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 your algebra skills, check out
Algebra For Dummies
by Mary Jane Sterling (Wiley Publishing, Inc.).
Keep in mind, however, that statistics is really quite different from math. Statistics is much more about the scientific method than anything else, determining research questions; designing studies and experiments; collecting data; organizing, summarizing, and analyzing the data; interpreting results; and drawing conclusions. In a nutshell, you're using data as evidence to answer interesting questions about the world. Math comes into play only in terms of calculating summary statistics and performing some of the analyses, but that's just a tiny part of what statistics is really about.
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.
This book is organized into seven major parts that explore the main objectives of this book, along with a final part that offers quick top-ten references for you to use. Each part contains chapters that break down each major objective into understandable pieces.
This part helps you become aware of the quantity and quality of statistics you encounter every day, in your workplace and in the rest of your life. You also find out that a great deal of that statistical information is incorrect, either by accident or by design. You also 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.
This part helps you become more familiar and comfortable with
data displays
(otherwise known as charts, graphs, and so on). It also gives you tips on interpreting these charts and graphs, as well as spotting a misleading graph right off the bat. You also find out how to summarize data by using some of the more common statistics.
This part uncovers the basics of probability: how you use it, what you need to know, and what you're up against when playing games of chance. The bottom line? Probability and intuition don't always mix!
You find out how probability factors into your daily life and get to know some basic rules of probability. You also get the lowdown on gambling: how casinos work and why the house always expects to win in the long run.
In this part, you understand the underpinnings that make statistics work, including sampling distributions, accuracy, margin of error, percentiles, and standard scores. You understand how to calculate and interpret two measures of relative standing: standard scores and percentiles. You also get the lowdown on what statisticians describe as the "crown jewel of all statistics" (the central limit theorem) and how much more easily you can interpret statistics because of it. Finally, you begin to understand how statisticians measure variability from sample to sample, and why that's so important.
In this part, you also find out exactly what that commonly used term — margin of error — means.
This part focuses on how you can make a good estimate for a population average or proportion when you don't know what it is. (For example, the average number of hours adults spend watching TV per week or the percentage of people in the United States who have at least one bumper sticker on their cars.) You also find out how you can make a pretty good estimate with a relatively small sample (compared to the population size). You get a general look at confidence intervals, find out what you use them for, understand how they're formed, and get the lowdown on the basic elements of a confidence interval (an estimate plus or minus a margin of error). You also explore the factors that influence the size of a confidence interval (such as sample size) and discover formulas, step-by-step calculations, and examples for the most commonly used confidence intervals.
This part is about the decision-making process and the huge role that statistics plays in it. It shows you how researchers (should) go about forming and testing their claims, and how you can evaluate their results to be sure that they did the statistics right and have credible conclusions. You also review step-by-step directions for carrying out the calculations for commonly used hypothesis tests and for interpreting the results properly.
This part gives an overview of surveys, experiments, observational studies, and quality-control processes. 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.
This quick and easy part shares ten criteria for a good survey and ten common ways that statistics are misused and abused by researchers, the media, and the public.
One of the main goals of this book is to motivate and empower you to be a statistical detective, digging deeper to find the real information you need to make informed decisions about statistics that you encounter. The
appendix
contains all of the sources that I use in my examples throughout this book, in case you want to follow up on any of them.
Icons are used in this book to draw your attention to certain features that occur on a regular basis. Here's what they mean:
| Tip | This icon refers to helpful hints, ideas, or shortcuts that you can use to save time. It also highlights alternative ways to think about a particular concept. |
| REMEMBER | This icon is reserved for particular ideas that I hope you'll remember long after you read this book. |
| HEADS UP | This icon refers to specific ways that researchers or the media can mislead you with statistics and tells you what you can do about it. |
| TECHNICAL STUFF | This icon is a sure bet if you have a special interest in understanding the more technical aspects of statistical issues. You can skip this icon if you don't want to get into the gory details. |
This book is written in such a way that you can start anywhere and still be able to understand what's going on. So take a peek at the Table of Contents or the Index, look up the information that interests you, and flip to the page listed.
