|
72 | (1) |
|
|
73 | (6) |
|
3 Origin of the Modern Concept of Probability |
|
|
79 | (38) |
|
3.1 Why Gambling per se Didn't Lead to a Theory of Mathematical Probability |
|
|
79 | (3) |
|
3.2 The Concept of Probability before the Seventeenth Century |
|
|
82 | (4) |
|
3.3 The Calculus of Expectation |
|
|
86 | (5) |
|
|
91 | (4) |
|
3.5 The Art of Conjecturing |
|
|
95 | (12) |
|
3.5.1 The Law of Large Numbers |
|
|
96 | (3) |
|
3.5.2 The Metaphysical Status of Probability |
|
|
99 | (2) |
|
3.5.3 One Word, Two Scales |
|
|
101 | (6) |
|
3.6 Implications for Future Developments |
|
|
107 | (7) |
|
|
114 | (3) |
|
4 The Classical Theory of Statistical Inference |
|
|
117 | (14) |
|
|
118 | (6) |
|
|
124 | (2) |
|
|
126 | (3) |
|
|
129 | (2) |
|
5 Nineteenth-Century Developments in Statistics |
|
|
131 | (28) |
|
5.1 Descriptive Statistics |
|
|
131 | (12) |
|
5.1.1 The Normal Curve in Astronomy |
|
|
132 | (2) |
|
5.1.2 Application of the Normal Distribution to Populations: Quetelet |
|
|
134 | (5) |
|
5.1.3 Galton, Pearson, and the Biometricians |
|
|
139 | (4) |
|
5.2 Precursors of Significance Testing |
|
|
143 | (13) |
|
5.2.1 Arbuthnot's and Gavarret's Use of the Binomial |
|
|
143 | (3) |
|
5.2.2 Probabilistic Criteria for the Rejection of Discordant Observations in Astronomy |
|
|
146 | (3) |
|
5.2.3 The Normal Model and Data in the Social Sciences |
|
|
149 | (1) |
|
5.2.4 The Pun on Significance |
|
|
150 | (3) |
|
5.2.5 Small Datasets in Agricultural Research |
|
|
153 | (3) |
|
|
156 | (3) |
|
6 The Frequency Theory of Probability |
|
|
159 | (28) |
|
6.1 The Principle of Indifference |
|
|
161 | (3) |
|
6.2 The Frequency Theorists |
|
|
164 | (14) |
|
|
165 | (1) |
|
|
166 | (2) |
|
|
168 | (4) |
|
|
172 | (4) |
|
|
176 | (2) |
|
6.3 The Concept of Randomness |
|
|
178 | (5) |
|
|
183 | (1) |
|
|
184 | (3) |
|
7 The Fisher and Neyman-Pearson Theories of Statistical Inference |
|
|
187 | (50) |
|
|
187 | (4) |
|
7.2 The Fisherian Theory of Statistical Inference |
|
|
191 | (18) |
|
|
192 | (2) |
|
7.2.2 Significance Testing |
|
|
194 | (9) |
|
7.2.3 Fiducial Probability |
|
|
203 | (6) |
|
|
209 | (17) |
|
|
211 | (11) |
|
7.3.2 Confidence Intervals |
|
|
222 | (4) |
|
7.4 Differences Between the Fisher and Neyman-Pearson Theories |
|
|
226 | (5) |
|
|
231 | (6) |
|
8 Bayesian Theories of Probability and Statistical Inference |
|
|
237 | (44) |
|
8.1 Logical Theories of Probability |
|
|
238 | (12) |
|
|
238 | (6) |
|
|
244 | (4) |
|
|
248 | (2) |
|
8.2 Personalist Theories of Probability |
|
|
250 | (10) |
|
|
251 | (2) |
|
|
253 | (3) |
|
|
256 | (2) |
|
8.2.4 Wald's Decision Theory |
|
|
258 | (2) |
|
8.3 General Structure of Bayesian Inference |
|
|
260 | (6) |
|
|
266 | (10) |
|
8.4.1 The Logical Allocation of Prior Probabilities |
|
|
266 | (3) |
|
8.4.2 The Subjective Allocation of Prior Probabilities |
|
|
269 | (3) |
|
|
272 | (4) |
|
8.5 Putting Theories to Work |
|
|
276 | (1) |
|
|
277 | (4) |
|
9 Statistical Inference in Psychological and Medical Research |
|
|
281 | (54) |
|
9.1 Psychological Measurement |
|
|
281 | (13) |
|
9.2 From Large-Sample to Small-Sample Theory in Psychology |
|
|
294 | (8) |
|
9.2.1 The Concept of Probability |
|
|
298 | (2) |
|
9.2.2 Significance Versus Confidence |
|
|
300 | (1) |
|
|
301 | (1) |
|
|
301 | (1) |
|
|
302 | (3) |
|
|
305 | (5) |
|
9.4.1 Contexts of Discovery Versus Verification |
