Stats Starts Here1 Chapter 1

Stats Starts Here1 chapter 1

“But where shall I begin?” tatistics gets no respect. People say things like “You can prove anything with asked Alice. “Begin at the Statistics.” People will write off a claim based on data as “just a statistical trick.” beginning,” the King said And a Statistics course may not be your friends’ first choice for a fun elective. But Statistics is fun. That’s probably not what you heard on the street, but it’s gravely, “and go on till you Strue. Statistics is about how to think clearly with data. We’ll talk about data in more detail come to the end: then stop.” soon, but for now, think of data as any collection of numbers, characters, images, or other —Lewis Carroll, items that provide information about something. Whenever there are data and a need for Alice’s Adventures understanding the world, you’ll find Statistics. A little practice thinking statistically is all in Wonderland it takes to start seeing the world more clearly and accurately. So, What Is (Are?) Statistics?

It seems every time we turn around, someone is collecting data on us, from every purchase Q: What is Statistics? we make in the grocery store, to every click of our mouse as we surf the Web. A: Statistics is a way of reason- Consider the following: ing, along with a collection of tools and methods, designed to ● If you have a Facebook account, you have probably noticed that the ads you see online help us understand the world. tend to match your interests and activities. Coincidence? Hardly. According to the Q: What are statistics? Wall Street Journal (10/18/2010),2 much of your personal information has probably A: Statistics (plural) are particu- been sold to marketing or tracking companies. Why would Facebook give you a lar calculations made from data. free account and let you upload as much as you want to its site? Because your data Q: So what is data? A: You mean, “what are data?” are valuable! Using your Facebook profile, a company might build a profile of your Data is the plural form. The singular is datum. 1We could have called this chapter “Introduction,” but nobody reads the introduction, and we wanted you to read Q: OK, OK, so what are data? this. We feel safe admitting this here, in the footnote, because nobody reads footnotes either. A: Data are values along with 2blogs.wsj.com/digits/2010/10/18/referers-how-facebook-apps-leak-user-ids/ their context. © 2015 Pearson Education, Inc. 1

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interests and activities: what movies and sports you like; your age, sex, education level, and hobbies; where you live; and, of course, who your friends are and what they like. From Facebook’s point of view, your data are a potential gold mine. Gold ore in the ground is neither very useful nor pretty. But with skill, it can be turned into something both beautiful and valuable. What we’re going to talk about in this book is how you can mine your own data and learn valuable insights about the world. ● Like many other retailers, Target stores create customer profiles by collecting data about purchases using credit cards. Patterns the company discovers across similar customer profiles enable it to send you advertising and coupons that promote items you might be particularly interested in purchasing. As valuable to the company as these marketing insights can be, some may prove startling to individuals. Recently coupons Target sent to a Minneapolis girl’s home revealed she was pregnant before her father knew!3 ● How dangerous is texting while driving? Researchers at the University of Utah tested drivers on simulators that could present emergency situations. They compared reaction times of sober drivers, drunk drivers, and texting drivers.4 The results were striking. The texting drivers actually responded more slowly and were more dangerous than Are You a Statistic? those who were above the legal limit for alcohol. The ads say, “Don’t drink and In this book, you’ll learn how to design and analyze experiments like this. You’ll drive; you don’t want to be a learn how to interpret data and to communicate the message you see to others. You’ll also statistic.” But you can’t be a learn how to spot deficiencies and weaknesses in conclusions drawn by others that you statistic. We say: “Don’t be a datum.” see in newspapers and on the Internet every day. Statistics can help you become a more informed citizen by giving you the tools to understand, question, and interpret data. Statistics in a Word

It can be fun, and sometimes useful, to summarize a discipline in only a few words. So, Statistics Is about Variation Economics is about . . . Money (and why it is good). Data vary because we don’t Psychology: Why we think what we think (we think). see everything and because Biology: Life. even what we do see and measure, we measure Anthropology: Who? imperfectly. History: What, where, and when? So, in a very basic way, Philosophy: Why? Essential Statistics is about the real, imperfect world in Engineering: How? which we live. Accounting: How much? In such a caricature, Statistics is about . . . Variation.

3http://www.forbes.com/sites/kashmirhill/2012/02/16/how-target-figured-out-a-teen-girl-was-pregnant-before- her-father-did/ 4“Text Messaging During Simulated Driving,” Drews, F. A. et al. Human Factors: hfs.sagepub.com/content/51/5/762 © 2015 Pearson Education, Inc.