Or, if you aren't sure where you want to start, consider starting with
Chapter 1
and reading your way straight through the book.
When you turn on the TV or open a newspaper, you're bombarded with numbers, charts, graphs, and statistical results. From today's poll to the latest major medical breakthroughs, the numbers just keep coming. Yet much of the statistical information you're asked to consume is actually wrong by accident — or even by design. How is a person to know what to believe? By doing a lot of good detective work.
This part helps awaken the statistical sleuth that lies within you by exploring how statistics affect your everyday life and your job, how bad much of the information out there really is, and what you can do about it. This part also helps you get up to speed with some useful statistical jargon.
Today's society is completely taken over by numbers. Numbers appear everywhere you look, from billboards telling of the latest abortion statistics, to sports shows discussing the Las Vegas odds for the upcoming football game to the evening news, with stories focusing on crime rates, the expected life span of someone who eats junk food, and the president's approval rating. On a normal day, you can run into five, ten, or even twenty different statistics (with even more on Election Night). Just by reading a Sunday newspaper all the way through, you come across literally hundreds of statistics in reports, advertisements, and articles covering everything from soup (how much does an average person consume per year?) to nuts (how many nuts do you have to eat to increase your IQ?).
The purpose of this chapter is to show you how often statistics appear in your life and work and how statistics are presented to the general public. After reading this chapter, you begin to see just how often the media hits you with numbers and how important it is to be able to unravel what all those numbers mean. Because, like it or not, statistics are a big part of your life. So, if you can't beat 'em, and you don't want to join 'em, you should at least try to understand 'em.
Open a newspaper and start looking for examples of articles and stories involving numbers. It doesn't take long before numbers begin to pile up. Readers are inundated with results of studies, announcements of breakthroughs, statistical reports, forecasts, projections, charts, graphs, and summaries. The extent to which statistics occur in the media is mind-boggling. You may not even be aware of how many times you're hit with numbers in
today's information age. Here are just a few examples from one Sunday paper's worth of news. While you're reading this, you may find yourself getting nervous, wondering what you can and can't believe anymore. Relax! That's what this book is for, helping you sort out the good from the bad information. (
Chapters 2
through
5
give you a great start.)
The first article I come across that deals with numbers is entitled, "Popcorn plant faces health probe." The subheading reads "Sick workers say flavoring chemicals caused lung problems." The article describes how the Centers for Disease Control (CDC) is expressing concern about a possible link between exposure to chemicals in microwave popcorn flavorings and some cases of fixed obstructive lung disease. Eight people from one popcorn plant alone contracted this lung disease, and four of them were awaiting lung transplants. According to the article, similar cases were reported at other popcorn factories. Now, you may be asking, "What about the folks who eat microwave popcorn?" According to the article, the CDC finds "no reason to believe that people who eat microwave popcorn have anything to fear." (Stay tuned.) They say that their next step is to evaluate employees more in-depth, including surveys to determine health and possible exposures to the said chemicals, checks of lung capacity, and detailed air samples. The question here is: How many cases of this lung disease constitute a real pattern, compared to mere chance or a statistical anomaly? (More about this in
Chapter 14
.)
The second article I find discusses the most recent cyber attack — a worm-like virus that has made its way through the Internet, slowing down Web browsing and e-mail delivery across the world. How many computers were affected? The experts quoted in the article say that 39,000 computers were infected, affecting hundreds of thousands of other systems. How did they get that number? Wouldn't that be a hard number to get hold of? Did they check each computer out there to see whether it was affected? The fact that this article was written less than 24 hours after the attack would suggest that this number is a guess. Then why say 39,000 and not 40,000? To find out more on how to guesstimate with confidence (and how to evaluate someone else's numbers) see
Chapter 11
.
Next in the paper appears an alert about the soaring number of motorcycle fatalities. Experts say that these fatalities are up more than 50% since 1997, and no one can figure out why. The statistics tell an interesting story. In 1997,
2,116 motorcyclists were killed; in 2001, the number was 3,181, as reported by the National Highway Traffic Safety Administration (NHTSA). In the article, many possible causes for the increased motorcycle death rate are discussed, including the fact that riders today tend to be older (the average age of motorcyclists killed in crashes increased from 29.3 years in 1990 to 36.3 years in 2001).
