3 M I N U T E R E A D7 Ways To Lie WithStatistics And .docx

3 M I N U T E R E A D
7 Ways To Lie With
Statistics And Get Away
With It
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What does excess email usage have to do with low IQ
scores? Nothing at all, but that doesn’t mean
someone didn’t to make a point.
I don’t know about you, but I am tired of the
incorrect, misleading, or just plain bogus statistics
used to sell me a product, elicit support for a
candidate, or get me to ‘Like’ some new trend. I’m
mad as hell and I’m not going to take it
anymore...and neither should you.
Misleading with statistics is called ‘statisticulation’

and it is nothing new. In 1954, former Better Homes
and Gardens editor Darrell Huff wrote a small book
called, , which is the best-
selling statistics book of the last 60 years, according
, a professor of statistics and
operations and information management at
Wharton.
What was true in 1954 is just as true today. According
to Huff, here are seven common tactics used to knead
statistical data into "dough."
create a connection
How To Lie with Statistics
J. Michael Steele
• Biased sampling: This involves polling a
non-representative group. For example, a
survey that finds "41% of retail bank customers
would use mobile banking if it were available,"
becomes meaningless when you find out the

survey only polled people on their mobile
devices.
• Small sample sizes: Picking an
adequate sample size is part science and part
art, but sweeping statements, like "14% of
companies plan to deploy cloud-based email
this year" becomes suspect when the sample
size is 24 companies. Another example of this
kind of ‘statistics gone wild’ phenomenon was a
" " conducted by HP that found excessive
email usage reduces a person’s IQ by 10 points.
study
• Poorlychosen averages: This often
involves averaging values across non-uniform
populations. For example, I recently saw an
article that identified a neighborhood as one of
the wealthiest in the city. The article went on to
state that neighborhood residents had an
average annual income of around $100,000.
What the article failed to point out is that the
neighborhood is in the process of
gentrification; one part of the neighborhood is
very wealthy, and the other part’s income
levels are below the national average. Giving a
single average value for two populations is

incorrect and misleading. (The median value
for income would be a better indication of the
neighborhood income.) Another classic
example of this is the story about the man who
drowned in a pool of water whose average
depth was 1 inch.
• Results falling within the standard
error: No sampling or measuring technique
is perfect; all inherently incorporate a degree
of error. This means that a survey can only be
as accurate as its standard error. Without
getting technical, suffice it to say that the
headline, "E-books Preferred Over Paper By
Men More Than By Women" sounds
remarkable until you find out that of the actual
polling results found that 52% of men preferred
T E C H N O L O G Y L E A D E R S H I P M A G A Z I N E
M O S T I N N O V A T I V E C O M P A N I E S M O S T C
R E A T I V E P E O P L E V I D E O N E W SM E N U S U
B S C R I B E
e-books versus 49% for women, and the error
of the survey was +/-5%.
• Using graphs to create an
impression: Both of the charts below contain
exactly the same information, but which one
more accurately shows the increase in venture
capital investment in mobile technologies

between the years 2006-2007? The only
difference between the graphs is the
scale. Graphing data creatively provides a lot
of room for creating false impressions. The
same goes for pictograms and infographics.
• "The semi-attached figure": This means
stating one thing as a proof for something else.
For example, if an ad says "15% of CEOs drive
a Buick; more than any other brand"— what
does that prove? The implication is that CEOs
are some sort of authorities on cars. This is a
common tactic. Remember the old Certs
commercials, where the narrator says, "Certs.
Now with Retsyn!" Did anyone even know
what Retsyn is or why should we care?
• "Posthoc fallacy": This is incorrectly
asserting that there is a direct correlation
between two findings. This is particularly
nefarious but it is often more difficult to catch

than the other tactics. For example, if a study
finds that vegetarians have a higher average
T E C H N O L O G Y L E A D E R S H I P M A G A Z I N E
M O S T I N N O V A T I V E C O M P A N I E S M O S T C
R E A T I V E P E O P L E V I D E O N E W SM E N U S U
B S C R I B E
Huff presents an entire chapter of how to identify
spotty statistics, which I will revisit those in a future
post. In the meantime, the best advice, as always, is
to be skeptical. Caveat emptor!
I am collecting stories about bogus, misleading, or
inaccurate marketing statistics; please send me
stories to or tweet me
.
Author David Lavenda is a high tech marketing and
product strategy executive who also does academic
research on the effects of information overload on
organizations. He is an international scholar for the

Society for the History of Technology.
[Image: Flickr user ]
income than meat-eaters, it would be absurd to
conclude that you can raise your income by
abstaining from meat. But that is exactly what
some ‘researchers’ do.
[email protected]
@dlavenda
MervC
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4 M I N U T E R E A D W O R K S M A R T
Exactly What To Do To
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Exactly What To Do To
Convince Your Boss To
Let You Work From Home
On Fridays
[Photo: clownbusiness/iStock; App Photo: Vincent van Gogh's
"Bedroom in
Arles"]
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Trust and results are essential when you are making a
play to work from home.
If you think working from home on Fridays sounds
good, you’re not alone. "Flexible work hours" is the
most desired benefit among workers, with more than
half of adult U.S. workers picking it as their top perk,
according to the technology staffing firm .
While 80% of companies offer flexible hours, just
44% advertise this to employees, according to a
by WorldatWork, the nonprofit human resources
association. That means working from home on

