Publisher:

Chapman & Hall/CRC

Number of Pages:

543

Price:

79.95

ISBN:

9781466512108

Date Received:

Monday, June 17, 2013

Reviewable:

Yes

Series:

Texts in Statistical Science

Publication Date:

2013

Format:

Hardcover

Audience:

Category:

Textbook

**Introduction: Probability, Statistics, and Science**

Reality, Nature, Science, and Models

Statistical Processes: Nature, Design and Measurement, and Data

Models

Deterministic Models

Variability

Parameters

Purely Probabilistic Statistical Models

Statistical Models with Both Deterministic and Probabilistic Components

Statistical Inference

Good and Bad Models

Uses of Probability Models

**Random Variables and Their Probability Distributions**

Introduction

Types of Random Variables: Nominal, Ordinal, and Continuous

Discrete Probability Distribution Functions

Continuous Probability Distribution Functions

Some Calculus–Derivatives and Least Squares

More Calculus–Integrals and Cumulative Distribution Functions

**Probability Calculation and Simulation**

Introduction

Analytic Calculations, Discrete and Continuous Cases

Simulation-Based Approximation

Generating Random Numbers

**Identifying Distributions**

Introduction

Identifying Distributions from Theory Alone

Using Data: Estimating Distributions via the Histogram

Quantiles: Theoretical and Data-Based Estimates

Using Data: Comparing Distributions via the Quantile–Quantile Plot

Effect of Randomness on Histograms and *q*–*q *Plots

**Conditional Distributions and Independence**

Introduction

Conditional Discrete Distributions

Estimating Conditional Discrete Distributions

Conditional Continuous Distributions

Estimating Conditional Continuous Distributions

Independence

**Marginal Distributions, Joint Distributions, Independence, and Bayes’ Theorem**

Introduction

Joint and Marginal Distributions

Estimating and Visualizing Joint Distributions

Conditional Distributions from Joint Distributions

Joint Distributions When Variables Are Independent

Bayes’ Theorem

**Sampling from Populations and Processes**

Introduction

Sampling from Populations

Critique of the Population Interpretation of Probability Models

The Process Model versus the Population Model

Independent and Identically Distributed Random Variables and Other Models

Checking the iid Assumption

**Expected Value and the Law of Large Numbers**

Introduction

Discrete Case

Continuous Case

Law of Large Numbers

Law of Large Numbers for the Bernoulli Distribution

Keeping the Terminology Straight: Mean, Average, Sample Mean, Sample Average, and Expected Value

Bootstrap Distribution and the Plug-In Principle

**Functions of Random Variables: Their Distributions and Expected Values**

Introduction

Distributions of Functions: The Discrete Case

Distributions of Functions: The Continuous Case

Expected Values of Functions and the Law of the Unconscious Statistician

Linearity and Additivity Properties

Nonlinear Functions and Jensen’s Inequality

Variance

Standard Deviation, Mean Absolute Deviation, and Chebyshev’s Inequality

Linearity Property of Variance

Skewness and Kurtosis

**Distributions of Totals**

Introduction

Additivity Property of Variance

Covariance and Correlation

Central Limit Theorem

**Estimation: Unbiasedness, Consistency, and Efficiency**

Introduction

Biased and Unbiased Estimators

Bias of the Plug-In Estimator of Variance

Removing the Bias of the Plug-In Estimator of Variance

The Joke Is on Us: The Standard Deviation Estimator Is Biased after All

Consistency of Estimators

Efficiency of Estimators

**Likelihood Function and Maximum Likelihood Estimates**

Introduction

Likelihood Function

Maximum Likelihood Estimates

Wald Standard Error

**Bayesian Statistics**

Introduction: Play a Game with Hans!

Prior Information and Posterior Knowledge

Case of the Unknown Survey

Bayesian Statistics: The Overview

Bayesian Analysis of the Bernoulli Parameter

Bayesian Analysis Using Simulation

What Good Is Bayes?

**Frequentist Statistical Methods**

Introduction

Large-Sample Approximate Frequentist Confidence Interval for the Process Mean

What Does *Approximate *Really Mean for an Interval Range?

Comparing the Bayesian and Frequentist Paradigms

**Are Your Results Explainable by Chance Alone?**

Introduction

What Does *by Chance Alone *Mean?

The *p*-Value

The Extremely Ugly "*pv *≤ 0.05" Rule of Thumb

**Chi-Squared, Student’s t, and F-Distributions, with Applications**

Introduction

Linearity and Additivity Properties of the Normal Distribution

Effect of Using an Estimate of

Chi-Squared Distribution

Frequentist Confidence Interval for

Student’s

Comparing Two Independent Samples Using a Confidence Interval

Comparing Two Independent Homoscedastic Normal Samples via Hypothesis Testing

**Likelihood Ratio Tests**

Introduction

Likelihood Ratio Method for Constructing Test Statistics

Evaluating the Statistical Significance of Likelihood Ratio Test Statistics

Likelihood Ratio Goodness-of-Fit Tests

Cross-Classification Frequency Tables and Tests of Independence

Comparing Non-Nested Models via the AIC Statistic

**Sample Size and Power**

Introduction

Choosing a Sample Size for a Prespecified Accuracy Margin

Power

Noncentral Distributions

Choosing a Sample Size for Prespecified Power

Post Hoc Power: A Useless Statistic

**Robustness and Nonparametric Methods**

Introduction

Nonparametric Tests Based on the Rank Transformation

Randomization Tests

Level and Power Robustness

Bootstrap Percentile-*t *Confidence Interval

**Final Words**

**Index**

Publish Book:

Modify Date:

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