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Data vary. Ask different people the same question and you’ll get a variety of answers. Statistics helps us to make sense of the world described by our data by seeing past the underlying variation to find patterns and relationships. This book will teach you skills to help with this task and ways of thinking about variation that are the foundation of sound reasoning about data.

But What Are Data?

Amazon.com opened for business in July 1995, bill- ing itself as “Earth’s Biggest Bookstore.” By 1997, Amazon had a catalog of more than 2.5 million book titles and had sold books to more than 1.5 million customers in 150 countries. In 2010, the company’s sales reached $34.2 billion (a nearly 40% increase from the previous year). Amazon has sold a wide variety of merchandise, including a $400,000 necklace, yak cheese from Tibet, and the largest book in the world. How did Amazon become so successful and how can it keep track of so many customers and such a wide variety of products? The answer to both questions is data. But what are data? Think about it for a minute. What exactly do we mean by “data”? Do data have to be numbers? The amount of your last purchase in dollars is numerical data. But your name and address in Amazon’s database are also data even though they are not numerical. What about your ZIP code? That’s a number, but would Amazon care about, say, the average ZIP code of its customers? Let’s look at some hypothetical values that Amazon might collect:

105-2686834-3759466 Ohio Nashville Kansas 10.99 440 N B00000I5Y6 Katherine H. 105-9318443-4200264 Illinois Orange County Boston 16.99 312 Y B000002BK9 Samuel P. 105-1872500-0198646 Massachusetts Bad Blood Chicago 15.98 413 N B000068ZVQ Chris G. 103-2628345-9238664 Canada Let Go Mammals 11.99 902 N B000001OAA Monique D. 002-1663369-6638649 Ohio Best of Kansas Kansas 10.99 440 N B002MXA7Q0 Katherine H.

A S Try to guess what they represent. Why is that hard? Because there is no context. If we Activity : What Is (Are) Data? Do don’t know what values are measured and what is measured about them, the values are you really know what are data and what are just numbers? meaningless. We can make the meaning clear if we organize the values into a data table such as this one:

Previous Album New Purchase Order Number Name State/Country Price Area Code Download Gift? ASIN Artist 105-2686834-3759466 Katherine H. Ohio 10.99 440 Nashville N B0000015Y6 Kansas 105-9318443-4200264 Samuel R Illinois 16.99 312 Orange County y B000002BK9 Boston 105-1372500-0198646 Chris G. Massachusetts 15.98 413 Bad Blood N B000068ZVQ Chicago 103-2628345-9238664 Monique D. Canada 11.99 902 Let Go N B0000010AA Mammals 002-1663369-6638649 Katherine H. Ohio 10.99 440 Best of Kansas N B002MXA7Q0 Kansas

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Now we can see that these are purchase records for album download orders from The W’s: Amazon. The column titles tell what has been recorded. Each row is about a particular Who purchase. What information would provide a context? Newspaper journalists know that the lead What paragraph of a good story should establish the “Five W’s”: who, what, when, where, and and in what units (if possible) why. Often, we add how to the list as well. The answers to the first two ques- When tions are essential. If we don’t know what values are measured and who those values are Where measured on, the values are meaningless. Why How Who and What

In general, the rows of a data table correspond to individual cases about Whom (or about which—if they’re not people) we record some characteristics. Cases go by different names, depending on the situation.

● Individuals who answer a survey are called respondents. ● People on whom we experiment are subjects or (in an attempt to acknowledge the importance of their role in the experiment) participants. ● Animals, plants, websites, and other inanimate subjects are often called experimental units. ● Often we simply call cases what they are: for example, customers, economic quarters, or companies. ● In a database, rows are called records—in this example, purchase records. Perhaps the most generic term is cases, but in any event the rows represent the who of the data. The characteristics recorded about each individual are called variables. These are usually shown as the columns of a data table, and they should have a name that identifies What has been measured. Name, Price, Area Code, and whether the purchase was a Gift are some of the variables Amazon collected data for. Variables may seem simple, but we’ll need to take a closer look soon. We must know who and what to analyze data. Without knowing these two, we don’t have enough information to start. Of course, we’d always like to know more. The more we know about the data, the more we’ll understand about the world. If possible, we’d like to know the when and where of data as well. Values recorded in 1803 may mean something different than similar values recorded last year. Values measured in Tanzania may differ in meaning from similar measurements made in Mexico. And knowing why the data were collected can tell us much about its reliability and quality. Often, the cases are a sample of cases selected from some larger population that we’d A S : Consider the context Activity like to understand. Amazon certainly cares about its customers, but also wants to know how . . .Can you tell who’s Who and what’s What ? And Why ? This activity offers to attract all those other Internet users who may never have made a purchase from Amazon’s real-world examples to help you practice site. To be able to generalize from the sample of cases to the larger population, we’ll want the identifying the context. sample to be representative of that population—a kind of snapshot image of the larger world.