Fridays might be as simple as asking.
"When a company values an employee, managers are
usually willing to have a conversation about working
from home, and often are willing to work out some
type of an agreement when feasible," says MaryAnne
Hyland, professor of human resource management at
the at
Adelphi University.
The real issue is about trust, says Anna Conrad,
founder of , a Denver-
based leadership development and consulting firm.
"You are asking your manager to trust not only your
willingness to stay focused and work, but your ability
to work autonomously with little or no guidance," she
says.
PREPARATION IS KEY
Before you ask, Conrad suggests knowing how you
will use your time and how you will provide evidence

of the work you accomplished. "This is especially
critical during the first month when trust is being
established," she says. "Assure your manager you will
be readily available when needed, just as if he wanted
to stop by your cubicle."
Modis
study
Robert B. Willumstad School of Business
Impact Leadership
Solution
s
You also have to prove that you can work
autonomously. Consider your last performance
review, suggests Conrad. "Was any of the feedback
related to your inability to get things done with little
or no guidance? Was any of it related to your inability

to meet deadlines?" she asks. "If your answer to
either of these is ‘yes,’ explain to your manager things
you have done to prove this is no longer an issue."
You also need to make sure you have the required
information technology tools and skills, says
, author of "High-speed
internet and excellent telephone service are required
at your home office," she says. "Working from
Starbucks every Friday is not a sufficient
arrangement. And make sure you have an Ethernet
cable so you can hardwire into your router if your
computer has a Wi-Fi issue," she cautions. "It
happens. Be prepared."
Finally, think about your typical Friday schedule and
identify how telecommuting might enhance it, says
Jones. "For example, you have reports to complete,
and working from home allows you to concentrate
with fewer interruptions," she says. "Or you have a
day full of conference calls, and you can focus
without your cubicle neighbor's noise and
distractions."

HOW AND WHEN TO ASK
Timing is everything. "You can’t just stand up on
your desk one Friday afternoon and declare, ‘From
now on, I will work from home!’ says Ramit Sethi,
author of . "Everyone will
think you’re a weirdo, and building security will
usher you out of the office," says Sethi.
Wilma
Jones Is It Monday Already?!
I Will Teach You To Be Rich
The best time to ask is immediately after you’ve
received a glowing performance review or had a
business success, says Sethi, and approach the topic
using the "ARMS" technique:
Sethi suggests starting the conversation like this: "I’d

love to provide even more value to the company in
the future. But lately, I’ve been getting burnt out
from the commute. It would make a world of
difference if I could work from home a day or two
each week."
If your manager says ‘no,’ adding that it isn’t a perk
the company offers, agree with what was said, and
then reframe your request by turning it into an
opportunity. For example: "I understand that Acme
Co. hasn’t done it in the past. But this could be a
great opportunity for the company. If it works out, we
can find candidates in other states for X role that
we’ve had a hard time filling. And given my track

record here, testing it out with me on a small scale is
low risk. If it doesn’t work out, we can always go back
to the old way."
After you’ve made your case, shut up and wait, says
Sethi. "The important thing to remember is that
you’re proving the concept for now. Once your boss
agrees to this small request, and it works out well,
they’re more likely to agree to you working from
home regularly," he says.
STRENGTHEN YOUR CASE
• Agree
• Reframe

• Make your case
• Shut up
STRENGTHEN YOUR CASE
You can improve your odds of getting a 'yes' if you
share research that shows employees who have
flexible work arrangements are actually more
productive than those who don't, adds Katina
Sawyer, assistant professor of psychology and
graduate programs in human resource development
at . "This may be because
employees feel valued and trusted, or it may be
because it allows employees to better multitask," she
says.
Finally, do your homework to find out if there are
other employees in your department that currently
have approval to telework, says Jones. "If their
situation is working well, accentuate how your
arrangement would be similar or even better," she
says. "If it's not going very well, contrast how you
would handle your telework arrangement to ensure

the same concerns will not exist with you."
Villanova University
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Chapter X Randomness and Uncertainty

Reports that say that something hasn't happened are always
interesting to me, because as we know, there are known knowns;
there are things we know we know. We also know there are
known unknowns; that is to say we know there are some things
we do not know. But there are also unknown unknowns – the
ones we don't know we don't know. Donald Rumsfeld, February
12, 2002
What do randomness and uncertainty have to do with clear
thinking? Isn’t randomness the antithesis of thinking? It might
be surprising that there is an element of randomness in most
things we do. Without randomness, we would get exactly the
same result each time we repeated the exact same action. The
drive to work would be completely predictable, friends would
always react the same way, and sports would be boring to
watch. Even if something seems like it should be completely
predictable, inherent variability comes into play. If the alarm is
set for exactly the same time every day, there are still bound to
be a few minutes of difference between the time it goes off and
the time you are ready to leave each day. Traffic is affected by
any number of variables; weather, the number of other drivers,
problems caused by other drivers cutting in and out of lanes,
and road construction. On any given day, these factors may or
may not affect what is usually a fairly predictable trip. While
clear thinking isn’t the result of randomness, it acknowledges

