Introduction

You get hit with an incredible amount of statistical information on a daily basis. You know what I'm talking about: charts, graphs, tables, and headlines that talk about the results of the latest poll, survey, experiment, or other scientific study. The purpose of this book is to develop and sharpen your skills in sorting through, analyzing, and evaluating all that info, and to do so in a clear, fun, and pain-free way. You also gain the ability to decipher and make important decisions about statistical results (for example, the results of the latest medical studies), while being ever aware of the ways that people can mislead you with statistics. And you see how to do it right when it's your turn to design the study, collect the data, crunch the numbers, and/or draw the conclusions.

This book is also designed to help those of you out there who are taking an introductory statistics class and can use some back-up. You'll gain a working knowledge of the big ideas of statistics and gather a boatload of tools and tricks of the trade that'll help you get ahead of the curve when you take your exams.

This book is chock-full of real examples from real sources that are relevant to your everyday life - from the latest medical breakthroughs, crime studies, and population trends to the latest U.S. government reports. I even address a survey on the worst cars of the millennium! By reading this book, you'll understand how to collect, display, and analyze data correctly and effectively, and you'll be ready to critically examine and make informed decisions about the latest polls, surveys, experiments, and reports that bombard you every day. You even find out how to use crickets to gauge temperature!

You also get to enjoy poking a little fun at statisticians (who take themselves too seriously at times). After all, with the right skills and knowledge, you don't have to be a statistician to understand introductory statistics.

About This Book

This book departs from traditional statistics texts, references, supplemental books, and study guides in the following ways:

• It includes practical and intuitive explanations of statistical concepts, ideas, techniques, formulas, and calculations found in an introductory statistics course.
• It shows you clear and concise step-by-step procedures that explain how you can intuitively work through statistics problems.
• It includes interesting real-world examples relating to your everyday life and workplace.
• It gives you upfront and honest answers to your questions like, "What does this really mean?" and "When and how will I ever use this?"

Conventions Used in This Book

You should be aware of three conventions as you make your way through this book:

• Definition of sample size (n): When I refer to the size of a sample, I mean the final number of individuals who participated in and provided information for the study. In other words, n stands for the size of the final data set.
• Dual-use of the word statistics: In some situations, I refer to statistics as a subject of study or as a field of research, so the word is a singular noun. For example, "Statistics is really quite an interesting subject." In other situations, I refer to statistics as the plural of statistic, in a numerical sense. For example, "The most common statistics are the mean and the standard deviation."
• Use of the word data: You're probably unaware of the debate raging amongst statisticians about whether the word data should be singular ("data is .") or plural ("data are ."). It got so bad that recently one group of statisticians had to develop two different versions of a statistics T-shirt: "Messy Data Happens" and "Messy Data Happen." At the risk of offending some of my colleagues, I go with the plural version of the word data in this book.
• Use of the term standard deviation: When I use the term standard deviation, I mean s, the sample standard deviation. (When I refer to the population standard deviation, I let you know.)

Here are a few other basic conventions to help you navigate this book:

• I use italics to let you know a new statistical term is appearing on the scene.
• If you see a boldfaced term or phrase in a bulleted list, it's been designated as a keyword or key phrase.
• Addresses for Web sites appear in monofont.

What You're Not to Read

I like to think that you won't skip anything in this book, but I also know you're a busy person. So to save time, feel free to skip anything marked with the Technical Stuff icon as well as text in sidebars (the shaded gray boxes that appear throughout the book). These items feature information that's interesting but not crucial to your basic knowledge of statistics.

Foolish Assumptions

I don't assume that you've had any previous experience with statistics, other than the fact that you're a member of the general public who gets bombarded every day with statistics in the form of numbers, percents, charts, graphs, "statistically significant" results, "scientific" studies, polls, surveys, experiments, and so on.

What I do assume is that you can do some of the basic mathematical operations and understand some of the basic notation used in algebra, such as the variables x and y, summation signs, taking the square root, squaring a number, and so on. If you need to brush up on your algebra skills, check out Algebra I For Dummies, 2nd Edition, by Mary Jane Sterling (Wiley).

I don't want to mislead you: You do encounter formulas in this book, because statistics does involve a bit of number crunching. But don't let that worry you. I take you slowly and carefully through each step of any calculations you need to do. I also provide examples for you to work along with this book, so that you can become familiar and comfortable with the calculations and make them your own.

How This Book Is Organized

This book is organized into five parts that explore the major areas of introductory statistics, along with a final part that offers some quick top-ten nuggets for your information and enjoyment. Each part contains chapters that break down each major area of statistics into understandable pieces.

Part 1: Vital Statistics about Statistics

This part helps you become aware of the quantity and quality of statistics you encounter in your workplace and your everyday life. You find out that a great deal of that statistical information is incorrect, either by accident or by design. You take a first step toward becoming statistically savvy by recognizing some of the tools of the trade, developing an overview of statistics as a process for getting and interpreting information, and getting up to speed on some statistical jargon.

Part 2: Number-Crunching Basics

This part helps you become more familiar and comfortable with making, interpreting, and evaluating data displays (otherwise known as charts, graphs, and so on) for different types of data. You also find out how to summarize and explore data by calculating and combining some commonly used statistics as well as some statistics you may not know about yet.

Part 3: Distributions and the Central Limit Theorem

In this part, you get into all the details of the three most common statistical distributions: the binomial distribution, the normal (and standard normal, also known as Z-distribution), and the t-distribution. You discover the characteristics of each distribution and how to find and interpret probabilities, percentiles, means, and standard deviations. You also find measures of relative standing (like percentiles).

Finally, you discover how statisticians measure variability from sample to sample and why a measure of precision in your sample results is so important. And you get the lowdown on what some statisticians describe as the "Crowning Jewel of all Statistics": the Central Limit Theorem (CLT). I don't use quite this level of flourishing language to describe the CLT; I just tell my students it's an MDR ("Mighty Deep Result"; coined by my PhD adviser). As for how my students describe their feelings about the CLT, I'll leave that to your imagination.

Part 4: Guesstimating and Hypothesizing with Confidence

This part focuses on the two methods for taking the results from a sample and generalizing them to make conclusions about an entire population. (Statisticians call this process statistical inference.) These two methods are confidence intervals and hypothesis tests.

In this part, you use confidence intervals to come up with good estimates for one or two population means or proportions, or for the difference between them (for example, the average number of hours teenagers spend watching TV per week or the percentage of men versus women in the United States who take arthritis medicine every day). You get the nitty-gritty on how confidence intervals are formed, interpreted, and evaluated for correctness and credibility. You explore the factors that influence the width of a...