Using Real-world Examples to Enhance the Relevance of the Introductory Statistics PDF

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Using Real-world Examples to Enhance the Relevance of the Introductory Statistics Course...

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Using Real-world Examples to Enhance the Relevance of the Introductory Statistics Course Hershey H. Friedman, Ph.D. Professor of Marketing and Business Department of Finance and Business Management School of Business Brooklyn College of the City University of New York e-mail: [email protected] Linda W. Friedman, Ph.D. Professor of Statistics & Computer Information Systems Baruch College Zicklin School of Business and the Graduate Center of the City University of New York e-mail: [email protected] Taiwo Amoo, Ph.D. Associate Professor of Quantitative Methods and Business Department of Finance and Business Management School of Business Brooklyn College of the City University of New York e-mail: [email protected] Keywords: Teaching statistics; evidence-based research; health research; happiness research; teacher cheating; attractiveness research; college rankings.

ABSTRACT This paper discusses various cases, stories, and examples involving the use of statistics that can add excitement to an introductory statistics course. Teaching statistics as a mathematics course does not work for students interested in careers in business and accounting. What is needed, the authors feel, are attention-grabbing examples. The authors provide instructors with interesting material for making a statistics course exciting and relevant.

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Using Real-world Examples to Enhance the Relevance of the Introductory Statistics Course

Introduction

Most instructors of the introductory statistics course will recognize that eye-roll moment – one brave, sassy student asks the question on everyone’s mind: “Why do I have to know this?” Other than the equally sassy, “Builds character,” we don’t often keep a well thought out response in our back pockets. This paper is that response.

The purpose of this paper is to identify real-world examples, from a variety of fields of study that emphasize the importance of taking on a statistical, evidence-based view of reality.

This paper will discuss the benefits of using interesting cases, stories, and examples when teaching quantitative material, and will show how they can be incorporated into the standard introductory statistics course. In a somewhat similar vein, several researchers have demonstrated the value of using humor in the introductory statistics course (Friedman, Friedman, and Amoo, 2002; Friedman, Halpern, and Salb, 1999). Some have also advocated using real life data in the basic statistics course so that students can have a feel for what it is like to work with real data (Davies, 2006; Larsen and Stroup, 1976; Libman, 2010; Schafer and Ramsey, 2003; Trumbo, 2002). This paper will take a different approach and show how using attention-grabbing examples can make a statistics course interesting, thoughtprovoking, and relevant. Students do not actually have to work with the data to appreciate the importance of statistics. Once they hear how evidence-based research (using statistics)

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and statistics have transformed so many different disciplines, they will understand why it is important to learn and understand statistics.

Health

Health has improved greatly in most of the world thanks to the use of experiments. Simple experiments comparing an experimental group with a placebo group and using very simple statistics have done much to improve world health.

Semmelweis: One doctor who had a great deal of trouble convincing his colleagues to do the right thing was Ignaz Philipp Semmelweis (1818-1865). In those days – not that long ago – puerperal infection (an infection of the female reproductive organs after childbirth) was very common. Women who gave birth in maternity hospitals had mortality rates of 25% to 30%. Semmelweis noticed that women who gave birth in the first division of the clinic where medical students were taught had a much higher mortality rate than women who gave birth in the second division where midwives were trained. He surmised that the medical students who were coming from the dissecting room to the maternity ward were bringing infection with them (this was before anyone knew about bacteria). Semmelweis instructed students to wash their hands in a solution of chlorinated lime before treating the pregnant women. Semmelweis observed that the mortality rates in the first division went from 18.27% to 1.27%. Today, we would say that this is a statistically significant difference. Later on, he worked at a hospital in Pest and, after an epidemic of puerperal fever broke out, successfully

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put an end to the epidemic by making doctors wash their hands. In 1861 Semmelweis published his major article, Die Ätiologie, der Begriff und die Prophylaxis des Kindbettfiebers (“Etiology, Understanding and Preventing of Childbed Fever”). Unfortunately, most doctors in other countries did not take his work seriously and refused to wash their hands before treating women ready to give birth. Indeed, his research was attacked by German physicians at a conference. In 1865, Semmelweis died in a mental institution; the stress had taken its toll (Zoltan, 2012).

