Elements of Statistics for the Life and Social Sciences

ISBN-13: 9781461291381 / Angielski / Miękka / 2011 / 190 str.

Braxton M. Alfred

Opis

This book was written to myself at about the time I began graduate studies in anthropology-the sort of thing a Samuel Beckett character might do. It is about the conduct of research. In a very real sense the purpose is partially to compensate for the inadequacies of my professors. Perhaps this is what education is about. The effort has not been an unqualified success, but it has been extremely gratifying. I was trained in anthropology. After completing the Ph. D. I went to Stanford on a post-doctoral fellowship. At the time, this was a novelty and the depart ment was not prepared for such a thing. To stay occupied I began attending lectures, seminars, and discussion groups in mathematics and statistics. This was about the luckiest choice I ever made. The excitement was easily as intense as that which I experienced upon encountering anthropology. On one oc casion I innocently and independently proved a theorem that had first been done 2000 years earlier. It is currently used as an exercise in high school mathematics so it is neither difficult nor arcane. Learning all this did not tarnish my sense of discovery. (On reflection I am puzzled by my failure to have seen all this "beauty" when I was exposed to it as an undergraduate. The unparalleled excellence of the Stanford program was undoubtedly responsible for my belated conversion."

Spis treści

1 Introduction.- 2 Some Elementary Principles of Deductive Argument.- 2.1 Common Connectives for Statements.- 2.1.1 Conjunction and Disjunction.- 2.1.2 The Conditional.- 2.2 Argument.- 2.2.1 Affirm the Antecedent.- 2.2.2 Deny the Consequent.- 2.2.3 Deny the Antecedent.- 2.2.4 Affirm the Consequent.- 2.2.5 Decomposition of Arguments.- 2.2.6 Paradox.- 2.2.7 Summary of Deductive Propositional Logic.- 3 The Logic of Scientific Argument.- 3.1 The Program of Science.- 3.2 Elements of a Good Test.- 3.2.1 The First Condition.- 3.2.2 The Second Condition.- 3.2.3 Failure to Satisfy Condition 2.- 3.3 Examples.- 3.3.1 Halley’s Comet.- 3.3.2 Mendelian Genetics.- 3.3.3 The Genetic Structure of Populations.- 3.3.4 Blood Pressure Change.- 3.3.5 Criminal Behavior Is a Mendelian System.- 3.3.6 Innate Principles of Geometry.- 3.3.7 Suicide as a Degenerative Disease.- 3.3.8 Kin Selection Theory and Mother’s Brother.- 3.3.9 Fraternal Polyandry in Tibet.- 3.4 Causation, Mill’s Methods.- 3.5 Description, Pre-Science, Science.- 3.6 Summary.- 4 Generating Predictions.- 4.1 Introduction and Orientation.- 4.2 Background.- 4.2.1 The Sample Description Space.- 4.2.2 Sampling.- 4.2.3 The Binomial Coefficient.- 4.2.4 Conditional Probability and Independence.- 4.2.5 Distributions.- 4.3 Processes.- 4.3.1 The Poisson Process.- 4.3.2 Markov Chains.- 4.3.3 Information and Markovian Dependence.- 4.3.4 Games with Strategic Uncertainty.- 5 Topics in Hypothesis Testing.- 5.1 Introduction.- 5.2 Testing a One-Dimensional Hypothesis.- 5.3 Testing a Two-Dimensional Hypothesis.- 5.3.1 The 2 x 2 Table.- 5.3.2 The 2 x C Table.- 5.3.3 The R x C Table.- 5.4 Tests of Hypotheses in Three or More Dimensions.- 5.4.1 The 2 x 2 x 2 Table.- 5.4.2 The 2 x 2 x 2 x 2 Table: Sickle-Cell Trait, Age, Sex, and City.- 5.5 Special Topics.- 5.5.1 Test of a Markovian Hypothesis.- 5.5.2 Test of a Causal Hypothesis.- 6 Summary and Conclusions.- Appendix A Matrix Manipulation.- Appendix B Conversion of the Base of Logarithms.- Appendix C Bayes’ Theorem.- Appendix D Table of Chi-Square Distribution, 5% Points.- Appendix E The Choice of Computing Software for Log Linear Models.- References.