Bigger bikes are listed as another possibility. The engine size of an average motorcycle has increased almost 25% — from 769 cubic centimeters in 1990 to 959 cubic centimeters in 2001. Another possibility may be that some states are weakening their helmet laws. The experts quoted in the article say that a more comprehensive causation study is needed, but such a study probably won't be done because it would cost between 2 and 3 million dollars. One issue that is not addressed in the article is the number of people riding motorcycles in 2001, compared to the number of riders in1997. More people on the roads generally means more fatalities, if all the other factors remain the same. However, along with the article is a graph showing motorcycle deaths per 100 million vehicle miles traveled in the United States from 1997 to 2001; does that address the issue of more people on the roads? A bar graph is also included, comparing motorcycle deaths to deaths that occurred in other types of vehicles. This bar graphs shows that motorcycle deaths occur at a rate of 34.4 deaths per 100 million vehicle miles traveled, compared to just 1.7 deaths for the same number of miles traveled in cars. This article has lots of numbers and statistics, but what does it all mean? The number and types of statistics can quickly get confusing.
Chapter 4
helps you sort out graphs and charts and the statistics that go along with them.
Further along in the newspaper is a report about a recent medical malpractice insurance study, which may affect you in terms of the fees your doctor charges and your ability to get the health care you need. So what's the extent of the problem? The article indicates that 1 in 5 Georgia doctors has stopped doing risky procedures (like delivering babies) because of the ever-increasing malpractice insurance rates in the state. This is described as a "national epidemic" and a "health crisis" around the country. Some brief details of the study are included, and the article states that of the 2,200 Georgia doctors surveyed, 2,800 of them — which they say represents about 18% of those sampled — were expected to stop providing high risk procedures. Wait a minute! Can that be right? Out of 2,200 doctors, 2,800 don't perform the procedures, and that is supposed to represent 18%? That's impossible! You can't have a bigger number on the top of a fraction, and still have the fraction be under 100%, right? This is one of many examples of errors in statistics that are reported in the media. So what's the real percentage? You can only guess.
Chapter 5
nails down the particulars of calculating statistics, so that you can know what to look for and immediately tell when something's not right.
In the same Sunday paper is an article about the extent of land development and speculation across the country. Given the number of homes likely being built in your neck of the woods, this is an important issue to get a handle on. Statistics are given regarding the number of acres of farmland that are being lost to development each year and also translates those acres to square miles. To further illustrate how much land is being lost, the area is also listed in terms of the number of football fields. In this particular example, experts say that the mid-Ohio area is losing 150,000 acres per year, which is 234 square miles, or 115,385 football fields (including end zones). How do people come up with these numbers, and how accurate are they? And does it help to visualize land loss in terms of the corresponding number of football fields?
The next topic in the paper is school proficiency, specifically whether extra school sessions are helping students perform better. The article states that 81.3% of students in this particular district who attended extra sessions passed the writing proficiency test, while only 71.7% of those who didn't participate in the extra school sessions passed the proficiency test. But is this enough of a difference to account for the $386,000 price tag per year? And what's happening in these sessions to account for an improvement? Are students in these sessions spending more time just preparing for those exams, rather than learning more about writing in general? And here's the big question: Were those who participated in these extra sessions student volunteers who may be more motivated than the average student to try to improve their test scores? No one knows. Studies like this are going on all the time, and the only way to know what to believe is to understand what questions to ask, and to be able to critique the quality of the study. That's all part of statistics! The good news is, with a few clarifying questions, you can quickly critique statistical studies and their results.
