Critique: Write a critique of the paper. Do you agree with the authors that statistics is important? Why? Feel free to provide your own examples of a valuable statistical study. I want to see several paragraphs of insightful comments.
joefra
ssrn-id2129750.pdf
Electronic copy available at: http://ssrn.com/abstract=2129750
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.
Electronic copy available at: http://ssrn.com/abstract=2129750
1
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, thought-
provoking, 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 cross-
sectional 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 life saved.
It is mandatory in every state to use car seats for every child; seat belts do not fit small
children. Levitt and Dubner (2009: 152-153) examined the Fatality Analysis Reporting
System (FARS) to determine the value of car seats for children older than 2 years. Their
findings were that the death rates were about the same for car seats and adult seat belts. They
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hired a crash-test lab to compare seat belts with car seats using dummies. The results also
showed that car seats do not outperform seat belts. They examined a different data set and
found that when it came to serious injuries, seat belts do just as well as car seats. With
respect to minor injuries, however, car seats did a better job (25% better).
We are all aware of the dangers of global warming. We have been told that it will cause the
oceans to rise, flooding of the lowlands, crazy weather patterns, and much more. What
people do not realize is that ruminants (cows, sheep, etc.) give off methane when they pass
gas which is about 25 times more problematic as a greenhouse gas than carbon dioxide. If
we switched our diet away from red meat to vegetables, fish, and chicken, we would do a lot
more for the environment than switching to a hybrid car (Levitt and Dubner, 2009: 168-173).
Ratings and Rankings
Today, we can find ratings and rankings for all sorts of institutions and professionals,
including hospitals, nursing homes, schools, physicians, etc. Students who understand
statistics have a better chance of understanding how easy it is to manipulate ratings.
Newsweek publishes a list of the 1,000 best high schools. To understand how the list works,
one has to know what factors are used in the ratings and the weights assigned to each factor.
Winerip (2012) observes that Newsweek uses six factors: On-time graduation rate (25%
weight), percent of graduates accepted to college (25%), A.P. and International
Baccalaureate tests per student (25%), average SAT/ACT score (10%), Average A.P.
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(advanced placement)/International Baccalaureate score (10%), and A.P./International
Baccalaureate courses per student (5%). Another important factor to consider is the number
of high schools that sent data to Newsweek. It turns out that only 2,000 of 26,000 high
schools actually submitted data. This means that 24,000 high schools never had a chance to
be on the list. Of those that submitted data, 50% would make it to the list. The biggest
problem with the list is that schools that do extensive screening and are targeted to the
brightest students are quite likely to make the list. Schools in the wealthiest areas with
children from affluent families will also do well. What we are getting, according to Winerip
(2012), is a “Best in, best out, best school.” On the other hand, schools that admit weak
students and dramatically improve their abilities may not score as well. The same is true
when comparing, say, two hospitals on survival rates for a particular type of surgery. The
hospital that admits the sickest, unhealthiest, and poorest patients will have a much higher
mortality rate than one which only admits the healthiest, most affluent patients.
The Mayo Clinic (2012) explains how the measure is calculated and describes how it can be
adjusted for risk:
Hospital mortality rates refer to the percentage of patients who die while
in the hospital. Mortality rates are calculated by dividing the number of
deaths among hospital patients with a specific medical condition or
procedure by the total number of patients admitted for that same medical
condition or procedure. This risk adjustment method is used to account
for the impact of individual risk factors such as age, severity of illness
and other medical problems that can put some patients at greater risk of
death than others.
Perez-Pena and Slotnik (2012) describe how several colleges have manipulated the U.S.
News & World Report rankings. One college – Iona College – was dishonest about various
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measures used in the determination of rankings. These included SAT scores, graduation
rates, freshman retention, student-faculty ratio, alumni giving and acceptance rates. Other
colleges use other approaches. Baylor University offered students financial incentives to
retake the SAT exams in order to improve the average scores of admitted students. Some
colleges delay the admission of students with low SAT scores so that these scores do not
affect the reported averages. Some colleges work hard to get more applications —from
unqualified applicants— in order to show a lower rate of admitted students. Even law
schools have admitted to fudging the statistics. Villanova University admitted that their
deception was deliberate. In 2009, several colleges were found to be inflating the percentage
of classes taught by full-time professors.
Recently, a number of law schools around the country have been accused of being deceptive
as far as job placement ratios and salary data (Goldberg, 2012). Job placement success is one
of four key factors in the U.S. News and World Report rankings of law schools. In fact,
David Anziska, an New York attorney is suing 20 law schools. What some of the schools do
is inflate the employment data by including students working part time and/or include
students working in jobs unrelated to law. Salary figures are not reliable if the rate of
response is low. Students making very little or unemployed will not respond to a
questionnaire asking how much they are earning. Obviously, the students who are employed
full time and making a robust salary are more likely to respond. Indeed, about two-thirds of
University of Miami’s School of Law 2010 graduates did not respond to the income question.
