统计思想(英文版)

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内容简介: Utts和Heckard所著“Mind On Statistics”一书是理工科和管理、经济类专业的大学统计学的入门教科书。本书只要求学生具备高中数学知识就能阅读。作者力求使读者认识到统计学非常有用,且容易掌握, 因此用丰富、新鲜的例子说明统计学的概念、原则和运算程序,通过例子中的趣味性以及对以前学习知识的联想,使读者能牢记有关的统计学知识。本书内容包括数据的采集、整理、概括(抽样方法和描述性统计)、变量之间的相关关系、概率和随机变量、随机变量数字特征、点估计和区间估计、假设检验、回归分析和方差分析。分类数据的统计分析在本书中也占有重要位置和较大篇幅, 因而增强了实用性。从而也使本书成为一本全面、实用的统计学入门教科书。全书篇幅不很大,适合于大专院校理工科各专业、财经和管理类各专业的教学使用。该教材本身自成体系,不需要先学习概率论,也不必先学习微积分,本书对统计学的原则和概念叙述得相当清楚和准确。因此本书的出版将能填补国内这类教材的空白,也能使国内大学教学中所用的统计术语、软件等与国际接轨。


目录: CHAPTER 1 Statistics Success Stories and Cautionary Tales
1.1 What Is Statistics?
1.2 Seven Statistical Stories with Morals
1.3 The Common Elements in the Seven Stories
CHAPTER 2 Turning Data into Information
2.1 Raw Data
2.2 Types of Data
2.3 Summarizing One or Two Categorical Variables
2.4 Finding Information in Quantitative Data
2.5 Pictures for Quantitative Data
2.6 Numerical Summaries of Quantitative Variables
2.7 Bell-Shaped Distributions of Numbers
EHAPTER 3 Gathering Useful Data
3.1 Description or Decision? Using Data Wisely
3.2 Speaking the Language of Research Studies
3.3 Designing a Cood Experiment
3.4 Designing a Good Observational Study
3.5 Difficulties and Disasters in Experiments and
Observational Studies
CHAPTER 4 Sampling: Surveys and How To Ask Questions
4.1 The Beauty of Sampling
4.2 Sampling Methods
4.3 Difficulties and Disasters in Sampling
4.4 How to Ask Survey Questions
EHAPTER 5 Relationships Betwenn Quantitative Variables
5.1 Looking for Patterns with Scatterplots
5.2 Describing Linear Patterns with a Regression Line
5.3 Measuring Strength and Direction with Correlation
5.4 Why Answers May Not Make Sense
5.5 Correlation Does Not Prove Causation
CHAPTER 6 Relationships Betwreen Categorical Variables
6.1 Displaying Relationships Between Categorical Variables
6.2 Risk, Relative Risk, Odds Ratio, and Increased Risk
6.3 Misleading Statistics about Risk
6.4 The Effect of a Third Variable and Simpson's Paradox
6.5 Assessing the Statistical Significance of a 2x2 Table
EHAPTER 7 Probability
7.1 Random Circumstances
7.2 Interpretations of Probability
7.3 Probability Definitions and Relationships
7.4 Basic Rules for Finding Probabilities
7.5 Strategies for Finding Complicated Probabilities
7.6 Using Simulation to Estimate Probabilities
7.7 Coincidences and Intuitive Judgments
about Probability
CHAPTER 8 Random Variables
8.1 What is a Random Variable?
8.2 Discrete Random Variables
8.9 Expectations for Random Variables
8.4 Binomial Random Variables
8.5 Continuous Random Variables
8.6 Normal Random Variables
8.7 Approximating Binomial Distribution Probabilities
8.8 Sums, Differences, and Combinations of
Random Variables
CHAPTER 9 Means and Proportions as Random Variables
9.1 Understanding Dissimilarity among Samples
9.2 Sampling Distributions for Sample Proportions
9.3 What to Expect of Sample Means
9.4 What to Expect in Other Situations: Central
Limit Theorem
8.5 Sampling Distribution for Any Statistic
9.6 Standardized Statistics
9.7 Student's t-Distribution: Replacing with s
9.8 Statistical Inference
CHAPTER 10 Estimating Proportions with Confidence
10.1 The Language and Notation of Estimation
10.2 Margin of Error
10.3 Confidence Intervals
10.4 Calculating a Margin of Error for 95% Confidence
10.5 Ceneral Theory of Confidence Intervals for a
Proportion