Chapter 17
helps you to do just that.
| Tip | Trying to win the big one Do you ever imagine winning the Super Lotto, a 1 in 89 million chance, on average? Don't hold your breath! To put 1 in 89 million into perspective, imagine 89 million lottery tickets in one giant pile, with yours among them somewhere. Suppose I said that you have one chance to reach into the pile and pull out your own ticket — do you think you could do it? That is the same as your chance of winning one of those big lotteries. But with a bit of insider information, you can increase your jackpot if you do win. (I'd like a cut of your winnings if this turns out to work for you.) For more information on this and other gambling tips, see |
| REMEMBER | Studying surveys of all shapes and sizes Surveys and polls are probably the biggest vehicle used by today's media to grab your attention. It seems that everyone wants to do a survey, including market managers, insurance companies, TV stations, community groups, and even students in high-school classes. Here are just a few examples of survey results that are part of today's news. With the aging of the American work force, companies are planning for their future leadership. (How do they know that the American workforce is aging, and if it is, by how much is it aging?) A recent survey shows that nearly 67% of human resources managers polled said that planning for succession had become more important in the past five years than it had been in the past. Now if you're thinking you want to quit your day job and apply to be a CEO, hold on. The survey also says that 88% of the 210 respondents said they usually or often fill senior positions with internal candidates. (But how many managers did Some surveys are based on lighter fare. For example, which device do Americans find most crucial today, their toothbrushes, bread machines, computers, cars, or cellphones? In a survey of 1,042 adults and 400 teens (how did they decide on those numbers?) 42% of adults and 34% of teens ranked the toothbrush as more important to them than cars, computers, or cellphones. Is this really big news? Since when should something as critical to daily hygiene as a toothbrush be lumped in with cellphones and bread machines? (The car came in second. But did you really need a survey to tell you that?) For more information on surveys, see |
The sports section is probably the most numerically jam-packed section of the newspaper. Besides the scores of the last game, the win/lose percentages for each team in the league, and the relative standing for each team, the specialized statistics reported in the sports world are so thick that they require wading boots to get through. For example, the basketball statistics are broken down by team, by quarter, and even by player. And you need to be a basketball junkie to interpret all of this, because everything is abbreviated (with no legend provided if you're out of the loop):
MIN: Minutes played
FG: Field goals
FT: Free throws
RB: Rebounds
A: Assists
PF: Personal fouls
TO: Turnovers
B: Blocks
S: Steals
TP: Total points
Who needs to know this, besides the players' mothers? Statistics are something that sports fans can never get enough of and that players can't stand to hear about. Stats are the substance of water-cooler debates and the fuel for armchair quarterbacks around the world.
In the business section of the newspaper, you find statistics about the stock market. It was a bad week last week, with the stock market going down 455 points; is that decrease a lot or a little? You need to calculate a percentage to really get a handle on that. In the same business section, you also find reports on the highest yields nationwide on every kind of CD imaginable. (By the way, how do they know they're the highest?) You also see reports about loan rates: rates on 30-year fixed loans, 15-year fixed loans, 1-year adjustable rate loans, new car loans, used car loans, home equity loans, and loans from your grandmother (well actually no, but if grandma knew how to read these statistics, she may consider increasing the cushy rates she lets you have on her money!). Finally, you see numerous ads for those beloved credit cards — ads listing the interest rates, the annual fees, and the number of days in the billing cycle for the credit cards. How do you compare all of the information about investments, loans, and credit cards in order to make a good decision? What statistics are most important? The real question is, are the numbers reported in the paper giving the whole story, or do you need to do more detective work to get at the truth?
Chapter 3
helps you start tearing apart these numbers and making decisions about them.
You can't even escape the barrage of numbers by escaping to the travel section. In that section, I find that the most frequently asked question coming in to the Transportation Security Administration's response center (which receives about 2,000 telephone calls, 2,500 e-mail messages, and 200 letters per week on average — would you want to be the one counting all of those?) is, "Can I carry this on a plane?" where "this" can refer to anything from an animal to a giant tin of popcorn. (I wouldn't recommend the tin of popcorn.
You have to put it in the overhead compartment horizontally, and because things shift during flight, the cover will likely open; and when you go to claim your tin at the end of the flight, you and your seatmates will be showered. Yes, I saw it happen once.)
This leads to an interesting statistical question: How many operators will you need at various times of the day to field those calls that will come in? Estimating the number of anticipated calls is your first step, and being wrong can cost you money (if you overestimated it) or a lot of bad PR (if you underestimated it).