Introduction to Statistics Through Resampling Methods and R/S-PLUS

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Format: Paperback
Pub. Date: 2005-07-13
Publisher(s): Wiley-Interscience
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Summary

Introduction to Statistics Through Resampling Methods and R/S-PLUS(r) aspires to introduce statistical methodology to a wide audience, simply, intuitively, and efficiently, through resampling from data at hand and by way of the computer programs R and S-PLUS. The objective of the book is to use quantitative methods to characterize, review, report on, test, estimate, and classify findings. Features include: * The R and S-PLUS¨ programming are used to illustrate the concepts and to aid the reader in completing the exercises. R may be downloaded, without charge, for use under Windows, UNIX, or the Macintosh. * One hundred or more exercises included in each chapter plus dozens of thought-provoking questions serve the needs of both classroom and self-study. The discovery method is utilized as often as possible, thereby forcing the conscientious reader to think her or his way to a solution rather than copy the answer or apply a formula straight out of the text * Chatty, informal, sometimes humorous writing style allows greater access to a variety of reader backgrounds and interests * Covers unusual topics such as tests and estimation procedures for one, two, and many samples; correlation; multivariable analysis; and complex experimental designs * Provides a web site free of charge to all end-users that includes all data sets and programs in the text

Author Biography

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 more than thirty scholarly works, more than 600 articles, and fourteen 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 from Wiley.