For Example Identifying the “Who” In December 2011, Consumer Reports published an evaluation of 25 tablets from a variety of manufacturers. Question: Describe the population of interest, the sample, and the Who of the study. Answer: The magazine is interested in the performance of tablets currently offered for sale. It tested a sample of 25 tablets, which are the “Who” for these data. Each tablet selected represents all tablets of that model offered by that manufacturer.

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How the Data Are Collected

How the data are collected can make the difference between insight and nonsense. As we’ll see later, data that come from a voluntary survey on the Internet are almost always worthless. One primary concern of Statistics is the design of sound methods for collecting data.5 Throughout this book, whenever we introduce data, we’ll provide a margin note listing the W’s (and H) of the data. Identifying the W’s is a habit we recommend. A S The first step of any data analysis is to know what you are trying to accomplish and Activity : Collect data in an what you want to know. To help you use Statistics to understand the world and make deci- experiment on yourself. With the computer, you can experiment on yourself and sions, we’ll lead you through the entire process of thinking about the problem, showing then save the data. Go on to the sub- what you’ve found, and telling others what you’ve learned. Every guided example in this sequent related activities to check your book is broken into these three steps: Think, Show, and Tell. Identifying the problem and understanding. the who and what of the data is a key part of the Think step of any analysis. Make sure you know these before you proceed to Show or Tell anything about the data.

More About Variables (What ?)

The Amazon data table displays information about several variables: Order Number, Privacy and the Name, State/Country, Price, and so on. These identify what we know about each indi- Internet You have many vidual. Variables such as these can play different roles, depending on how we plan to Identifiers: a social security use them. While some are merely identifiers, others may be categorical or quantitative. number, a student ID number, possibly a passport number, a Making that distinction is an important step in our analysis. health insurance number, and probably a Facebook account name. Privacy experts are wor- Identifiers ried that Internet thieves may For some variables, such as a student ID, each individual receives a unique value. We match your identity in these dif- call a variable like this, an identifier variable. Identifiers are useful, but not typically for ferent areas of your life, allow- ing, for example, your health, analysis. education, and financial records Amazon wants to know who you are when you sign in again and doesn’t want to to be merged. Even online confuse you with some other customer. So it assigns you a unique identifier. Amazon also companies such as Facebook wants to send you the right product, so it assigns a unique Amazon Standard Identification and Google are able to link your Number (ASIN) to each item it carries. Identifier variables themselves don’t tell us any- online behavior to some of these thing useful about their categories because we know there is exactly one individual in identifiers, which carries with each. You’ll want to recognize when a categorical variable is playing the role of an identi- it both advantages and dan- fier so you aren’t tempted to analyze it. gers. The National Strategy for Trusted Identities in Cyberspace (www.wired.com/images_blogs/ threatlevel/2011/04/NSTIC Categorical Variables strategy_041511.pdf) proposes Some variables just tell us what group or category each individual belongs to. Are you ways that we may address this male or female? Pierced or not? What color are your eyes? We call variables like these challenge in the near future. categorical variables.6 Some variables are clearly categorical, like the variable State/ Country. Its values are text and those values tell us what category the particular case falls into. Descriptive responses to questions are often categories. For example, the responses to the questions “Who is your cell phone provider?” or “What is your marital status?” yield categorical values. But numerals are often used to label categories, so categorical variable values can also be numerals. For example, Amazon collects telephone area codes that categorize each phone number into a geographical region. So area code is considered a categorical variable even though it has numeric values.

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Quantitative Variables When a variable contains measured numerical values with measurement units, we call it a quantitative variable. Quantitative variables typically record an amount or degree of something. For a quantitative variable, its measurement units provide a meaning for the numbers. Even more important, units such as yen, cubits, carats, angstroms, nanoseconds, miles per hour, or degrees Celsius tell us the scale of measurement, so we know how far apart two values are. Without units, the values of a measured variable have no meaning. It does little good to be promised a raise of 5000 a year if you don’t know whether it will be paid in Euros, dollars, pennies, yen, or Estonian krooni.