and accounts for randomness and uncertainty when making
choices and planning for the future.
Most people chronically underestimate the effects of
randomness. Good luck rarely gets the credit it deserves, while
bad luck receives too much blame. When we make plans, we
often forget to factor in variability.
Randomness is intrinsic to the laws of probability, with which
people also have trouble. However, it should be given its due.
Many times one’s efforts seem to be highly effective when, in
reality, external circumstances may be more responsible for
success. The converse is also true – a great decision cannot
always compensate for the effects of the economy, Mother
Nature, or changing consumer tastes.
What are the benefits of understanding randomness and
uncertainty? With the flood of information we are constantly
subject to, we need to know what to believe and what to ignore
and how to use information to make realistic decisions. Too few
people understand the difference between correlation and
causality, whether a new product or medical treatment will
make any difference in our well-being, whether we should risk
an investment, or what news is credible. A little skepticism
about claims can go a long way toward developing a realistic
view of the world. Understanding of the variability of the
conditions that shape our decisions will foster improved choices
and plans. The ability to recognize that something is a

coincidence, and not inherently meaningful, keeps us from
developing false beliefs. It’s important to know when
information is reliable and when it’s not. Choices, both
personal and professional, work out better when they are based
on reality, not assumptions or misperceptions.
What is Randomness?
What does it mean for something to be “random”? People use
the word random to describe events that are unexpected or seem
to be unrelated to the topic at hand (“That was a random
comment”). The typical definition is “without any discernable
pattern.” An easy way to understand randomness is to look at
examples from gambling.
The bouncing ping-pong balls that determine lottery winners are
drawn at random. Every ball has an equal chance of being
selected every time the lottery is played, despite beliefs about
lucky numbers or relatives’ birthdays. Although the balls can’t
remember which ones were drawn in the past, some people
persist in trying to find patterns, thinking they will improve
their chances of winning the jackpot.
Many people don’t know what randomness looks like. If
someone were asked to pick a random number between 1 and
50, few would select 1 or 50, even though those numbers are as
likely as something more “random-sounding” like 19 or 37. If

we flipped a coin repeatedly and saw the patterns HTHTHTHT,
HHHTTT, HHHHHT, TTTTTT, and HHTHTT, most people
would say the last one is random, but the others aren’t. The
truth is that they are all equally likely, because each coin toss is
an independent event – the coin doesn’t remember what the
outcome of the last flip was. Even though we eventually expect
an equal number of heads and tails from repeated flips, it takes
many, many flips to get this kind of result. This is due to the
“law of large numbers.”
Simply put, the law of large numbers says that as the number of
trials (flips of a coin, dice rolls, spin of a roulette wheel, pulls
of a slot machine lever, etc.) increases, the more likely the
average result will be the expected value (in this case, 50%
heads and tails). While a long series of trials will converge on
the expected value, short series seldom do. Most people know
that there is supposed to be a 50:50 chance of heads or tails, but
relatively few understand that this is the long-run outcome.
When there is a streak of several heads or tails in a row, it
seems surprising.
One phenomenon that sports fans wholeheartedly believe in is
the “hot hand.” This is the idea that an athlete is on a winning
streak (or conversely, a losing streak). The usual explanations
point to momentum or the confidence from one success leading
to another success. From a probability perspective, a hot hand
implies that when a player scores, the probability that he or she

will score on the next try should be higher than average.
Psychologists Robert Vallone and Tom Gilovich wondered
whether the hot hand could be documented, so they analyzed the
shooting records of each player on the Philadelphia 76ers for 48
games. Much to the dismay of players, coaches, and fans, they
found no evidence of a hot hand for any player. The reaction to
this finding was, and continues to be, disbelief. However, think
back to the coin-flipping example; remember that a series of
flips doesn’t usually alternate between heads and tails, even
though the average over the long run is 50:50. In a short series,
a streak of heads or tails may not look random, but it is. It’s
the same with the hot hand. Great players make more shots than
average players, but the likelihood that he or she will make the
next shot isn’t a function of the last shot. Since people are
generally not very good at recognizing randomness, and the idea
that momentum and confidence affect performance is very
appealing, the myth of the hot hand rings true despite reality.
The “gambler’s fallacy” is another common belief. When
someone is betting on a random outcome, like a particular
number on a roulette wheel, a common misperception is that the
longer he or she goes without winning, the more likely the
desired number is to come up. The problem is that each spin is
independent and the roulette wheel has no memory. Luck
doesn’t self-correct. The same is true for slot machines, the
lottery, and just about any other kind of gambling. Thinking

that they are due to win on the next spin, or the one after that,
or maybe the one after that, gamblers keep betting, often ending
up with significant financial losses.
What do these examples have to do with everyday life? You
don’t have to be a gambler to encounter problems caused by
misunderstanding randomness or probability. Believing that
success will continue based on prior success can lead to
overconfidence and less careful decision making. Continuing to
make risky decisions in an expectation that a win is due is
wishful thinking. There are three main areas in decision making
where understanding randomness will help you make better
choices and plans:
· Understanding cause and effect
· Developing more accurate expectations about future outcomes
· Being a smart consumer of information
Understanding Cause and Effect
Many athletes swear by pre-game rituals to give them an edge,
from lucky shirts to a specific way to tie shoes to special foods.
Michael Jordan, famed Chicago Bull basketball player, always
wore his University of North Carolina uniform shorts under his
Chicago uniform. These rituals may give athletes a boost of
confidence, but do they really cause better performance?