|
|
305 | (4) |
|
9.4.2 Statistical Significance as an Indicator of Research Quality |
|
|
309 | (1) |
|
9.5 Problems in Application of Statistical Inference to Psychological Research |
|
|
310 | (11) |
|
9.5.1 Epistemic Versus Behavioral Orientation |
|
|
310 | (1) |
|
9.5.2 The Literalness of Acceptance |
|
|
311 | (1) |
|
9.5.3 The Individual Versus the Aggregate |
|
|
312 | (2) |
|
9.5.4 The Paradox of Precision |
|
|
314 | (2) |
|
9.5.5 Identification with the Null |
|
|
316 | (1) |
|
9.5.6 Random Sampling from Hypothetical Infinite Populations |
|
|
317 | (2) |
|
9.5.7 Assumption Violation |
|
|
319 | (2) |
|
9.5.8 The Impact of the Preceding Problems |
|
|
321 | (1) |
|
9.6 Possible Responses by Frequentists and Bayesians |
|
|
321 | (2) |
|
9.7 Toward Resolution: the Frequentists Versus the Bayesians |
|
|
323 | (3) |
|
9.8 The Recent Integration of Bayesian Concepts and Methods Into Psychological and Medical Research |
|
|
326 | (2) |
|
9.8.1 Hierarchical Models |
|
|
326 | (1) |
|
9.8.2 Multiple Imputation of Missing Data |
|
|
327 | (1) |
|
9.9 Postscript on Statistics in Medicine |
|
|
328 | (1) |
|
|
329 | (6) |
|
10 Recent Work in Probability and Inference |
|
|
335 | (58) |
|
10.1 Statistical and Nonstatistical Inference |
|
|
335 | (19) |
|
10.1.1 The Putative Philosophical Distinction |
|
|
335 | (4) |
|
10.1.2 Psychological Research on Reasoning in Statistical Contexts |
|
|
339 | (1) |
|
10.1.3 Models of Inference |
|
|
339 | (8) |
|
|
347 | (4) |
|
10.1.5 Randomness, Representativeness, and Replication in Psychological Research |
|
|
351 | (3) |
|
10.2 The Ontogenesis of Probability |
|
|
354 | (4) |
|
10.3 The Propensity Theory of Probability |
|
|
358 | (4) |
|
10.4 The Likelihood Theory of Statistical Inference |
|
|
362 | (3) |
|
10.5 Shafer's Theory of Belief Functions |
|
|
365 | (6) |
|
10.6 Recent Work on Reasoning in Philosophy and Artificial Intelligence |
|
|
371 | (8) |
|
10.6.1 Some Recent Concepts from Artificial Intelligence |
|
|
372 | (3) |
|
10.6.2 Bayesian versus Dempster-Shafer Formalisms |
|
|
375 | (4) |
|
|
379 | (6) |
|
|
379 | (2) |
|
10.7.2 The Relation Between Philosophy and Psychology: Bayesian Theory |
|
|
381 | (2) |
|
|
383 | (2) |
|
10.8 Summary of Challenges to Bayesian Theory |
|
|
385 | (1) |
|
10.9 Postscript on Bayesian Neuropsychology |
|
|
386 | (1) |
|
|
387 | (6) |
|
11 Conclusions and the Future of Psychological Research |
|
|
393 | (52) |
|
|
393 | (7) |
|
11.1.1 The Concept of Probability |
|
|
393 | (3) |
|
11.1.2 The Concept of Statistical Inference |
|
|
396 | (4) |
|
11.2 The Future of Psychological Research |
|
|
400 | (13) |
|
11.2.1 Surface Obstacles to Change |
|
|
400 | (5) |
|
11.2.2 Possible Paths for Quantitative Research |
|
|
405 | (3) |
|
11.2.3 The Ambivalent Promise of Qualitative Methods |
|
|
408 | (3) |
|
11.2.4 Toward Deeper Obstacles to Change |
|
|
411 | (2) |
|
11.3 The Philosophical, Social, and Psychological Context for the Emergence of a New Epistemology |
|
|
413 | (18) |
|
|
415 | (5) |
|
|
420 | (5) |
|
11.3.3 Objectivity, Skeuomorphosis, and the Problem of Scale |
|
|
425 | (4) |
|
11.3.4 The Scarecrows of Relativism and Anarchy |
|
|
429 | (2) |
|
11.4 Biomedical Research Without a Biomedical Model |
|
|
431 | (3) |
|
11.5 Postscript on Perceptual Control Theory |
|
|
434 | (3) |
|
|
437 | (8) |
Index |
|
445 | |