Either/Or? Some variables with numeric values can be treated as either categorical or quantitative depending on what we want to know. Amazon could record your Age in years. That seems quantitative, and it would be if the company wanted to know the average age of those customers who visit their site after 3 a.m. But suppose Amazon wants to decide which album to feature on its site when you visit. Then thinking of your age in one of the categories Child, Teen, Adult, or Senior might be more useful. So, sometimes whether a variable is treated as categorical or quantitative is more about the question we want to ask rather than an intrinsic property of the variable itself. Suppose a course evaluation survey asks, “How valuable do you think this course will be to you?” 1 = Worthless; 2 = Slightly; 3 = Middling; 4 = Reasonably; 5 = Invaluable. Is Educational Value categorical or quantitative? A teacher might just count the number of students who gave each response for her course, treating Educational Value as a categorical variable. Or if she wants to see whether the course is improving, she might treat the responses as the amount of perceived value—in effect, treating the variable as quantitative. A S Activity : Recognize variables But what are the units? There is certainly an order of perceived worth: Higher num- measured in a variety of ways. This bers indicate higher perceived worth. A course that averages 4.5 seems more valuable activity shows examples of the many ways than one that averages 2, but the teacher will have to imagine that it has “educational to measure data. value units,” whatever they are. Because there are no natural units, she should be cautious. Variables that report order without natural units are often called ordinal variables. But A S Activities : Variables. Several saying “that’s an ordinal variable” doesn’t get you off the hook. You must still look to activities show you how to begin working the why of your study and understand what you want to learn from the variable to decide with data in your statistics package. whether to treat it as categorical or quantitative.

For Example Identifying “What” and “Why” of Tablets Recap: A Consumer Reports article about 25 tablet computers lists each tablet’s manufacturer, cost, battery life (hrs.), operating system (iOS/Android/RIM), and overall performance score (0–100). Question: Are these variables categorical or quantitative? Include units where appropriate, and describe the “Why” of this investigation. Answer: The variables are • manufacturer (categorical) • cost (quantitative, $) • battery life (quantitative, hrs.) • operating system (categorical) • performance score (quantitative, no units) The magazine hopes to provide consumers with the information to choose a good tablet.

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Just Checking

In the 2004 Tour de France, Lance Armstrong made his- 1. List as many of the W’s as you can for this data set. tory by winning the race for an unprecedented sixth time. 2. Classify each variable as categorical or quantitative; In 2005, he became the only 7-time winner and set a new if quantitative, identify the units. record for the fastest average speed—41.65 kilometers per hour. A cancer survivor, Armstrong became an international celebrity. But it was all too good to be true. In 2012, following revelations of doping, the International Cycling Union stripped Armstrong of all of his titles and records and banned him from professional cycling for life. You can find data on all the Tour de France races on the DVD. Keep in mind that the entire data set has over 100 entries.

Total Distance Starting Finishing Year Winner Country of Origin Total Time (h/min/s) Avg. Speed (km/h) Stages Ridden (km) Riders Riders

1903 Maurice Garin France 94.33.00 25.3 6 2428 60 21 1904 Henri Cornet France 96.05.00 24.3 6 2388 88 23 1905 Louis Trousseller France 112.18.09 27.3 11 2975 60 24 A 1999 Lance Armstrong (DQ) USA 91.32.16 40.30 20 3687 180 141 2000 Lance Armstrong (DQ) USA 92.33.08 39.56 21 3662 180 128 2001 Lance Armstrong (DQ) USA 86.17.28 40.02 20 3453 189 144 2002 Lance Armstrong (DQ) USA 82.05.12 39.93 20 3278 189 153 2003 Lance Armstrong (DQ) USA 83.41.12 40.94 20 3427 189 147 2004 Lance Armstrong (DQ) USA 83.36.02 40.53 20 3391 188 147 2005 Lance Armstrong (DQ) USA 86.15.02 41.65 21 3608 189 155 A 2011 Cadel Evans Australia 86.12.22 39.788 21 3430 198 167 2012 Bradley Wiggins Great Britain 87.34.47 39.928 20 3497 219 153 2013 Chris Froome Great Britain 83.56.40 40.551 21 3404 219 170