On a more serious note, a number of parents in the U.S. refuse
to vaccinate their children against childhood diseases such as
measles and whooping cough. The basis for this practice was a
now widely discredited paper by Andrew Wakefield, a British
doctor who claimed that childhood vaccination caused autism.
He subsequently lost his medical license for falsifying data.
Still, some Hollywood celebrities helped spread the idea that
vaccines contain harmful ingredients that cause autism, giving
legitimacy to the anti-vaccination trend in the eyes of some
parents. Despite wide agreement in the medical community that
there is no link between vaccines and autism, many parents
persist in refusing vaccinations for their children.
Vaccination provides “herd immunity” – if the majority of a
population is immune to a disease, it’s much less likely to
spread widely. In populations where the anti-vaccination
movement is strong, diseases such as measles, mumps,
whooping cough and chicken pox are on the rise. For most
healthy individuals, these illnesses cause minor discomfort for a
few days. However, for those with a compromised immune
system or infants too young to be vaccinated, these illnesses can
be severe or even fatal. How can we determine whether
vaccination causes autism?
If you have ever taken a statistics course, you will have heard
“Correlation does not imply causation.” Correlation is a
measure of the relationship between two variables, such as total

revenue and the amount of money spent on advertising or time
spent exercising and cardiovascular health. Correlation is
necessary to demonstrate causal relationships, but it’s not
enough. Two variables can be highly correlated such that an
effect is present when a possible cause is present and an effect
is absent when a possible cause is absent. That’s because other
variables might be responsible. For example, deaths from
drowning are highly correlated with ice cream consumption.
When ice cream consumption is high, deaths by drowning are
high. When ice cream consumption is low, deaths by drowning
decrease. Would water safety be improved if the ice cream
supply were restricted? Do people go back into the water too
soon after eating ice cream? In this case, the answer is
obvious. There is a correlation between deaths by drowning and
ice cream consumption because both swimming (and,
unfortunately, drowning) and eating ice cream occur more
frequently in hot weather and less frequently in cold weather.
To assess whether a causal relationship exists between two
variables, we need information about each variable. Let’s look
at the relationship between vaccination and autism. The
variables are whether or not a child is vaccinated and whether
or not the child is diagnosed with autism. According to the
Center for Disease Control, the current prevalence of autism in
the U.S. is about 1.5% among children aged 3 to 10. With a
sample of 100,00 children of whom 10% are not vaccinated, this

is what we would expect to see.
VaccinatedNot Vaccinated
Autism 1,350 150
No Autism 88,650 9,850
Total90,00010,000
The number of autism cases is proportional to the number of
children in each group. There are more autism cases in the
vaccinated group because there are 9 times as many children,
not because they were vaccinated.
If vaccinations did cause autism, our table should look more
like this.
VaccinatedNot Vaccinated
Autism 90,0000
No Autism 0 10,000
Total90,000 10,000
Of course, there might be cases of autism unrelated to
vaccination, and not every vaccinated child would end up with
an autism diagnosis, so these numbers are an exaggeration. But
the general pattern would look like this.
Here’s what you need to determine cause and effect:
Cause PresentCause Not Present
Effect PresentYesNo
Effect AbsentNoYes
If the possible cause is present, it should lead to the effect the

majority of the time, and it should seldom lead to cases where
there is no effect. If the possible cause is absent, there should
not be an effect, and most of the time, absence of the possible
cause should mean no effect.
Why do people falsely believe that one thing causes another,
when in reality there is no relationship? Essentially, they only
look at one cell of the table above – the cell for Cause Present
and Effect Present. When two events happen close together,
people sometimes think the first one caused the second one.
They forget to check whether other causes account for the effect
or whether the effect ever happens without the possible cause.
Interestingly, even pigeons can be conditioned to act
“superstitious” by providing food at predictable intervals that
have nothing to do with the bird’s behavior. (Pigeons are
usually trained by receiving food after they perform a specific
task.) The pigeons engage in behaviors like whirling around or
flapping their wings in a certain way – whatever they were
doing when the food first arrived. They look as though they
believe their behavior caused the food to appear and continue to
repeat the specific behavior so the food will keep coming.
When people hold strong beliefs, they are likely to see causality
when there is only coincidence. In the case of superstitious
sports stars, a good performance coincides with a lucky shirt (or
meal, socks, etc.). When the athlete seeks a reason for the
performance, attention falls on the shirt. Superstitions like this

