APPLIED UNIVARIATE, BIVARIATE, AND MULTIVARIATE STATISTICS
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Module
STATISTICS
Institution
STATISTICS
Preface xix
About the Companion Website xxxiii
1 Preliminary Considerations 1
1.1
The Philosophical Bases of Knowledge: Rationalistic versus
Empiricist Pursuits, 1
1.2
What is a “Model”?, 4
1.3
Social Sciences versus Hard Sciences, 6
1.4
Is Complexity a Good Depiction of Reality? Are...
APPLIED UNIVARIATE,
BIVARIATE, AND
MULTIVARIATE
STATISTICS
DANIEL J. DENIS
,Copyright 2016 John Wiley & Sons, Inc.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
Library of Congress Cataloging-in-Publication Data:
Denis, Daniel J., 1974
Applied univariate, bivariate, and multivariate statistics / Daniel J. Denis.
pages cm
Includes bibliographical references and index.
ISBN 978-1-118-63233-8 (cloth)
1. Analysis of variance–Textbooks. 2. Multivariate analysis–Textbooks.
I. Title.
QA279.D4575 2016
519.5 ´3–dc23
2015016660
Printed in the United States of America
, CONTENTS
Preface xix
About the Companion Website xxxiii
1 Preliminary Considerations 1
1.1 The Philosophical Bases of Knowledge: Rationalistic versus
Empiricist Pursuits, 1
1.2 What is a “Model”?, 4
1.3 Social Sciences versus Hard Sciences, 6
1.4 Is Complexity a Good Depiction of Reality? Are Multivariate
Methods Useful?, 8
1.5 Causality, 9
1.6 The Nature of Mathematics: Mathematics as a Representation
of Concepts, 10
1.7 As a Social Scientist, How Much Mathematics Do You Need
to Know?, 11
1.8 Statistics and Relativity, 12
1.9 Experimental versus Statistical Control, 13
1.10 Statistical versus Physical Effects, 14
1.11 Understanding What “Applied Statistics” Means, 15
Review Exercises, 15
2 Mathematics and Probability Theory 18
2.1 Set Theory, 20
2.1.1 Operations on Sets, 22
, vi CONTENTS
2.1.2 Denoting Unions and Intersections of Many Sets, 23
2.1.3 Complement of a Set, 24
2.2 Cartesian Product A × B, 24
2.3 Sets of Numbers, 26
2.4 Set Theory Into Practice: Samples, Populations, and Probability, 27
2.5 Probability, 28
2.5.1 The Mathematical Theory of Probability, 29
2.5.2 Events, 29
2.5.3 The Axioms of Probability: And Some of Their Offspring, 30
2.5.4 Conditional Probability, 31
2.5.5 Mutually Exclusive versus Independent Events, 32
2.5.6 More on Mutual Exclusiveness, 34
2.6 Interpretations of Probability: Frequentist versus Subjective, 35
2.6.1 Law of Large Numbers, 36
2.6.2 Problem with the Law of Large Numbers, 37
2.6.3 The Subjective Interpretation of Probability, 37
2.7 Bayes’ Theorem: Inverting Conditional Probabilities, 39
2.7.1 Decomposing Bayes’ Theorem, 40
2.7.2 A Medical Example—Probability of HIV:
The Logic of Bayesian Revision, 41
2.7.3 Recap of Bayes’ Theorem: The Idea of Revising
Probability Estimates and Incorporating New Data, 42
2.7.4 The Consideration of Base Rates and Other Information:
Why Priors Are Important, 42
2.7.5 Conditional Probabilities and Temporal Ordering, 43
2.8 Statistical Inference, 44
2.8.1 Shouldn’t the Stakes Matter?, 45
2.9 Essential Mathematics: Precalculus, Calculus, and Algebra, 48
2.9.1 Polynomials, 48
2.9.2 Functions, 48
2.9.3 What is a Mathematical Function?, 49
2.9.4 Spotting Functions Graphically: The Vertical-Line Test, 50
2.9.5 Limits, 52
2.9.6 Why Limits? How Are Limits Useful?, 54
2.9.7 Asymptotes, 55
2.9.8 Continuity, 56
2.9.9 Why Does Continuity Matter? Leaping from Rationalism
to Empiricism, 58
2.9.10 Differential and Integral Calculus, 59
2.9.11 The Derivative as a Limit, 61
2.9.12 Derivative of a Linear Function, 62
2.9.13 Using Derivatives: Finding Minima and Maxima
of Functions, 63
2.9.14 The Integral, 64
2.9.15 Calculus in R, 65
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