There’s a World of Data on the Internet These days, one of the richest sources of data is the Internet. With a bit of practice, you can learn to find data on almost any subject. Many of the data sets we use in this book were found in this way. The Internet has both advantages and disadvantages as a source of data. Among the advantages are the fact that often you’ll be able to find even more current data than those we present. The disadvantage is that references to Internet addresses can “break” as sites evolve, move, and die. Our solution to these challenges is to offer the best advice we can to help you search for the data, wherever they may be residing. We usually point you to a website. We’ll sometimes suggest search terms and offer other guidance. A S Self-Test : Review concepts Some words of caution, though: Data found on Internet sites may not be formatted in the about data. best way for use in statistics software. Although you may see a data table in standard form, an Like the Just Checking sections of this attempt to copy the data may leave you with a single column of values. You may have to work textbook, but interactive. (Usually, we in your favorite statistics or spreadsheet program to reformat the data into variables. You will won’t reference the ActivStats self-tests also probably want to remove commas from large numbers and extra symbols such as money here, but look for one whenever you’d like indicators ($, ¥, £); few statistics packages can handle these. to check your understanding or review material. © 2015 Pearson Education, Inc.

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What Can Go Wrong?

■ Don’t label a variable as categorical or quantitative without thinking about the question you want it to answer. The same variable can sometimes take on different roles. ■ Just because your variable’s values are numbers, don’t assume that it’s quantitative. Categories are often given numerical labels. Don’t let that fool you into thinking they have quantitative meaning. Look at the context. ■ Always be skeptical. One reason to analyze data is to discover the truth. Even when you are told a context for the data, it may turn out that the truth is a bit (or even a lot) different. Think about how the data were collected. People who want to influence what you think may slant the context. A survey that seems to be about all students may in fact report just the opinions of those who visited a fan website. The question that respondents answered may be posed in a way that influences responses.

TI Tips Working with data

You’ll need to be able to enter and edit data in your calculator. Here’s how:

To enter data: Hit the STAT button, and choose EDIT from the menu. You’ll see a set of columns labeled L1, L2, and so on. Here is where you can enter, change, or delete a set of data. Let’s enter the heights (in inches) of the five starting players on a basketball team: 71, 75, 75, 76, and 80. Move the cursor to the space under L1, type in 71, and hit ENTER (or the down arrow). There’s the first player. Now enter the data for the rest of the team.

To change a datum: Suppose the 76'' player grew since last season; his height should be listed as 78''. Use the arrow keys to move the cursor onto the 76, then change the value and ENTER the correction.

To add more data: We want to include the sixth man, 73'' tall. It would be easy to simply add this new datum to the end of the list. However, sometimes the order of the data matters, so let’s place this datum in numerical order. Move the cursor to the de- sired position (atop the first 75). Hit2ND INS, then ENTER the 73 in the new space.

To delete a datum: The 78'' player just quit the team. Move the cursor there. Hit DEL. Bye.

To clear the datalist: Finished playing basketball? Move the cursor atop the L1. Hit CLEAR, then ENTER (or down arrow). You should now have a blank datalist, ready for you to enter your next set of values.

Lost a datalist? Oops! Is L1 now missing entirely? Did you delete L1 by mistake, instead of just clearing it? Easy problem to fix: buy a new calculator. No? OK, then simply go to the STAT EDIT menu, and run SetUpEditor to recreate all the lists.

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What Have We Learned? We’ve learned that data are information in a context. ■ The W’s help nail down the context Who, What, When, Why, Where, and hoW. ■ We must know at least the Who, What, and hoW to be able to say anything useful based on the data. The Who are the cases. The What are the variables. A variable gives information about each of the cases. The hoW helps us decide whether we can trust the data. We treat variables in two basic ways: as categorical or quantitative. ■ Categorical variables identify a category for each case. Usually, we think about the counts of cases that fall into each category. (An exception is an identifier variable that just names each case.) ■ Quantitative variables record measurements or amounts of something; they must have units. ■ Sometimes we treat a variable as categorical or quantitative depending on what we want to learn from it, which means that some variables can’t be pigeonholed as one type or the other. That’s an early hint that in Statistics we can’t always pin things down precisely. Terms

Data Systematically recorded information, whether numbers or labels, together with its context. (p. 1) Data table An arrangement of data in which each row represents a case and each column represents a variable. (p. 3)