are harmless, but when mistaken beliefs about causality affect
public health and policy decisions, we are worse off.
In business settings, there are numerous occasions when it’s
important to know whether two variables have a causal
connection. Do training programs improve employee
performance? If more funds are allocated to the social media
budget, will brand image improve in proportion to the extra
spending? Does increased customer satisfaction really increase
sales? Many online firms conduct A/B testing to determine
whether one variable has a causal relationship with another.
Too often, businesses don’t have the luxury to conduct those
real world experiments and must work with the data that are
available. In these cases, it’s important to look at all the
information that bears on the question, not just that which
supports the idea of a causal relationship.
Expectations about the future
Will the future be like the past?
It’s human nature to wonder what will happen in the future.
Most of us end up basing our predictions on our prior
experiences, or those of people we know. When thinking about
how you will do on a final exam, it’s natural to think about how
well you did on the midterm. If you have an exceptionally good
meal at a restaurant, you look forward to sampling it again.

How could randomness be part of predicting your performance
on an exam or the quality of a restaurant meal? If you aced
the midterm, shouldn’t you expect to ace the final?
You may well ace the final, but making that prediction just on
the basis of your midterm score is a mistake. Performance on
exams, quality of restaurant meals, stock prices, race times,
heights of siblings, download speeds, and almost anything else
that can be measured are a combination of an average
performance plus some random variation. Performance varies
from one time to the next, so a truly exceptional performance
(either positive or negative) is unlikely to be followed by
another that is equally exceptional. This is due to a
phenomenon called regression to the mean. The basic principle
is that over time, extreme values are followed by more moderate
values. Simply put, scores typically return to their long-run
average. That doesn’t mean extreme values can’t be followed
by other extreme values, just that it’s unlikely. With no
additional information, the average value is the best prediction.
If a student consistently aces all exams, his or her average
performance is pretty high and the student may well ace the
next one. For more typical students, an exceptionally high or
low score will likely be followed by something closer to his or
her usual score. If a restaurant meal is exceptional, it’s more
likely that the next one won’t stand out as much unless the
average quality is very high.

An easy way to understand this is to think about peoples’
heights. This is actually where the idea of regression to the
mean originated, with British scientist Francis Galton in 1886.
He noted that very tall people usually had tall children, but at
least some of them were shorter than their parents. Very short
people usually had short children, but at least some of them
were taller than their parents. If the children of tall people
were always taller than their parents, eventually their
descendants would be extremely tall. The same holds for short
people. Without regression to the mean, the range for adult
human height eventually might go from 1 foot to 12 feet, or
even more extreme sizes.
Regression to the mean should be taken into account when
making plans and predictions. One of several factors
contributing to the 2008 recession was an unrealistic belief that
housing prices only went in one direction – up. Had that been
the case, the risky loans made to homebuyers with bad credit
and few resources would have been secured by continually
appreciating assets. Instead, as was inevitable, home prices
fell. Because so many risky loans had been made, a cascade of
bad debt severely impacted the economy.
A similar phenomenon is the “Sports Illustrated effect,” where
some people believe a team that appears on the cover of Sports
Illustrated will be jinxed and perform worse following the cover
feature. Similarly, the performance of CEOs who appear on the

cover of Business Week often declines following the cover
story. Does this publicity really affect performance? It’s much
more likely that the events that prompted the athletes and
executives to be featured on magazine covers were outliers and
their performance returned to historic averages after the
magazine covers appeared.The problem with over-specified
plans
When we think about the future, we often engage in
daydreaming about what we think our lives will be like when we
finish graduate school, have a new job, move to a different part
of the country, or whatever other event we hope will actually
happen. The more detail we add, the more real it seems.
Daydreaming about the details of your future life is fun, but it
shouldn’t be the basis of planning. While details make your
daydreams seem more real, the more detail you add, the less
likely it is that those details will be correct.
This may seem counterintuitive, but the reason lies with a
simple rule of probability. The probability of two independent
events co-occurring is always lower than the probability of
either individual event. Probabilities are always between 0 and
1: a probability of 0 means the event will never happen and a
probability of 1 means that it is certain to happen. To
determine the joint probability of two events co-occurring (e.g.,
taking a specific job in a specific city) you multiply the

individual probabilities. So if you have a 20% chance of being
hired for a specific job and a 30% chance of finding a job in a
specific city, the probability of both happening is 6%. Every
time a detail is added, the joint probability is reduced. We will
see more about the probability of multiple events in later
chapters.
So, how should people think about the future? Do we need to
be statisticians before we can start making good plans? Should
uncertainty strike fear into our hearts? Absolutely not. The
most important thing to remember is that there is variability
around future events. Rather than making plans depend on a
specific outcome, we need to try to figure out a likely range of
outcomes. Remember that trends rarely continue in a single
direction indefinitely. Investment firms always include the
statement, “Past performance does not guarantee future results.”
It’s true well beyond the domain of stock prices. Rather than
evoking fear, accounting for uncertainty will lead to plans that
are more realistic and flexible.
The best way to account for uncertainty is to first establish what
is known and what is unknown, then develop estimates for the
likelihood of different situations. With the combination of what
is known and what is estimated, different contingency plans can
be developed. This may seem a bit formal, but for important
decisions it’s worth taking the time to be as accurate as
possible.

