Introduction to Statistics Through Resampling Methods and R

PHILLIP I. GOOD, PhD, is Operations Manager of Information Research, a consulting firm specializing in statistical solutions for private and public organizations. He has published over thirty scholarly works, more than 600 articles, and forty-four books, including Common Errors in Statistics (and How to Avoid Them) and A Manager's Guide to the Design and Conduct of Clinical Trials, both published by Wiley.

Preface

1. Variation

1.1. Variation

1.2. Collecting Data

1.2.1 A worked through example

1.3. Summarizing Your Data

1.3.1 Learning to Use R

1.4. Reporting Your Results

1.4.1 Picturing Data

1.4.2. Better Graphics

1.5. Types of Data

1.5.1. Depicting Categorical Data

1.6. Displaying Multiple Variables

1.6.1. From Observations to Questions

1.7. Measures of Location

1.7.1. Which Measure of Location?

1.7.2 Estimating Precision

1.7.3. Estimating with the Bootstrap

1.8. Samples and Populations

1.8.1. Drawing a Random Sample

1.8.2. Ensuring the Sample is Representative

1.9. Summary and Review

2. Probability

2.1. Probability

2.1.1.Events and Outcomes

2.1.2 Venn Diagrams

2.2. Binomial Trials

2.2.1. Permutations and Rearrangements

2.2.2Programming Your Own Functions in R

2.2.3.Back to The Binomial

2.2. 4.    Problem Jury

2.3. Conditional Probability

2.3.1. Market Basket Analysis

2.3.2 Negative Results

2.4. Independence

2.5. Applications to Genetics

2.6. Summary and Review

3. Two Natural Distributions

Distribution of Values

1. Cumulative Distribution Function

2. Empirical Distribution Function                             

Discrete Distributions

Binomial Distribution

1. Properties of the Binomial

Variance and Standard Deviation

Events Rare in Time and Space

1. Applying the Poisson

2. Comparing Observed and Theoretical Distributions

3. Comparing Two Poisson Processes Continuous Distributions

1. Exponential Distribution

Summary and Review

4. Estimation and the Normal Distribution

Point Estimates

Properties of the Normal Distribution

Student's t

Mixtures of Normal Distributions

Using Confidence Intervals to Test Hypotheses

Should we have used the bootstrap

The Parametric Bootstrap

Properties of Independent Observations

Summary and Review

5. Testing Hypotheses

Analyzing an Experiment

Two Types of Errors

Estimating Effect Size

Using Confidence Intervals to Test Hypotheses

Applying the t-test to Measurements

One-sample Problem

Two-sample Problem

Paired Comparison

Permutation Monte Carlo

Which Test Should We Use

0. One-sided vs. Two-sided

1. p-values and Significance Levels

2. Test Assumptions

3. Robustness

4. Power of a Test Procedure

Summary and Review

6. Designing an Experiment or Survey

The Hawthorne Effect

Crafting an experiment.

Designing an Experiment or Survey

Objectives

Sample from the right population

Coping with variation

Matched pairs

Experimental unit

Formulate your hypotheses

What are you going to measure?

Random, representative samples

Treatment allocation

Choosing a random sample

Ensuring your observations are independent

How Large a Sample

Samples of fixed size

Known distribution

Almost normal data

Bootstrap

Sequential Sampling

Adaptive sampling

Meta-Analysis

Summary and Review

7. Guide to Entering, Saving, and Retrieving Large Quantities of Data Using R

Creating and Editing a Data File

Saving and Retrieving a Data File

Retrieving and Using Data Created by Other Programs

Example: Using R to Draw a Random Sample

8. Analyzing Complex Experiments

A. Changes Measured in Percentages

B. Comparing More Than Two Samples

1. Programming the Multi-sample Comparison in R

2. Reusing Your R Functions

3. What Is the Alternative?

4. Testing for a Dose Response or Other Ordered Alternative

C. Equalizing Variances

D. Categorical Data

a. One-Sided Fisher's Exact Test

b. The Two-Sided Test

c. Testing for Goodness of Fit

d. Multnomial Tables

E. Multivariate Analysis

Manipulating Multivariate Data in R

Hotelling's Statistic

Pesarin-Fisher Omnibus Statistic

F.  R Programming Guidelines

G. Summary and Review

9. Developing Models

Why Build Models?

Caveats

Classification and Regression Tree

1. How Trees are Grown

2. Examples

3. Incorporating existing knowledge

a) Prior probabilities

b) Misclassification costs

Regression

1. Linear Regression

2. Nonlinear Regression

3. Survival Analysis

Fitting a Regression Equation

a. Ordinary least squares

b. Least absolute deviation

c. Errors in both variables

d. Assumptions

Problems with Regression

a. Goodness-of-fit versus prediction

b. Which model?

Multiple Regression

Quantile Regression

Validation

a. Independent validation

b. Splitting the sample

c. Cross-validation with the bootstrap

Summary and Review

10. Reporting Your Findings

What to Report

Text, Table, or Graph?

R Graphic Packages

Summarizing Your Results

a. Center of the distribution

b. Dispersion

Reporting Analysis Results

a. p-Values or Confidence Intervals?

Exceptions Are the Real Story

n. Non-Responders

o. The Missing Holes

p. Missing Data

q. Recognize and Report Bias

Summary and Review

11. Problem Solving

Real Life Problems

Solving Practical Problems

a. Data Provenance

b. Inspect the Data

c. Validate Data Collection Methods

d. Formulate Hypotheses

Choose a Statistical Methodology

Be Aware of What You Don't Know

Qualify Your Conclusions

Answers to Selected Exercises

Subject Index

Index to R Functions

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