Context The context ideally tells Who was measured, What was measured, How the data were collected, Where the data were collected, and When and Why the study was performed. (p. 4)

Case A case is an individual about whom or which we have data. (Who). (p. 4) Respondent Someone who answers, or responds to, a survey. (p. 4) Subject A human experimental unit. Also called a participant. (p. 4) Participant A human experimental unit. Also called a subject. (p. 4) Experimental unit An individual in a study for which or for whom data values are recorded. Human experimental units are usually called subjects or participants. (p. 4) Record Information about an individual in a database. (p. 4)

Variable A variable holds information about the same characteristic for many cases. (What). (p. 4) Sample The cases we actually examine in seeking to understand the much larger population. (p. 4) Population All the cases we wish we knew about. (p. 4) Identifier variable A categorical variable that records a unique value for each case, used to name or identify it. (p. 5) Categorical variable A variable that names categories (whether with words or numerals) is called categorical. (p. 5)

Quantitative variable A variable in which the numbers act as numerical values is called quantitative. Quantitativ e variables always have units. (p. 6) Units A quantity or amount adopted as a standard of measurement, such as dollars, hours, or grams. (p. 6)

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On the Computer Data

Most often we find statistics on a computer using a program, orpackage , designed for A S : Examine the Data. Activity that purpose. There are many different statistics packages, but they all do essentially Take a look at your own data from your experiment (p. 8) and get comfortable the same things. If you understand what the computer needs to know to do what you with your statistics package as you want and what it needs to show you in return, you can figure out the specific details of find out about the experiment test most packages pretty easily. results. For example, to get your data into a computer statistics package, you need to tell the computer: “Computers are use- ■ Where to find the data. This usually means directing the computer to a file stored less; they can only on your computer’s disk or to data on a database. Or it might just mean that you give you answers.” have copied the data from a spreadsheet program or Internet site and it is currently on your computer’s clipboard. Usually, the data should be in the form of a data —Pablo Picasso table. Most computer statistics packages prefer the delimiter that marks the divi- sion between elements of a data table to be a tab character and the delimiter that marks the end of a case to be a return character. ■ Where to put the data. (Usually this is handled automatically.) ■ What to call the variables. Some data tables have variable names as the first row of the data, and often statistics packages can take the variable names from the first row automatically.

Exercises

1. Voters A February 2010 Gallup Poll question asked, (Exercises 5–12) For each description of data, identify Who and “In politics, as of today, do you consider yourself a What were investigated and the population of interest. Republican, a Democrat, or an Independent?” The 5. The news Find a newspaper or magazine article in which possible responses were “Democrat”, “Republican”, some data are reported. For the data discussed in the “Independent”, “Other”, and “No Response”. What kind article, answer the questions above. Include a copy of the of variable is the response? article with your report. 2. Job hunting A June 2011 Gallup Poll asked Americans, 6. The Internet Find an Internet source that reports on a “Thinking about the job situation in America today, study and describes the data. Print out the description and would you say that it is now a good time or a bad answer the questions above. time to find a quality jobs?” The choices were “Good 7. Bicycle safety Ian Walker, a psychologist at the time” or “Bad time”. What kind of variable is the University of Bath, wondered whether drivers treat bicy- response? cle riders differently when they wear helmets. He rigged his bicycle with an ultrasonic sensor that could measure 3. Medicine A pharmaceutical company conducts an how close each car was that passed him. He then rode on experiment in which a subject takes 100 mg of a sub- alternating days with and without a helmet. Out of 2500 stance orally. The researchers measure how many cars passing him, he found that when he wore his helmet, minutes it takes for half of the substance to exit the motorists passed 3.35 inches closer to him, on average, bloodstream. What kind of variable is the company than when his head was bare. [NY Times, Dec. 10, 2006] studying? 8. Investments Some companies offer 401(k) retirement 4. Stress A medical researcher measures the increase in plans to employees, permitting them to shift part of heart rate of patients under a stress test. What kind of their before-tax salaries into investments such as mutual variable is the researcher studying? funds. Employers typically match 50% of the employees’ © 2015 Pearson Education, Inc.