Following some significant intelligence failures, such as the
prediction that weapons of mass destruction would be found in
Iraq prior to the Gulf War, the Intelligence Advanced Research
Projects Activity funded research into how to improve
predictions. In response, psychologists Philip Tetlock and
Barbara Mellers developed the Good Judgment Project to
understand the characteristics of people who were good at
predictions and what might make them even better. The key
factors turned out to be training in basic probability theory,
education about cognitive biases, and working in a team that
included both specialists and generalists. Keeping track of
results and forming teams of “superforecasters” led to accuracy
that was almost double that of people with no training.
Being a smart consumer of information
More than 60 years ago, Darrell Huff published a small book
titled How to Lie with Statistics. The purpose of the book was
to help people understand how statistics in the news and
advertising could be technically correct, but misleading,
depending on the purpose of the news report or the ad. This
slim volume had dozens of printings and ultimately over half a
million copies were purchased. The examples Huff used were
tied to 1950s era concerns, but decades later the underlying
message is still important.

We hear statistics about government, sports, political races,
traffic accidents, crime and a myriad of other topics. Are we in
a recession or a recovery? How can the unemployment rate go
up when more new jobs are being created? The news is full of
reports about purported causes of cancer, heart disease, and
other health issues. Advertising makes promises that products
will make us more attractive, energetic, and slimmer. Should
we eat dark chocolate for its antioxidants or avoid it because it
might contribute to obesity and diabetes? Should we run for
cardiovascular health or walk to avoid joint damage? Do we
need to buy a standing desk to avoid the effects of too much
sitting? We often forget that news programs shape their
programming to maximize ratings and advertisements are
designed to influence our spending, not to help us make good
decisions.
Many of us glaze over at the mention of statistics. But statistics
is interesting because it enables us to summarize information in
order to learn about the world. Statistics is a tool to understand
whether a change has happened or not, whether variables are
related; a way to detect a signal in the noise of randomness.
Unfortunately, someone with an agenda can easily “lie with
statistics” to mislead us. We don’t have to look too far for
examples.
During the lead-up to the Brexit vote, in which Britain voted to
leave the European Union, the Vote Leave group repeatedly

claimed that the United Kingdom sent £350 million every week
to the European Union. This was true – but something was
missing. The European Union refunded about two-thirds of that
amount, so the net figure was actually £100 to £125 million.
A recently published study reported in the Wall Street Journal
(8-29-16) was titled “Eating Fruit While Pregnant May Boost
Your Baby’s Intelligence,” with a subtitle of “Infants whose
mothers ate more fruit were smarter one year after birth, a
preliminary study shows.” Fruit is part of a healthy diet, so this
news is not exactly earthshaking. However, the claim that the
fruit eaten during pregnancy is the reason for a baby’s higher
intelligence is stretching what the scientists found. Researchers
looked at cognitive development scores for 688 infants and
related the scores to data from a survey the mothers completed
during pregnancy. The finding was that there was a statistically
significant relationship between self-reported fruit consumption
and a composite of the scores on the Bayley Scales of Infant
and Toddler Development at age one. Test scores are not the
same as intelligence, and the increase in scores was 2.38 points
per serving of fruit, well within the standard deviation of the
Bayley Scale, which has a mean of 100 and standard deviation
of 15. The authors of the research study were careful to state
that these results are preliminary and that cognitive
development scores at one year don’t predict cognitive
development scores at the age of three. The journalist made a

claim in a catchy headline about intelligence, but the
researchers were talking about test scores at age one, not
intelligence, which is a much more complex concept.Questions
to Ask
There are a few things to keep in mind when someone is using
statistics to support a point of view. In How to Lie With
Statistics, Darrell Huff characterized these issues in a chapter
titled “How to Talk Back to a Statistic.”Who Benefits?
First, does the sponsor of the research have a reason to favor
one side of the argument? Here are two examples from
nutritional research where this question needed to be asked.
The California Walnut Commission sponsored a study that
found eating walnuts improved the health of people at risk for
diabetes. Another study found that Concord grape juice
improved driving performance and spatial memory among
mothers of pre-teens included an author who was an employee
of a major grape juice provider. It’s entirely possible that these
findings are legitimate, but in many cases, studies that are
funded by organizations with a vested interest in the results
tend to show more positive findings than studies funded by
neutral organizations. How Do They Know?What Sample?
A second issue to consider is the nature of the sample. Two

factors matter here: the size of the sample and how the people
in it were selected. When a sample is large, the data it provides
is more likely to be true of the population the sample represents
because of the law of large numbers. When the sample is small,
you really can’t draw solid conclusions from the data.
Problems with sample selection occur for a number of different
reasons. The ideal sample is one that accurately represents the
population of interest. Finding a truly random sample to answer
a pollster’s survey is difficult. If you select people from a
telephone directory, you’ll miss the growing number of those
who only use cell phones. With the prevalence of caller ID,
many people won’t answer the phone unless they recognize the
caller. If your survey is online, you miss the population that
doesn’t use the Internet.
There are many reputable polling organizations that take pains
to sample respondents and report statistics properly. Gallup,
Pew Research, Harris and NORC (National Opinion Research
Center) all apply sophisticated approaches to sampling and
analyzing opinion data, so you can be confident in what
organizations like these report.Which Average?
There is a joke about Microsoft founder Bill Gates walking into
a bar and everyone in the bar being happy because their average
income just went up dramatically. Technically, a scenario like
that would be true (about the average, not necessarily the