Lister: In the first part of the nineteenth century, surgery was often done by barbers. They often wore dirty clothing and reused their instruments; operating tables were dirty and surgeon’s hands were filthy. No one understood about bacteria. About 43% of amputees died from sepsis. Joseph Lister (1827-1912) read the research of Louis Pasteur and realized that microbes in the air (bacteria) were the cause of gangrene. He introduced acids as disinfectants into the operating room. He started with carbolic acid and used it to sterilize the equipment and the wound itself. He was able to reduce mortality rates to 15% and is considered the founder of antiseptic medicine (Bonnin and LeFanu, 1967). Needless to say, modern surgery could not happen until physicians understood the importance of cleanliness. Lister acknowledged the important contribution of Semmelweis to the concept of antiseptic surgery.

The above stories are a good way to show why we need evidence-based medicine. Lest students think that evidence-based medicine is no longer needed, here are some examples from our own time.

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The Annual Physical Exam: It is now becoming evident that such truisms as make sure to have an annual physical examination are incorrect. Annual physical exams often result in unnecessary procedures. In fact, we are one of the few countries in the world that still believe in them (Rosenthal, 2012). The American Board of Internal Medicine has come up with 10 unnecessary “routine” screening tests: annual physical, annual EKG, annual blood work, annual cholesterol test, annual Pap smear, prostate specific antigen test, pre-operation chest X-ray, bone scans to detect osteoporosis for women under 65, imaging for lower back pain of short duration, and imaging for common headaches (Rosenthal, 2012).

Prostate Cancer: There are 50,000 radical prostatectomies performed in the United States every year of which more than 80% are not necessary (Blum and Scholz, 2010). Only one in seven men who are diagnosed with prostate cancer might actually develop the dangerous, aggressive form of the disease. The overwhelming majority of men diagnosed with prostate cancer will live just as long if they leave it alone and have it watched and treated as a chronic condition. In fact, only one man in 48 has his life extended by the surgery; the rest have to suffer needlessly from symptoms ranging from incontinence to impotence.

Statins: Statins, used to lower cholesterol, are among the most popular drugs in the world. In 2006, statin sales were $27.8 billion with 50% going to Pfizer’s drug, Lipitor. Pfizer runs a campaign targeted to consumers that declares: “Lipitor reduces the risk of heart attack by 36%... in patients with multiple risk factors for heart disease.” While the advertisement is literally true (in an experiment, 3% of subjects taking a placebo had heart attacks vs. 2% taking Lipitor) it is very misleading. The results of the experiment indicate that 100 people

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had to take Lipitor for three years in order that one person would benefit and not get a heart attack. Ninety-nine people taking Lipitor will not benefit at all from taking Lipitor; however, they will have to deal with side effects. The measure that focuses on how many people must take the drug for one person to benefit, is known as the NNT (number needed to treat); Lipitor has an NNT of 100. Medical experts say that one should not take a drug with an NNT of over 50. There is evidence that the NNT for low-risk patients using statins for five years is 250 (Carey, 2008). These statistical measures, especially NNT, if made available to the public, can result in reduced medical costs and better health. Bach (2012) notes that “with routine mammography, you’d have to screen more than 1,000 women in their 40’s to prevent just one breast cancer death.”

Chemo: Chemotherapy is extremely effective for some kinds of cancers (leukemia, lymphoma, testicular cancer, Hodgkin’s disease) but ineffective for many other cancers (e.g., multiple myeloma, melanoma of the skin, cancer of the pancreas, uterus, prostate, bladder, and kidney). Despite this, a huge amount of money is spent on chemotherapy. In many cases, nothing is accomplished except possibly enriching oncologists and giving cancer patients false hope. With lung cancer, which kills more than 150,000 Americans each year, the chemotherapy treatment costs considerably more than $40,000 but life is only extended on average for about 2 months (Levitt and Dubner, 2009: 84-85).