10.6 Choosing a Sample Size for a Survey
10.7 Using Confidence Intervals to Guide Decisions
CHAPTER 11 Testing Hypotheses ahuut Proportions
11.1 Formulating Hypothesis Statements
11.2 The Logic of Hypothesis Testing: What if the Null
Is True?
11.3 Reaching a Conclusion about the
Two Hypotheses
11.4 Testing Hypotheses about a Proportion
11.5 The Role of Sample Size in Statistical Significance
11.6 Real Importance versus Statistical Significance
11.7 What Can Go Wrong: The Two Types of Errors
CHAPTER 12 More about Confidenee Intervals
12.1 Examples of Different Estimation Situations
12.2 Standard Errors
12.3 Approximate 95% Confidence Intervals
12.4 General Confidence Intervals for One Mean
or Paired Data
12.5 General Confidence Intervals for the Difference Between
Two Means (Independent Samples)
12.6 The Difference Between Two Proportions
(Independent Samples)
12.7 Understanding Any Confidence Interval
CHAPTER 13 More about Significance Tests
13.1 The General Ideas of Significance Testing
13.2 Testing Hypotheses about One Mean or
Paired Data
13.3 Testing the Difference Between Two Means
(Independent Samples)
13.4 Testing the Difference Between Two
Population Proportions
13.5 The Relationship Between Significance Tests and
Confidence Intervals
13.6 The Two Types of Errors and
Their Probabilities
13.7 Evaluating Significance in Research Reports
Summary of Chapter 13 Procedures
EHAPTER 14 More about Regression
14.1 Sample and Population Regression Models
14.2 Estimating the Standard Deviation
for Regression
14.3 Inference about the Linear Regression Relationship
14.4 Predicting the Value y for an Individual
14.5 Estimating the Mean y at a Specified x
14.6 Checking Conditions for Using Regression Models
for Inference
CHAPTER 15 More about Categorical Variables
15.1 The Chi-square Test for Two-Way Tables
15.2 Analyzing 2 x 2 Tables
15.3 Testing Hypotheses about One Categorical Variable:
Goodness 01 Fit
CHAPTER 16 Analysis of Varianee
16.1 Comparing Means with an ANOVA F-Test
16.2 Details of One-Way Analysis of Variance
16.3 Other Methods for Comparing Populations
16.4 Two-Way Analysis of Variance
CHAPTER 17 Turning Information into Wisdom
17.1 Beyond the Data
17.2 Transforming Uncertainty into Wisdom
17.3 Making Personal Decisions
17.4 Control of Societal Risks
17.5 Understanding Our World
17.6 Getting to Know You
17.7 Words to the Wise
Appendix of Tables
Answers to Selected Exercises
Index

前言: Before you continue, think about how you would answer the question in the first bullet, and read the statement in the second bullet. We will return to them a little later in this Preface.
* What do you really know is true, and how do you know it?
* The diameter of the moon is about 2160 miles.
Because people are curious about many things, chances are that your interests include topics to which the science of statistics has made a useful contribution. As written in Chapter 17, "information developed through the use of statistics has enhanced our understanding of how life works, helped us learn about each other, allowed control over some societal issues, and helped individuals make informed decisions. There is almost no area of knowledge that has not been advanced by statistical studies."
Statistical methods have contributed to our understanding of health, psychology, ecology, politics, music, lifestyle choices, and dozens of other topics.
