Introductory Statistics for Data Analysis

Preface
Contents
Part I Introduction
	1 Statistics and Probability Theory
		1.1 What is Statistics?
		1.2 The Relation Between Probability Theory and Statistics
		1.3 Problems
Part II Probability Theory
	2 Events
		2.1 What Are Events?
		2.2 Notation
		2.3 Derived Events: Complements, Unions and Intersections of Events
		2.4 Mutually Exclusive Events
		2.5 Problems
	3 Probabilities of Events
		3.1 Probabilities of Derived Events
		3.2 Independence of Two Events
		3.3 Conditional Probabilities
		3.4 Conditional Probabilities and Mutually Exclusive Events
		3.5 Conditional Probabilities and Independence
		Flowchart: Events
		3.6 Problems
	4 Probability: One Discrete Random Variable
		4.1 Random Variables
		4.2 Random Variables and Data
		4.3 The Probability Distribution of a Discrete Random Variable
		4.4 Parameters
		4.5 The Binomial Distribution
		4.6 The Hypergeometric Distribution
		4.7 The Mean of a Discrete Random Variable
		4.8 The Variance of a Discrete Random Variable
		Flowchart: Means and Variances of a Single Random Variable, X or P
		4.9 Problems
	5 Many Random Variables
		5.1 Introduction
		5.2 Notation
		5.3 Independently and Identically Distributed Random Variables
		5.4 The Mean and Variance of a Sum and of an Average
		5.5 The Mean and the Variance of a Difference
		5.6 The Proportion of Successes in n Binomial Trials
		Flowchart: Sums, Averages, and Differences of Random Variables
		5.7 Problems
	6 Continuous Random Variables
		6.1 Definition
		6.2 The Mean and Variance of a Continuous Random Variable
		6.3 The Normal Distribution
		6.4 The Standardization Procedure
		6.5 Numbers that Are Seen Often in Statistics
		6.6 Using the Normal Distribution Chart in Reverse
		6.7 Sums, Averages and Differences of Independent Normal Random Variables
		6.8 The Central Limit Theorem
		6.9 Approximating Discrete Random Variable Probabilities Using the Normal Distribution
			6.9.1 The Binomial Case
			6.9.2 The Die Example
		6.10 A Window Into Statistics
		Flowchart: Normal Random Variables and the CLT
		6.11 Problems
Part III Statistics
	7 Introduction
	8 Estimation of a Parameter
		8.1 Introduction
		8.2 Estimating the Binomial Parameter θ
			8.2.1 Properties of Estimates and Estimators
			8.2.2 The Precision of the Estimate of θ
		8.3 Estimating the Mean μ
			8.3.1 The Estimate of μ
			8.3.2 The Precision of the Estimate of μ
		8.4 Estimating the Difference Between Two Binomial Parameters θ1-θ2
			8.4.1 The Estimate of θ1 - θ2
			8.4.2 The Precision of the Estimate of θ1 - θ2
		8.5 Estimating the Difference Between Two Means μ1-μ2
			8.5.1 The Estimate of μ1 - μ2
			8.5.2 The Precision of the Estimate of μ1-μ2
		Flowchart: Estimation and Confidence Intervals
		8.6 Regression
		Flowchart: Linear Regression
		8.7 Problems
	9 Testing Hypotheses About the Value of a Parameter
		9.1 Introduction to Hypothesis Testing
		9.2 Two Approaches to Hypothesis Testing
			9.2.1 Both Approaches, Step 1
			9.2.2 Both Approaches, Step 2
			9.2.3 Both Approaches, Step 3
			9.2.4 Steps 4 and 5
			9.2.5 Approach 1, Step 4, the Medicine Example
			9.2.6 Approach 1, Step 5, the Medicine Example
			9.2.7 Approach 1, Step 4, the Coin Example
			9.2.8 Approach 1, Step 5, the Coin Example
			9.2.9 Approach 2 to Hypothesis Testing
			9.2.10 Approach 2, Step 4, the Medicine and the CoinExamples
			9.2.11 Approach 2, Step 5, the Medicine Example
			9.2.12 Approach 2, Step 5, the Coin Example
		9.3 The Hypothesis Testing Procedure and the Concepts of Deduction and Induction
		9.4 Power
		Flowchart: Hypothesis Testing and Power Calculations
		9.5 Problems
	10 Testing for the Equality of Two Binomial Parameters
		10.1 Two-by-Two Tables
		10.2 Simpson\'s Paradox and Fisher\'s Exact Test
		10.3 Notes on Two-by-Two Tables
		10.4 Two-Sided Two-by-Two Table Tests
		10.5 Problems
	11 Chi-Square Tests (i): Tables Bigger Than Two-by-Two
		11.1 Large Contingency Tables
		11.2 Problems
	12 Chi-Square Tests (ii): Testing for a Specified Probability Distribution
		12.1 Introduction
		12.2 Generalization
		12.3 A More Complicated Situation
		12.4 Problems
	13 Tests on Means
		13.1 The One-Sample t Test
		13.2 The Two-Sample t Test
		13.3 The Paired Two-Sample t Test
		13.4 t Tests in Regression
		13.5 General Notes on t Statistics
		13.6 Exact Confidence Intervals
		13.7 Problems
	14 Non-parametric Tests
		14.1 Introduction
		14.2 Non-parametric Alternative to the One-Sample t Test: The Wilcoxon Signed-Rank Test
		14.3 Non-parametric Alternative to the Two-Sample t Test: The Wilcoxon Rank-Sum Test
		14.4 Other Non-parametric Procedures
		14.5 Permutation Methods
			14.5.1 The Permutation Alternative to the Signed-Rank Test
			14.5.2 The Permutation Alternative to the Rank-Sum Test
		14.6 Problems
Useful Charts
Useful Charts
Solutions to Problems
Solutions to Problems
	Chapter 1
	Chapter 2
	Chapter 3
	Chapter 4
	Chapter 5
	Chapter 6
	Chapter 8
	Chapter 9
	Chapter 10
	Chapter 11
	Chapter 12
	Chapter 13
	Chapter 14
Index