Elements of Statistics for the Life and Social Sciencesby Braxton M. Alfred
Pub. Date: 08/28/1987
Publisher: Springer New York
This book is directed to advanced students who are encountering statistics without a background in either mathematics or the logic of science. The ultimate goal is to present the basic concepts and mechanics of hypothesis testing through examples from the journals. In order to avoid problems of measurements only counted data are used. The treatment opens with a… See more details below
This book is directed to advanced students who are encountering statistics without a background in either mathematics or the logic of science. The ultimate goal is to present the basic concepts and mechanics of hypothesis testing through examples from the journals. In order to avoid problems of measurements only counted data are used. The treatment opens with a summary of the logic of argument in order to establish a structure. Next, the problems of induction, the logic of induction and the logic of science are considered briefly. An overview of some concepts from probability theory and mathematical models of dynamic systems that have been useful in the generation of hypotheses follows. The book concludes with a description of the use of log-linear models of complex data structures.
Table of Contents1 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.
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