A quick look through this book, especially Chapters I and 17, should convince you of this. Watch for the influences of statistics in your daily life as you learn this material.
Although statistics courses are often offered through mathematics departments, statistics is not a branch of mathematics. Mathematics is to statistics as wood, hammer, and nails are to a house: a partial set of materials and tools. In addition to mathematics. statistics also draws materials and tools from philosophy, graphics, computing, psychology, and language.
HOW IS THIS BOOK DIFFERENT?
TWO BASIC PREMISES OF LEARNING
We wrote this book because we were tired of being told that what statisticians do is boring and difficult. We think statistics is useful and not difficult to learn,and yet the majority of college graduates we've met seem to have had a negative experience with a statistics class in college. We hope this book will help to overcome these misguided stereotypes.
Let's return to the two bullets at the beginning of this Preface. Without looting, do you remember the diameter of the moon? Unless you already had a pretty good idea, or have an excellent memory for numbers, you probably don't remember. One premise of this book is that new material is much easier to learn and renember if it is related to eom ething interesting or previously known. The diameter of the moon is about the same as the air distance between Atlanta and Los Angeles, San Francisco and Chicago, London and Cairo, or Moscow and Madrid.Picture the moon sitting between any of those pairs of cities, and you are not likely to forget the size of the moon again. Throughout this book, new material is presented in the context of interesting and useful examples. The first and last chapters (I and 17) are exclusively devoted to examples and case studies, which illustrate the wisdom that can be generated through statistical studies.
Now answer the question asked in the first bullet: What do you really know is true, and how do you know it? If you're like most people, you know because it's something you have experienced or verified for yourself. It's not likely to be something you were told or heard in a lecture. The second premise of this book is that new material Is easier to learn if you actively ask questions and answer them for yourself. Mind On Statistics is designed to help you learn statistical ideas by actively thinking about them.
TOOLS FOR EXPANDED LEARNING
There are a number of tools provided in this book and beyond to enhance your learning of statistics.
The Instructor's Resource Manual contains the complete solutions to all exercises, lecture suggestions and guidelines, additional examples, and other helpful ideas for teaching the course.
The Student Solutions Manual includes the complete solutions to all the end-of-book answers and offers many helpful hints and suggestions.
ACKNOWLEDGMENTS
We thank William Harkness, Professor of Statistics at Pennsylvania State University, for continued support and feedback throughout our careers and during the writing of this book and for his remarkable dedication to undergraduate statistics education. At Penn State, David Hunter and Steve Arnold provided many helpful insights during spirited hallway discussions; psychology professor Melvin Mark provided useful information for the butterfly ballot example in Chapter 15i; and Kellie Karak3r helped format several preliminary versions, usually in the final minute before a print shop deadline. Preliminary editions of Mind On Statistics were used at Penn State, the University of California at Davis,and Texas A & M University, and we thank the many students who provided comments and suggestions. Thanks to Dr. Melvin Morse (Valley Children's Clinic and University of Washington) for suggesting the title for Chapter 17.The following reviewers offered valuable suggestions: Patti B. Collings,Brigham Young University; James Curl. Modesto Junior College; Donald Harden, Georgia State University; Rosemary Hirschfelder, University Sound;Sue Holt. Cabrillo Community College; Tom Johnson, North Carolina University; Andre Mack, Austin Community College; D'Arcy Mays, Virginia Commonwealth; Mary Murphy. Texas A & M University; N. Thomas Rogness, Grand Valley State University; Heather Sasinouska, Clemson University; and Robert Alan Wolf, University of San Francisco. Our sincere appreciation and gratitude goes to Carolyn Crockett and the Duxbury staff, without whom this book could not have been written. Finally, for their support, patience, and numerous prepared dinners. we thank our families and friends, especially Candace Heckard, Molly Heckard, Wes Johnson, Claudia Utts-Smith, and Dennis Smith.
Jessica Utts
Robert Heckard