It is clear that what is needed is more transparency as far as job placement and salary data
(Goldberg, 2012).
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Crime
Compstat, a crime analysis and accountability system, was credited with dramatically
lowering the crime rate in New York City. It tracks crime and thus allows resources to be
allocated where they are needed. The weekly NYC Compstat report can be seen at the
following website:
http://www.nyc.gov/html/nypd/downloads/pdf/crime_statistics/cscity.pdf. The Compstat
model is being used all over the country by police departments as well as other agencies; its
proponents claim that it reduced crime in NYC by77% (MacDonald, 2010). Not everyone
believes that Compstat is responsible for the huge decrease in crime.
Levitt and Dubner (2005: 140-142) provide compelling statistical evidence that the
legalization of abortion is what reduced crime. In states where abortion was legalized in the
1970s, crime dropped dramatically in the 1990s. The reason for this, according to Levitt and
Dubner, is that unwanted children who were born because abortion was illegal are the ones
who are most likely to embark on a life of crime. Levitt and Dubner (2005: 141) assert that
“abortion was one of the greatest crime-lowering factors in American history,”
Can statistics be used to catch a serial killer? Maybe. The worst serial killer in history was
Dr. Harold Frederick Shipman (1946-2004). He was an English medical doctor who killed
many of his patients using drugs; some believe that he killed as many as 345. Most of his
patients were elderly women. A review of death certificates for patients 65 to 74 years of age
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signed by him indicated 47.2 deaths per 1,000 vs. 4.5 deaths per 1,000 for physicians with
similar practices (Eichenwald, 2001).
Teacher Cheating
When students hear of cheating, they automatically think of students who use dishonest
means to improve grades. Nowadays, because scores on standardized tests are used to rate
principals, determine merit pay, and to decide which schools will be closed, there is an
incentive for administrators and teachers to cheat. Levitt and Dubner (2005: 28-36) show
how statistics caught cheating administrators in the Chicago Public School system. They
used a program to examine the answer sheets. It looked for unusual answer patterns. For
example, if the program found a string of, say, 6 difficult questions in a row (the easy
questions are usually at the beginning) were answered correctly by a large number of weak
students, that would suggest teacher cheating, i.e., the teacher memorized a string of answers
and changed them for a number of students. It is relatively easy for a grader to remember
that the answers for questions 30 to 35 are, say, “b,c,a,d,a,d.” As a result, a number of
cheating teachers were fired.
One relatively inexpensive technique that is used to detect teacher cheating on standardized
tests using bubble sheets is erasure analysis. When the test is scanned, the rate of wrong
answer to right answer erasures are noted. If the rate is statistically higher than what is
expected, this could mean that the teacher erased the wrong answers. Erasure analysis
resulted in 62 New York State schools being suspected of cheating; 48 of those schools were
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in New York City. At one school, an assistant principal was alone with the 2008 algebra
tests and a suspicious pattern of erasures was discovered: of 1,013 erased answers, 94%
were changed from the wrong to right. Normally, about 50% of erasures are from wrong to
right. The assistant principal resigned, and will not be permitted to work in the New York
City school system (Otterman, 2011).
Attractiveness
There are numerous Internet dating websites such as eHarmony and Match.com. What kind
of information will make one desirable? That is a question that students will find fascinating.
Statistics again provides the answer (Levitt and Dubner, 2009: 80-85). One way not to get a
date is not to post a photograph; men who do not post photos get 25% of the email responses
of those who do; women, one-sixth. Men who claim they are looking for a long-term
relationship do much better than those seeking an occasional lover; for women it is the
opposite. For men, the way a woman looks is extremely important; for women, the man’s
income is important. Men prefer women with incomes in the middle of the distribution: too
little and too much is no good. Men prefer to date students, artists, musicians, veterinarians,
and celebrities. They are reluctant to date women who are secretaries, in law enforcement, or
in the military. Women have a preference for dating military men, police officers, lawyers,
financial executives, and firemen; they are reluctant to date laborers, actors, students, and
food service industry workers. Short men will have a problem getting dates; weight is not a
problem. Blond hair is great for a woman; red hair or baldness is a problem for men. About
50% of white women claimed that race did not matter. Yet, 97% of their emails went to
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white men. About 80% of white men said race did not matter and 90% of their emails went
to white women.
How important is attractiveness in achieving success in life? How about education?
Intelligence? These are questions that have been researched by many scholars. Some of the
key findings are as follows: Physical attractiveness does have a positive and significant
effect on income. Physical attractiveness also, surprisingly, has a significant effect on
educational attainment (1= some grade school, 2= junior high; …; 12= doctoral-level degree)
and core self-evaluation. Core self-evaluation has to do with how an individual sees
himself/herself in terms of success and control over one’s life. Core self-evaluations consist
of such factors as self-esteem, locus of control, and emotional stability. Educational
attainment is strongly correlated with income; the more education, the higher the income.