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contribution up to about 6% of salary. One company, They hoped to find a way to estimate weight from the concerned with what it believed was a low employee other, more easily determined quantities. participation rate in its 401(k) plan, sampled 30 other 14. Schools The State Education Department requires local companies with similar plans and asked for their 401(k) school districts to keep these records on all students: age, participation rates. race or ethnicity, days absent, current grade level, stan- 9. Honesty Coffee stations in offices often just ask users dardized test scores in reading and mathematics, and any to leave money in a tray to pay for their coffee, but disabilities or special educational needs. many people cheat. Researchers at Newcastle University 15. Arby’s menu A listing posted by the Arby’s restaurant alternately taped two posters over the coffee station. chain gives, for each of the sandwiches it sells, the type During one week, it was a picture of flowers; during the of meat in the sandwich, the number of calories, and the other, it was a pair of staring eyes. They found that the serving size in ounces. The data might be used to assess average contribution was significantly higher when the the nutritional value of the different sandwiches. eyes poster was up than when the flowers were there. Apparently, the mere feeling of being watched—even by 16. Age and party Gallup conducted a series of telephone eyes that were not real—was enough to encourage people polls involving 20,392 American adults during 2011. to behave more honestly. [NY Times, Dec. 10, 2006] Among the reported results were the voters’ gender, age, 10. Gaydar A study conducted by a team of American race, party affiliation, whether they were of Hispanic and Canadian researchers found that during ovulation, ethnicity, education, region, adults in the household, and a woman can tell whether a man is gay or straight by phone status (cell phone only/landline only/both, cell looking at his face. To explore the subject, the authors phone mostly, and having an unlisted landline number). conducted three investigations, the first of which involved 17. Babies Medical researchers at a large city hospital inves- 40 undergraduate women who were asked to guess the tigating the impact of prenatal care on newborn health sexual orientation of 80 men based on photos of their collected data from 882 births during 1998–2000. They face. Half of the men were gay, and the other half were kept track of the mother’s age, the number of weeks the straight. All held similar expressions in the photos or pregnancy lasted, the type of birth (cesarean, induced, were deemed to be equally attractive. None of the women natural), the level of prenatal care the mother had (none, were using any contraceptive drugs at the time of the test. minimal, adequate), the birth weight and sex of the baby, The result: the closer a woman was to her peak ovulation and whether the baby exhibited health problems (none, the more accurate her guess. minor, major). (Source: news.yahoo.com/does-ovulation-boost-womans- 18. Flowers In a study appearing in the journal Science, a gaydar-210405621.html) research team reports that plants in southern England are 11. Blindness: A study begun in 2011 examines the use of flowering earlier in the spring. Records of the first flower- stem cells in treating two forms of blindness, Stargardt’s ing dates for 385 species over a period of 47 years show disease, and dry age-related macular degeneration. Each that flowering has advanced an average of 15 days per of the 24 patients entered one of two separate trials in decade, an indication of climate warming, according to which embryonic stem cells were to be used to treat the the authors. condition. 19. Herbal medicine Scientists at a major pharmaceutical 12. Molten iron The Cleveland Casting Plant is a large, firm conducted an experiment to study the effectiveness highly automated producer of gray and nodular iron of an herbal compound to treat the common cold. They automotive castings for Ford Motor Company. The exposed each patient to a cold virus, then gave them company is interested in keeping the pouring tempera- either the herbal compound or a sugar solution known to ture of the molten iron (in degrees Fahrenheit) close to have no effect on colds. Several days later they assessed the specified value of 2550 degrees. Cleveland Casting each patient’s condition, using a cold severity scale rang- measured the pouring temperature for 10 randomly ing from 0 to 5. They found no evidence of the benefits selected crankshafts. of the compound. (Exercises 13–26) For each description of data, identify the 20. Vineyards Business analysts hoping to provide informa- W’s, name the variables, specify for each variable whether its tion helpful to American grape growers compiled these use indicates that it should be treated as categorical or quan- data about vineyards: size (acres), number of years in titative, and, for any quantitative variable, identify the units in existence, state, varieties of grapes grown, average case which it was measured (or note that they were not provided). price, gross sales, and percent profit. 13. Weighing bears Because of the difficulty of weighing a 21. Streams In performing research for an ecology class, stu- bear in the woods, researchers caught and measured 54 dents at a college in upstate New York collect data on local bears, recording their weight, neck size, length, and sex. streams each year. They record a number of biological, © 2015 Pearson Education, Inc.