happiness) – if the mean is the average that you use. Income
distributions are almost always positively skewed, meaning that
there are some individuals whose income is high enough to
distort the mean in a positive direction. If the distribution
weren’t skewed, the mean would be very close to two other
average measures – the median and the mode. The median is
the number that divides the distribution in two, so that half of
the people make less than the median and half make more.
Medians are usually used to report income, housing prices and
other government statistics because they aren’t sensitive to
extreme values like Bill Gates’s income. The mode is the most
frequent value in a distribution and isn’t used as commonly as
means and medians. You would use a mode if you wanted to
figure out which item (or flavor or size) was the most popular.
So, when you hear a news story that reports average income,
prices, scores on educational tests, or any of a host of other
topics, keep in mind which average is being reported.What’s
Missing?
When a new medical study comes out, we are often warned that
the risk of contracting a disease is increased by 50% among
people who fit a certain profile or promised that a new drug will
reduce the time required to recover from an illness by 20%.
What is left out is what is called the “base rate;” how many
people are affected by the disease or how long people are

typically sick. For example, Tamiflu is widely prescribed for
the flu because it cuts the duration of the illness by 20% when
taken within 36 hours of symptoms. The flu will make most
people miserable, but the misery usually lasts about 5 to 7 days
without medication. Tamiflu reduces the duration by 20% - to
about 4 to 6 days (from 123 hours with a placebo to 98 hours
with the drug, according to a 2015 study).
Since 1997, direct to consumer advertising for pharmaceuticals
has become widespread in the U.S. Although ads must include
disclosures about possible side effects, they rarely discuss the
risks and benefits of drugs in a transparent way. Most ads
mention benefits as a relative risk, such as a 50% reduction in
developing a disease. What is missing is absolute risk, without
which you can’t tell whether the 50% reduction is meaningful.
Does the 50% reduction mean that only 100 of 1000 people
would develop the disease compared to 200 of 1000 without the
drug? Or does it mean that only 1 of 1000 people would
develop the disease, compared to 2 of 1000 people without the
drug? The 50% reduction in relative risk is correct in both
cases, but the extent of the absolute risk is different by two
orders of magnitude. You can’t really get an idea of the risk
unless you know the base rate. That’s why (from a marketing
perspective) many pharmaceutical ads mention benefits only in
relative terms without including information about the absolute
risk.Does the picture tell the true story?

Many arguments are made using information presented in
charts. Well-constructed charts convey information more
quickly than tables and make it easy to understand relationships
that otherwise might be difficult to discern. Unfortunately,
charts are susceptible to the same kinds of manipulation as
statistics. Can you tell what’s wrong with the following chart?
It documents gun deaths over time in Florida, with a special
emphasis on 2005, the year the “Stand Your Ground” law was
passed.
The vertical axis starts at 1,000 rather than zero, so what you
might normally interpret as a decline when the law was enacted
in 2005 is actually a steep increase. This chart drew media
attention because it was so misleading.
There are many ways charts can mislead. As in this example,
axes can be misleading, especially when they start at a number
other than zero. Pie charts are often used inappropriately (they
should only be used to indicate proportions within a whole), and
sometimes add to more than 100%. Some figures on
infographics represent more of a difference between items than
is warranted, because the area of the figures varies in two
dimensions when the numbers they represent vary only in one.
When someone has a point of view they are trying to sell you,
be sure to look at how they are presenting the data.

Applications
The benefits of understanding the basics of randomness,
uncertainty, and probability are similar in both personal and
managerial settings. You will be at a significant advantage
because the evidence is that far too few people understand these
topics, even those who are educated. You will be less
susceptible to questionable claims and better able to assess
possibilities. Your plans will account for uncertainty and be
more realistic. There are two major types of benefits associated
with understanding randomness, probability and uncertainty.
The first is greater clarity in your thinking. The second is that
you will be able to make plans more successfully. Both benefits
apply to personal and business life.Clarity
The ability to discern when something is random or not is
helpful when you are trying to understand why things happened
and whether a causal relationship exists. When you see a true
causal relationship, your actions will be more effective and you
will be able to avoid problems. When you know something is
random, you can stop wasting time trying to change it. You
won’t be fooled into thinking something will succeed just
because there’s been a long string of misses.
When you understand the principle of regression to the mean,
you will have more realistic expectations about future events.

