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OpenIntro Statistics 3 edition
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We hope readers will take away three ideas from this book in addition to forming a foun- dation of statistical thinking and methods. (1) Statistics is an applied field with a wide range of practical applications. (2) You don’t have to be a math guru to learn from real, interesting data. (3) Data are messy, and statistical tools are imperfect. But, when you understand the strengths and weaknesses of these tools, you can use them to learn about the real world.
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OpenIntro Statistics
Third Edition
David M Diez
Quantitative Analyst
david@openintro.org
Christopher D Barr
Graduate Student
Yale School of Management
chris@openintro.org
Mine C¸ etinkaya-Rundel
Assistant Professor of the Practice
Department of Statistics
Duke University
mine@openintro.org
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If you’d like to buy the book, visit
openintro.org/os/amazon
For more resources, explore
openintro.org/os
Contents
1 Introduction to data 7
1.1 Case study: using stents to prevent strokes .................. 7
1.2 Data basics .................................... 9
1.3 Overview of data collection principles ..................... 15
1.4 Observational studies and sampling strategies ................. 19
1.5 Experiments .................................... 24
1.6 Examining numerical data ............................ 26
1.7 Considering categorical data ........................... 43
1.8 Case study: gender discrimination (special topic) ............... 50
1.9 Exercises ..................................... 55
2 Probability (special topic) 76
2.1 Defining probability (special topic) ....................... 76
2.2 Conditional probability (special topic) ..................... 88
2.3 Sampling from a small population (special topic) ............... 102
2.4 Random variables (special topic) ........................ 104
2.5 Continuous distributions (special topic) .................... 113
2.6 Exercises ..................................... 116
3 Distributions of random variables 127
3.1 Normal distribution ............................... 127
3.2 Evaluating the normal approximation ..................... 137
3.3 Geometric distribution (special topic) ..................... 141
3.4 Binomial distribution (special topic) ...................... 145
3.5 More discrete distributions (special topic) ................... 152
3.6 Exercises ..................................... 158
4 Foundations for inference 168
4.1 Variability in estimates .............................. 169
4.2 Confidence intervals ............................... 174
4.3 Hypothesis testing ................................ 180
4.4 Examining the Central Limit Theorem ..................... 194
4.5 Inference for other estimators .......................... 197
4.6 Exercises ..................................... 203
3
4 CONTENTS
5 Inference for numerical data 219
5.1 One-sample means with the t-distribution ................... 219
5.2 Paired data .................................... 228
5.3 Di↵erence of two means ............................. 230
5.4 Power calcul at i ons f or a di↵eren ce of means (special topic) .......... 239
5.5 Comparing many means with ANOVA (special topic) ............. 246
5.6 Exercises ..................................... 257
6 Inference for categorical data 274
6.1 Inference for a single proportion ......................... 274
6.2 Di↵erence of two proportions .......................... 280
6.3 Testing for good n ess of fit usi ng chi-square (special topic) .......... 286
6.4 Testing for i ndependence in two-way table s ( sp . topic) ............ 297
6.5 Small sample hypothesis testing for a proportion (special topic) ....... 302
6.6 Randomization test (special topic) ....................... 307
6.7 Exercises ..................................... 312
7 Introduction to linear regression 331
7.1 Line fitting, residuals, and correlation ..................... 333
7.2 Fitting a line by least squares regression .................... 340
7.3 Types of ou t li e rs in lin ear regression ...................... 349
7.4 Inference for linear regression .......................... 351
7.5 Exercises ..................................... 356
8 Multiple and logistic regression 372
8.1 Introduction to multiple regression ....................... 372
8.2 Model selection .................................. 378
8.3 Checking model assumptions using graphs ................... 382
8.4 Introduction to logistic regression ........................ 386
8.5 Exercises ..................................... 395
A End of chapter exercise solutions 405
B Distribu tion tables 427
B.1 Normal Probab i li ty Table ............................ 427
B.2 t-Probability Table ................................ 430
B.3 Chi-Square Probability Table .......................... 432
Preface
This book may be downloaded as a fre e PDF at openintro.org.
We hope readers will take away three ideas from this book in addi t i on to forming a f ou n-
dation of statistical thinking and methods.
(1) Statistics is an applied field wit h a wide range of practi cal app l ic at ion s.
(2) You don’t have to be a math guru to learn from real, interesting data.
(3) Data are messy, and statistical tools are imperfect. But, when you understand
the strengths and weak ne s ses of these tools, you can use them to learn about the
real world.
Textb ook overview
The chapters of t h is book are as foll ows:
1. Introduction to data. Data structur es , variables, summaries, graphics, and b asi c
data collection techniques.
2. Probability (special topic). The basic principles of probability. An understanding
of t hi s chapter is not re qu i r ed for the mai n content i n Chapt e rs 3-8.
3. Distributions of random variables. Introduction to the normal model and other
key distributions.
4. Foundations for inference. Gene r al ideas for statistical inference in the context of
estimating the population mean.
5. Inference for numerical data. Inference for one or two sample means using the
t-distribution, and also comparisons of many means using ANOVA.
6. Inference for categorical data. Inference for proporti ons using the normal and chi-
square distributions, as well as simulation and randomization techniques.
7. Introduction to linear regression. An introduction to regression with two variables.
Most of this chapter could be covered after Chapter 1.
8. Multiple and logistic regression. A light introduction to multiple regression and
logistic regression for an accelerated course.
OpenIntro Statistics was written to allow flexibility in choosing and ordering course
topics. Th e material is divided into two pieces: main text and special topics. The main
text has been structured to bring statistic al inference and modeling closer to the front of a
course. Special topics, labeled in the table of contents and in section titles , may be added
to a cour s e as they ari se natu r all y in t h e curr i cu lu m.
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