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E-grāmata: Myth of Statistical Inference

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  • Izdošanas datums: 05-Jul-2021
  • Izdevniecība: Springer Nature Switzerland AG
  • Valoda: eng
  • ISBN-13: 9783030732578
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  • Formāts: EPUB+DRM
  • Izdošanas datums: 05-Jul-2021
  • Izdevniecība: Springer Nature Switzerland AG
  • Valoda: eng
  • ISBN-13: 9783030732578
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This book proposes the claim that the forced union of the aleatory and epistemic aspects of probability is a sterile hybrid, inspired and nourished for 300 years by a false hope of formalizing inductive reasoning, making uncertainty the object of precise calculation.  Because this is not really a possible goal, statistical inference is not, cannot be, doing for us today what we imagine it is doing for us.  It is for these reasons that statistical inference can be characterized as a myth.

The book is aimed primarily at social scientists, for whom statistics and statistical inference are a common concern and frustration. Because the historical development given here is not merely anecdotal, but makes clear the guiding ideas and ambitions that motivated the formulation of particular methods, this book offers an understanding of statistical inference which has not hitherto been available. It will also serve as a supplement to the standard statistics texts. Finally, general readers will find here an interesting study with implications far beyond statistics.  The development of statistical inference, to its present position of prominence in the social sciences, epitomizes a number of trends in Western intellectual history of the last three centuries, and the 11th chapter, considering the function of statistical inference in light of our needs for structure, rules, authority, and consensus in general, develops some provocative parallels, especially between epistemology and politics.

 

Recenzijas

The myth of statistical inference has achieved a power arguably to rival that of any other myth in this Century . the entire edifice and provide a step-by-step refutation of the theory and practice of statistical inference, with special emphasis on psychology. The author is surprised that no one wrote just such a book during the 50 years that he has been working on it. (Victor V. Pambuccian, zbMATH 1532.62001, 2024)

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)
References
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)
2.1.1 Ancient Greece
35(2)
2.1.2 Medieval Europe
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)
2.3.3 Causality
51(4)
2.3.4 Representation
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)
2.5 Summary and Preview
72(1)
References
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)
3.4 Statistics
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)
References
114(3)
4 The Classical Theory of Statistical Inference
117(14)
4.1 Bayes
118(6)
4.2 Laplace
124(2)
4.3 Criticism
126(3)
References
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)
References
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)
6.2.1 Venn
165(1)
6.2.2 Peirce
166(2)
6.2.3 Richard von Mises
168(4)
6.2.4 Reichenbach
172(4)
6.2.5 Popper
176(2)
6.3 The Concept of Randomness
178(5)
6.4 Summary
183(1)
References
184(3)
7 The Fisher and Neyman-Pearson Theories of Statistical Inference
187(50)
7.1 Fisher
187(4)
7.2 The Fisherian Theory of Statistical Inference
191(18)
7.2.1 Maximum Likelihood
192(2)
7.2.2 Significance Testing
194(9)
7.2.3 Fiducial Probability
203(6)
7.3 Neyman and Pearson
209(17)
7.3.1 Hypothesis Testing
211(11)
7.3.2 Confidence Intervals
222(4)
7.4 Differences Between the Fisher and Neyman-Pearson Theories
226(5)
References
231(6)
8 Bayesian Theories of Probability and Statistical Inference
237(44)
8.1 Logical Theories of Probability
238(12)
8.1.1 Keynes
238(6)
8.1.2 Jeffreys
244(4)
8.1.3 Jaynes
248(2)
8.2 Personalist Theories of Probability
250(10)
8.2.1 Ramsey
251(2)
8.2.2 De Finetti
253(3)
8.2.3 Savage
256(2)
8.2.4 Wald's Decision Theory
258(2)
8.3 General Structure of Bayesian Inference
260(6)
8.4 Criticism
266(10)
8.4.1 The Logical Allocation of Prior Probabilities
266(3)
8.4.2 The Subjective Allocation of Prior Probabilities
269(3)
8.4.3 Subjectivity
272(4)
8.5 Putting Theories to Work
276(1)
References
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)
9.2.3 Power
301(1)
9.2.4 Random Sampling
301(1)
9.3 To the Present
302(3)
9.4 The Context of Use
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)
References
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)
10.1.4 General Issues
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)
10.7 On Formalization
379(6)
10.7.1 Limits
379(2)
10.7.2 The Relation Between Philosophy and Psychology: Bayesian Theory
381(2)
10.7.3 Purposes
383(2)
10.8 Summary of Challenges to Bayesian Theory
385(1)
10.9 Postscript on Bayesian Neuropsychology
386(1)
References
387(6)
11 Conclusions and the Future of Psychological Research
393(52)
11.1 Conclusions
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)
11.3.1 Empty Self
415(5)
11.3.2 Empty World
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)
References
437(8)
Index 445
Michael C. Acree received his Ph.D. in psychology from Clark University in 1978, where he completed the clinical training program and also worked as Data Analysis Consultant for the Department of Psychology.  At the University of NebraskaLincoln he was the first member of the psychology faculty to be elected to all three programsExperimental, Social, and Clinical.  During his 3 years there, he taught undergraduate courses in clinical and abnormal psychology and graduate statistics and supervised clinical practicum students.  After leaving Nebraska voluntarily in 1979, he was for 5 years Assistant Research Psychologist at the Center on Deafness at the University of California, San Francisco.  There he conducted long-term longitudinal research on prelingually deaf children, and was Principal Investigator on a $75,000 grant from the National Institute of Handicapped Research, entitled Dialogue with Deaf Children: Its Relation to Intellectual and Personal Growth.  From 1985 to 1990 he was Assistant Professor at the Pacific Graduate School of Psychology in Palo Alto, where he was awarded a $28,000 grant by the Chapman Research Fund on Roots of Social Science Methodology: Ontogenesis and History.  After 5 years as Associate Professor at the California Institute for Integral Studies in San Francisco, he joined the UCSF Center for AIDS Prevention Studies as Senior Statistician, and in 2001 he moved in the same capacity to the Osher Center for Integrative Medicine, until his retirement in 2017.