General mental ability is positively correlated with income, educational attainment, and core
self evaluations. It appears that good looks, intelligence, and a self-confident personality are
all important in explaining income (Judge, Hurst, and Simon, 2009).
A question students might ponder is whether they should spend their hard-earned money on
education or on cosmetic surgery. The good news for educators is that the simple correlation
between income and intelligence (.50), and income and educational attainment (.46), was
much higher than that of income and physical attractiveness (.24). Of course, the
combination of intelligence, education, and good looks cannot hurt in the job market (judge,
Hurst, and Simon, 2009).
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How important is weight when it comes to salary? A study by Judge and Cable (2011)
provides the answer to that question. It appears that overweight men and very thin women
do much better in the workplace than skinny men or plump women. According to the study:
average weight American women will earn almost $400,000 less across a 25-year career than
women who weigh 25 pounds less than their group mean. It does pay to be very thin if you
are a woman. As far as men, skinny individuals who are 25 lbs. below the average weight
for men will earn almost $211,000 less over a 25-year career than men who are at the mean
weight. For men, being thin is a problem when it comes to pay. Judge and Cable (2011) use
cultivation theory to explain these findings. According to this theory, the media acts as a
storyteller and affects our expectations as to what is the “ideal representation of reality.” In
the media (television, magazines, etc.) the ideal beauty of today is a very slim woman; with
men, on the other hand, the most handsome men are not skinny and tend to be beefy and
muscular. The authors conclude: “As such, it is troubling that average weight women and
thin men are penalized in the employment contest, whereas very thin women and men of
average or above-average weight are rewarded.” There is certainly no relationship between
job performance and being somewhat underweight or slightly overweight.
Sports
Many students will have seen the film, “Moneyball,” based on the book by Michael Lewis
(2003) with the same title. It is the story of Billy Beane, General Manager of the Oakland
A’s baseball team and how he used statistics to win several playoffs despite the fact that the
team had a payroll that was a fraction of the powerhouse teams such as the NY Yankees.
20
Beane was fascinated by Sabermetrics (Society for American Baseball Research). The key
person among the sabermetricians – a group of statisticians – was Bill James, who did much
of this work while working as a security guard. James had demonstrated using statistics that
many traditional baseball strategies were of no value. One measure developed by the
sabermetricians was OPS (on-base plus slugging). This measure combined on-base
percentage and slugging average (Kuper, 2011; Sternbergh, 2011).
The Oakland A’s had no money and were desperate to find talented baseball players but at a
low price. Between 1999 and 2006, Moneyball worked for Oakland and they won more
games than they lost. They did best in 2002 when they won 64% of their games despite
having a bunch of rejects as players. What they did was look for players who excelled in
aspects of the game that were not considered important, e.g., drawing walks. The money
players hit home runs and excel in runs batted in (RBIs). Moneyball stopped working once
other times starting using it. In fact, the New York Yankees now have 21 statisticians
working for them. Moneyball statistics are now being used in other sports (Kuper, 2011;
Sternbergh, 2011).
Education
When it comes to education, the public does not know who to believe: the unions, teachers,
administrators, or the politicians. What is known is that the United States is falling behind
many other countries.
21
One education myth is that the best way to learn is in a traditional face-to-face classroom
setting. The evidence, however, does not support this view. Means et al. (2009) did a meta-
analysis of more than 1,000 studies published from 1996 to 2008 comparing online with
traditional classroom teaching. What they found was that online learning does offer many
advantages over traditional classroom learning. In fact, students who take courses that are
either completely or partially online will perform better than students taking traditional, face-
to-face courses. Interestingly, hybrid courses that combine classroom learning with online
learning seem to be the best of all delivery methods. They acknowledge that there were very
few studies done comparing the different delivery methods for K-12 (kindergarten through
12 th
grade) students. Therefore, one must be cautious before generalizing their results to all
levels of education before additional studies are conducted contrasting online and face-to-
face learning at the K-12 level.
There is another area of disagreement in the field of education. Does class size affect student
performance? Numerous studies have been done comparing small classes with large classes.
The results have been mixed. There is some agreement that small classes can have a
significant impact on achievement in grades K-3. After that, the results are mixed. Other
interesting findings are that the optimum class size if a school wishes to maximize student
achievement is 18 students per teacher. Minority students in particular benefit greatly from
small classes in K-3 (Center for Public Education, 2009).
There is also a bigger question that has yet to be answered: Should money be spent on
reducing class size or on improving teacher effectiveness. The cost of reducing class size is
22
quite high and will require a huge increase in the number of teachers, many of which may not
be effective.
Conclusion
The above examples and cases from many different areas of research including health,
education, sports, school ratings, crime, etc. should help statistics instructors make their
courses more interesting. In addition, these examples and cases, we feel, will answer the
question students often ask: “Why do I need to learn this?” Having looked at these
examples, we can safely say that whatever path our students will follow through life,
statistics will likely be critically important to understanding their professions and the world
around them.
23
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