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chemical, and physical variables, including the stream T 26. Indy 2013 The 2.5-mile Indianapolis Motor Speedway name, the substrate of the stream (limestone, shale, or has been the home to a race on Memorial Day weekend mixed), the acidity of the water (pH), the temperature (°C), nearly every year since 1911. Even during the first and the BCI (a numerical measure of biological diversity). race, there were controversies. Ralph Mulford was given the checkered flag first but took three extra laps 22. Fuel economy The Environmental Protection Agency just to make sure he’d completed 500 miles. When he (EPA) tracks fuel economy of automobiles based on finished, another driver, Ray Harroun, was being pre- information from the manufacturers (Ford, Toyota, etc.). sented with the winner’s trophy, and Mulford’s protests Among the data the agency collects are the manufacturer, were ignored. Harroun averaged 74.6 mph for the 500 vehicle type (car, SUV, etc.), weight, horsepower, and gas miles. In 2013, the winner, Tony Kanaan, averaged mileage (mpg) for city and highway driving. 187.433 mph. 23. Refrigerators In 2012, Consumer Reports rated bottom- Here are the data for the first five races and five recent freezer refrigerators. It listed 102 models, giving the Indianapolis 500 races. brand, cost, size (cu ft), temperature performance, noise (poor, fair, etc.), ease of use, energy efficiency, estimated annual energy cost, an overall rating (good, excellent, etc.), and the exterior dimensions. Year Winner Time Average Speed (mph) 1911 Ray Harroun 6:42:08.039 74.602 24. Walking in circles People who get lost in the desert, 1912 Joe Dawson 6:21:06.144 78.719 mountains, or woods often seem to wander in circles 1913 Jules Goux 6:35:05.108 75.933 rather than walk in straight lines. To see whether people 1914 René Thomas 6:03:45.060 82.474 naturally walk in circles in the absence of visual clues, 1915 Ralph DePalma 5:33:55.619 89.840 researcher Andrea Axtell tested 32 people on a football field. One at a time, they stood at the center of one goal . . . line, were blindfolded, and then tried to walk to the other 2009 Hélio Castroneves 3:19:34.6427 150.318 goal line. She recorded each individual’s sex, height, 2010 Dario Franchitti 3:05:37.0131 161.623 handedness, the number of yards each was able to walk 2011 Dan Wheldon 2:56:11.7267 170.265 before going out of bounds, and whether each wandered 2012 Dario Franchitti 2:58:51 167.734 off course to the left or the right. No one made it all the 2013 Tony Kanaan 2:40:03.4181 187.433 way to the far end of the field without crossing one of the sidelines. [STATS No. 39, Winter 2004]

T 25. Kentucky Derby 2012 The Kentucky Derby is a horse race that has been run every year since 1875 at Churchill Downs, Louisville, Kentucky. The race started as a 1.5-mile race, but in 1896, it was shortened to 1.25 miles because experts felt that 3-year-old horses shouldn’t run such a long race that early in the season. (It has been run in May every year but one—1901—when it took place on April 29). Here are the data for the first four and several recent races.

Year Winner Jockey Trainer Owner Time 2013 Orb J. Rosario C. McGaughey III Phipps/Janney 2:02.89 2012 I’ll Have Another M. Gutierrez D. O’Neill Reddam Racing 2:01.83 2011 Animal Kingdom J. Velazquez H. G. Motion Team Valor 2:02.04 2010 Super Saver C. Borel T. Pletcher WinStar Farm 2:04.45 2009 Mine That Bird C. Borel B. Woolley Double Eagle 2:02.66 Ranch . . . 1878 Day Star J. Carter L. Paul T.J. Nichols 2:37.25 1877 Baden Baden W. Walker E. Brown Daniel Swigert 2:38 1876 Vagrant R. Swim J. Williams William Astor 2:38.25 1875 Aristides O. Lewis A. Williams H.P. McGrath 2:37.75

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Just Checking Answers

1. Who—Tour de France races; What—year, winner, country of origin, total time, average speed, stages, total distance ridden, starting riders, finishing riders; How— official statistics at race; Where—France (for the most part); When—1903 to 2012; Why—not specified (To see progress in speeds of cycling racing?)

2. Variable Type Units Year Quantitative or Categorical Years Winner Categorical Country of Origin Categorical Total Time Quantitative Hours/minutes/seconds Average Speed Quantitative Kilometers per hour Stages Quantitative Counts (stages) Total Distance Quantitative Kilometers Starting Riders Quantitative Counts (riders) Finishing Riders Quantitative Counts (riders)

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