Salt: The conventional wisdom is that salt is extremely dangerous and we should all reduce our consumption of it. Surprisingly, there is very little scientific evidence to back up this claim. It is not clear that consuming too much salt causes hypertension, and then results in

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strokes and premature death. Meta-analyses examining the entire literature dealing with salt and health have resulted in findings that are “inconsistent and contradictory.” There are new studies that suggest that reducing salt consumption can actually increase the risk of death. The reason given is that the less salt consumed, the more renin secreted by the kidneys. Renin seems to be linked to an increase in heart disease (Taubes, 2012). Not everyone agrees with Taubes, however, it is important for students to realize that the answer to many health questions will require statistical tests.

How to Prep for Surgery: Another piece of conventional wisdom that research has refuted is that patients should be shaved before surgery. One study actually demonstrated that shaved patients had a 5.6% infection rate vs. a rate of less than 1% whose hair was removed with clippers. The theory is that shaving results in microscopic nicks that make it easy for bacteria to breed and thereby cause a post-operative infection (O’Connor, 2012).

Scanning Our Kids: Medical research is finding that CT scans on children (computed topography, i.e., numerous X-rays taken from various angles in order to produce crosssectional images) may result in a significant increase in brain cancer and leukemia. In fact, 500 of 600,000 children under the age of 15 who had CT scans would “ultimately die of cancer caused by the CT radiation.” This does not mean that CT scans should never be used. Rather, it should not be the first choice and should only be used if absolutely necessary (Grady, 2012).

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Survival Stats: Who is more likely to survive when there is serious famine and a lack of food, men or women? Grayson (1994) studied this and compared the death rates for men and women in the Donner party. The people in the Donner party were on their way, using covered wagons, to California from Illinois and found themselves stranded for 6 months in the mountains. They had no food and eventually resorted to cannibalism and ate anyone who died. The death rate for men was 30/53 and for women it was 10/34. The women did significantly better than the men. Grayson’s conclusion was that women have an extra layer of fat that men do not have. That is there for the baby in case food is a problem. That extra layer of fat protects women in times of food deprivation (Grayson, 1994).

Diet: This is something most students probably know about; almost everyone has tried to lose weight at some time. Most diets do not work. Research demonstrates that people will lose weight on many different kinds of diets. Unfortunately, most of the weight loss occurs early on and a year later, most dieters gain everything back (Taubes, 2011: 36-37). Taubes (2011) feels that diets that are based on the principle of eating less, rarely work since people cannot starve themselves indefinitely. Moreover, they are training their bodies to make do with fewer calories which will make it more and more difficult to keep the extra pounds off. Taubes (2011: 191-192) cites numerous studies that believe that the trick to losing weight is to shift away from carbohydrates and consume more fat and protein. There is quite a bit of research demonstrating that low-carbohydrate diets that are high in fat result in better health (lower blood pressure, lower level of triglycerides, greater weight loss, and higher levels of the good cholesterol) than several other diets that allow more carbohydrates. The conventional wisdom that all fat is bad for us has little scientific evidence to back it up. In

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fact, according to Taubes (2011: 10-11), until the 1960s, the conventional wisdom was that people who wanted to lose weight should stay away from foods rich in carbohydrates (e.g., beer, bread, pasta, potatoes, sugary foods, and sweets). Carbs were the villain, not fat. Is Taubes right? The answer will eventually come from evidence-based research, not anecdotal evidence.

Happiness

Everyone wants to be happy. Students will be very interested in knowing what research using statistical techniques has to say about happiness.

