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# Statistics For Dummies, 2nd Edition

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## Book Preface

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 confidence interval (such as sample size) and work through formulas, step-by-step calculations, and examples for the most commonly used confidence intervals.

The hypothesis tests in this part show you how to use your data to test someone’s claim about one or two population means or proportions, or the difference between them. (For example, a company claims their packages are delivered in two days on average — is this true?) You discover how researchers (should) go about forming and testing hypotheses and how you can evaluate their results for accuracy and credibility. You also get detailed step-by-step directions and examples for carrying out and interpreting the results of the most commonly used hypothesis tests.

### Part 5: Statistical Studies and the Hunt for a Meaningful Relationship

This part gives an overview of surveys, experiments, and observational studies. You find out what these studies do, how they are conducted, what their limitations are, and how to evaluate them to determine whether you should believe the results.

You also get all the details on how to examine pairs of numerical variables and categorical variables to look for relationships; this is the object of a great number of studies. For pairs of categorical variables, you create two-way tables and find joint, conditional, and marginal probabilities and distributions. You check for independence, and if a dependent relationship is found, you describe the nature of the relationship using probabilities. For numerical variables you create scatterplots, find and interpret correlation, perform regression analyses, study the fit of the regression line and the impact of outliers, describe the relationship using the slope, and use the line to make predictions. All in a day’s work!

### Part 6: The Part of Tens

This quick and easy part shares ten ways to be a statistically savvy sleuth and root out suspicious studies and results, as well as ten surefire ways to boost your statistics exam score.

Some statistical calculations involve the use of statistical tables, and I provide quick and easy access to all the tables you need for this book in the appendix. These tables are the Z-table (for the standard normal, also called the Z-distribution), the t-table (for the t-distribution), and the binomial table (for — you guessed it — the binomial distribution). Instructions and examples for using these three tables are provided in their corresponding sections of this book.