Table of Contents

Preface xi
1 Variation 1(28)
1.1 Variation
1(2)
1.2 Collecting Data
3(1)
1.3 Summarizing Your Data
4(3)
1.3.1 Learning to Use R
4(3)
1.4 Reporting Your Results
7(4)
1.4.1 Picturing Data
8(2)
1.4.2 Better Graphics
10(1)
1.5 Types of Data
11(1)
.5.1 Depicting Categorical Data
12(1)
1.6 Displaying Multiple Variables
12(2)
1.6.1 From Observations to Questions
14(1)
1.7 Measures of Location
14(7)
1.7.1 Which Measure of Location?
15(4)
1.7.2 The Bootstrap
19(2)
1.8 Samples and Populations
21(4)
1.8.1 Drawing a Random Sample
22(1)
1.8.2 Using R to Draw a Sample
23(2)
1.8.3 Ensuring the Sample Is Representative
25(1)
1.9 Variation-Within and Between
25(2)
1.10 Summary and Review
27(2)
2 Probability 29(23)
2.1 Probability
29(4)
2.1.1 Events and Outcomes
31(1)
2.1.2 Venn Diagrams
31(2)
2.2 Binomial
33(10)
2.2.1 Permutations and Rearrangements
35(3)
2.2.2 Back to the Binomial
38(1)
2.2.3 The Problem Jury
38(1)
2.2.4 Properties of the Binomial
39(4)
2.2.5 Multinomial
43(1)
2.3 Conditional Probability
43(4)
2.3.1 Market Basket Analysis
45(1)
2.3.2 Negative Results
46(1)
2.4 Independence
47(2)
2.5 Applications to Genetics
49(1)
2.6 Summary and Review
50(2)
3 Distributions 52(24)
3.1 Distribution of Values
52(3)
3.1.1 Cumulative Distribution Function
53(1)
3.1.2 Empirical Distribution Function
54(1)
3.2 Discrete Distributions
55(3)
3.3 Poisson: Events Rare in Time and Space
58(2)
3.3.1 Applying the Poisson
58(1)
3.3.2 Comparing Empirical and Theoretical Poisson Distributions
59(1)
3.4 Continuous Distributions
60(4)
3.4.1 The Exponential Distribution
61(1)
3.4.2 Normal Distribution
62(2)
3.4.3 Mixtures of Normal Distributions
64(1)
3.5 Properties of Independent Observations
64(2)
3.6 Testing a Hypothesis
66(5)
3.6.1 Analyzing the Experiment
67(2)
3.6.2 Two Types of Errors
69(2)
3.7 Estimating Effect Size
71(3)
3.7.1 Additional Applications
71(2)
3.7.2 Using Confidence Intervals to Test Hypotheses
73(1)
3.8 Summary and Review
74(2)
4 Testing Hypotheses 76(20)
4.1 One-Sample Problems
76(4)
4.1.1 Percentile Bootstrap
76(1)
4.1.2 Parametric Bootstrap
77(1)
4.1.3 Student's t
78(2)
4.2 Comparing Two Samples
80(7)
4.2.1 Comparing Two Poisson Distributions
80(1)
4.2.2 What Should We Measure?
80(1)
4.2.3 Permutation Monte Carlo
81(2)
4.2.4 One- versus Two-Sided Tests
83(1)
4.2.5 Bias-Corrected Nonparametric Bootstrap
83(3)
4.2.6 Two-Sample t-Test
86(1)
4.3 Which Test Should We Us?
87(7)
4.3.1 p-Values and Significance Levels
87(1)
4.3.2 Test Assumptions
88(1)
4.3.3 Robustness
89(1)
4.3.4 Power of a Test Procedure
90(2)
4.3.5 Testing for Correlation
92(2)
4.4 Summary and Review
94(2)
5 Designing an Experiment or Survey 96(33)
5.1 The Hawthorne Effect
97(3)
5.1.1 Crafting an Experiment
98(2)
5.2 Designing an Experiment or Survey
100(12)
5.2.1 Objectives
100(1)
5.2.2 Sample from the Right Population
101(2)
5.2.3 Coping with Variation
103(1)
5.2.4 Matched Pairs
104(1)
5.2.5 The Experimental Unit
105(1)
5.2.6 Formulate Your Hypotheses
106(1)
5.2.7 What Are You Going to Measure
107(1)
5.2.8 Random Representative Samples
108(1)
5.2.9 Treatment Allocation
109(1)
5.2.10 Choosing a Random Sample
110(1)
5.2.11 Ensuring Your Observations Are Independent
111(1)
5.3 How Large a Sample?
112(14)
5.3.1 Samples of Fixed Size
113(7)
Known Distribution
114(3)
Almost Normal Data
117(2)
Bootstrap
119(1)
5.3.2 Sequential Sampling
120(10)
Stein's Two-Stage Sampling Procedure
120(1)
Wald Sequential Sampling
121(5)
Adaptive Sampling
126(1)
5.4 Meta-analysis
126(1)
5.5 Summary and Review
126(3)
6 Analyzing Complex Experiments 129(26)
6.1 Changes Measured in Percentages
129(1)
6.2 Comparing More Than Two Samples
130(7)
6.2.1 Programming the Multisample Comparison in R
131(2)
6.2.2 Reusing Your R Functions
133(1)
6.2.3 What Is the Alternative?
133(1)
6.2.4 Testing for a Dose Response or Other Ordered Alternative
134(3)
6.3 Equalizing Variances
137(2)
6.4 Categorical Data
139(6)
6.4.1 One-Sided Fisher's Exact Test
142(1)
6.4.2 The Two-Sided Test
143(1)
6.4.3 Multinomial Tables
144(1)
6.5 Multivariate Analysis
145(9)
6.5.1 Manipulating Multivariate Data in R
146(1)
6.5.2 Pesarin-Fisher Omnibus Statistic
147(2)
6.5.3 Programming Guidelines
149(5)
6.6 Summary and Review
154(1)
7 Developing Models 155(37)
7.1 Models
155(3)
7.1.1 Why Build Models?
156(2)
7.1.2 Caveats
158(1)
7.2 Regression
158(3)
7.2.1 Linear Regression
160(1)
7.3 Fitting a Regression Equation
161(8)
7.3.1 Ordinary Least Squares
161(4)
Types of Data
165(1)
7.3.2 Least Absolute Deviation Regression
165(1)
7.3.3 Errors-in-Variables Regression
166(2)
7.3.4 Assumptions
168(1)
7.4 Problems with Regression
169(12)
7.4.1 Goodness of Fit Versus Prediction
170(1)
7.4.2 Which Model?
170(2)
Measures of Predictive Success
172(1)
7.4.3 Multivariable Regression
172(9)
7.5 Quantile Regression
181(2)
7.6 Validation
183(3)
7.6.1 Independent Verification
184(1)
7.6.2 Splitting the Sample
184(2)
7.6.3 Cross-validation with the Bootstrap
186(1)
7.7 Classification and Regression Trees (CART)
186(4)
7.8 Summary and Review
190(2)
8 Reporting Your Findings 192(16)
8.1 What to Report
193(3)
8.2 Text, Table, or Graph?
196(1)
8.3 Summarizing Your Results
197(5)
8.3.1 Center of the Distribution
199(2)
8.3.2 Dispersion
201(1)
8.4 Reporting Analysis Results
202(3)
8.4.1 p-Values or Confidence Intervals?
203(2)
8.5 Exceptions Are the Real Story
205(2)
8.5.1 Nonresponders
205(1)
8.5.2 The Missing Holes
205(1)
8.5.3 Missing Data
206(1)
8.5.4 Recognize and Report Biases
206(1)
8.6 Summary and Review
207(1)
9 Problem Solving 208(10)
9.1 The Problems
208(5)
9.2 Solving Practical Problems
213(5)
9.2.1 The Data's Provenance
213(1)
9.2.2 Inspect the Data
213(1)
9.2.3 Validate the Data Collection Methods
214(1)
9.2.4 Formulate Hypotheses
215(1)
9.2.5 Choosing a Statistical Methodology
215(1)
9.2.6 Be Aware of What You Don't Know
216(1)
9.2.7 Qualify Your Conclusions
216(2)
Appendix: S-PLUS 218(7)
Index to R Commands 225(2)
Index 227

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