Money: A major finding is that increases in income do not do much to help increase happiness once a person’s basic needs are satisfied; what matters more than absolute wealth is relative wealth (Johnson and Krueger, 2006; Kahneman, et. al., 2006; McConvill, 2005; McGowan, 2005; Myers and Diener, 1995; Wallis, 2005). Layard (2005: 48-49) describes the “hedonic treadmill” that families find themselves on. Their income increases so they buy a bigger and better house, a nicer car, go out more, and within a few months have adapted to the new lifestyle and are no happier than before the income increase. People compare their own income with those of neighbors and people similar to themselves. If a family’s income doubles but the income of friends and neighbors triples, the family will actually become less happy (Layard, 2006: 43-46). A simple trick for being happy is not moving to a wealthier neighborhood once your income increases. Stay in the old neighborhood where you are among the (relatively) wealthy ones. Another trick that researchers in the field mention is to

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keep a gratitude journal and be happy with what you have. Dunn and Norton (2012) cite research that asserts that “the beneficial effects of money tapered off entirely after the $75,000 mark.”

Individuals are very poor judges as to what will make them happy (Gilbert, 2006). They will therefore overestimate the joy that additional money will bring them and underestimate the joy they will receive from having more time to spend with family and friends. Long commutes to work are rough on happiness; yet people will change jobs to make more money and end up with reduced happiness. In most cases, a person with an easy commute and a job that is not demanding in terms of time will be much happier than the person who has no time to spend with family and friends because of work. Winning lotteries also does not do much in the long run to increase happiness (Seligman, 2004).

Job satisfaction: Myers and Diener (1995) cite numerous studies that show that there is a strong relationship between job satisfaction and life satisfaction. In fact, people want to be engaged in productive, meaningful work. Meaningful work, Myers and Diener (1995), note is more important than the size of the paycheck; people want challenging, fulfilling work that gives them a sense of accomplishment. Thottam (2005) cites numerous studies showing relationships between meaningful work and happiness.

Social Relationships: There is a strong correlation between happiness and social friendships; socializing and having many friends does a lot to increase happiness. (Futrelle, 2006; Lambert, 2007; Myers, 2000; Diener and Seligman, 2002; Wallis, 2005). People have a

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need to belong to and be part of a group. This gives them identity and support. There is also a strong correlation between social connections and health (Myers, 2000). The need to belong can be fulfilled by religion, work, family, or other support groups.

There is a correlation between marriage and happiness (Myers, 2000). People in a happy marriage are among the happiest people. People who are separated are among the most unhappy. Myers (2000) also found that those who are married are less likely to suffer from depression. What is especially interesting is that about 75% of Americans say that their spouse is their best friend; 80% say they would marry the same person again if they had the chance.

Blanchflower and Oswald (2004) found a strong, positive correlation between sexual activity and happiness. Sexual activity appears to have very strong effects on happiness for those who are educated. This confirms the findings of Kahneman et al. (2003) regarding the importance of sexual activity in happiness. This was true for young and old, male and female. Those with one sexual partner exhibited more happiness than those with multiple partners. Individuals who had sex outside their marriage had lower happiness scores than those who did not.

Safety

Safety is a big issue with everyone. It is now quite clear that smoking is extremely hazardous to one’s health, but there are many myths about other safety issues. Levitt and Dubner

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(2005: 150) cite evidence demonstrating that the risks that frighten us are not necessarily correlated with the risks that actually kill. People are more frightened, for example, of risks they control (e.g., driving) than risks they do not control (e.g., flying). Actually, the per-hour death rate (which takes into account how much time is spent in a car or plane) is about equal for flying and driving. Both are very unlikely to lead to death. Most people think that having a gun in one’s house is more dangerous than a swimming pool. Levitt and Dubner (2005: 150) show that the likelihood of death by swimming pool is 1 in 11,000 vs. death by gun which is less than 1 in a 1,000,000. A child is 100 times more likely to die in a house that has a pool than in one which has a gun.

Seat belts cost about $25 and research demonstrates that they have saved many lives. In 1950, approximately 40,000 people died in traffic accidents; the same number die in traffic accidents today. However, we drive many more miles today. The correct way to compare this is by examining the per mile fatality rate. Today, it is 20% of what it was back in 1950; one death for every 75 million miles driven. The major reason for the huge drop in the fatality rate: seat belts (Levitt and Dubner, 2009: 146-149). We should make sure to wear our seat belts. The cost for every life saved works out to about $30,000. Air bags, on the other hand, cost about $1.8 million for every lif...