Spectacularly good and spectacularly bad events can occur to
anyone, but they are unlikely to be repeated and shouldn’t be
taken as an indication of how future events will unfold.
Investors who do the best tend to be the ones who don’t react on
the basis of day-to-day swings in the market. Instead, they
recognize that outliers occur on both the positive and negative
side and focus on the long-term return. The less fortunate
investors are those who check their portfolios daily, reacting to
what is essentially random noise.
Understanding which events are meaningful and which are just
noise requires a skeptical eye. Inclusion of base rates helps you
understand whether a risk or benefit is significant or not.
Statistics are so easily distorted that it’s worth your while to
consider the source and ask the basic questions:
· Who says so?
· How do they know?
· Are they comparing apples to apples?
· Do they have an interest in a particular
interpretation?Planning
Planning involves making choices about what we will do in the
future on the basis of what we expect the state of the world to
be in the future. The problem is that the future is uncertain,
except as Benjamin Franklin famously noted, “… in this world
nothing can be said to be certain, except death and taxes.”

What we want to be true in the future doesn’t necessarily have
an impact on what will happen. If you don’t smoke, eat wisely,
and stay fit, you will be more likely than not to enjoy a long
and energetic life, but there’s no guarantee. You may want to
win the lottery and quit your job, but the probability remains 1
in 292 million, so you’ll likely need to find an alternative for
retirement. Rare events do happen, but they are by definition
rare.
How can understanding randomness and probability help in
planning? If your plans depend on economic conditions,
competitors’ responses, and consumer demand, you are already
well aware that the past doesn’t predict the future. Certainly the
present and recent past provide a baseline to initiate planning,
but how can you go beyond looking at the past and present to
predict the most likely future?
As mentioned above, regression to the mean should be taken
into account when trying to determine whether trends are likely
to continue. Extreme results are most often outliers, so unless
you can identify the specific causes and can expect those causal
factors to continue to impact your business, you are better off
with a more moderate forecast. If you are experiencing
phenomenal success, how much of it can be attributed to you or
your firm’s actions and how much can be attributed to external
factors? Similarly, if you’ve had a disastrous year, can you
identify the causes? Was it something over which you had

control?
To make good predictions, you need to distinguish those aspects
of your life or your business that you can’t control. For each of
these, what is most likely to happen? How much variability
exists? For example, if you are a manufacturer, what factors
affect your supply chain and how likely are they to occur? The
2011 earthquake and subsequent tsunami in Japan led to
massive shortages in the automotive supply chain. These
shortages affected not only Japanese carmakers, but an
estimated 350,000 – 400,000 fewer vehicles were produced in
the US due to parts shortages. While it isn’t possible to predict
specific earthquakes, Japan is part of the “Ring of Fire”, a
seismically active area that stretches around the Pacific from
New Zealand to Chile and is home to about 90% of the world’s
earthquakes and most of the active volcanoes. Earthquakes are
a fact of daily life in Japan, although most are quite minor.
They are unpredictable as far as timing, but they are
unsurprising due to Japan’s location. It is more surprising that
automakers did not already have plans in place to deal with the
aftermath of a severe earthquake. In the spring of 2016, two
major earthquakes again struck Japan, but this time the impact
on the supply chain was less severe – automakers had adopted a
policy of multiple sources for parts. While they didn’t know
when the next big earthquake would be, they knew it was
coming eventually and developed a back-up plan.

Our plans are typically affected by factors that are much more
predictable than earthquakes. Most guides to business planning
recommend a standard list of items to consider. That’s a great
starting point. How can we improve on that list?
A useful planning exercise, developed by psychologist Gary
Klein, involves imagining the project you are planning has
failed, then coming up with as many plausible reasons for
failure as you can. The benefit of the exercise, which is usually
done with other members of your workgroup, is that you have to
think carefully about threats to your success. In the process,
issues often surface about which no one has thought much, but
many will recognize as potentially important. These are
examples of “unknown unknowns,” to use Donald Rumsfeld’s
phrase.
Like earthquakes in Japan, severe weather events can be hard to
predict. A truly unusual event, like a blizzard in Georgia, is
probably an outlier; but a blizzard in Chicago is a typical winter
event. There are regions of the US where floods, blizzards and
tornadoes occur often enough to be included as a risk in plans.
We can’t really plan for an unexpected extreme event, but we
should have contingencies in place for the unsurprising extreme
event, the “known unknowns”.
Planning should include estimations of probabilities for events
that can affect you or your business, along with what the
consequences of those events are. For example, how likely is a

significant increase in the price of gasoline? If you drive a
hybrid car, it wouldn’t affect you significantly, but someone
with a fleet of delivery vehicles could be severely impacted.
The probability of the price increase is the same in both cases,
but the consequences are very different. Thinking through
issues in this way will help you distinguish the risks you should
worry about from the ones you can let go.
Along with probability estimates, remember that the probability
of independent events co-occurring is always a lot lower than
the probability of each occurring separately.
When we don’t incorporate randomness and uncertainty into our
thinking, our vision of the future tends to be flawed. We can
mistake coincidence for causality and develop false beliefs. We
make plans as though the present state of the world will
continue into the future. That’s fine as a starting point, but it’s
important to remember that the future comes with a range of
outcomes, not just the ones we want.
Quick Tips to Deal with Randomness
Before accepting a claim that one thing causes another, ask
yourself
· Does the outcome ever occur without the cause?
· Does the cause always lead to the outcome?

· Does the person making the claim have a strong belief about
the topic?
When assessing risks, be sure to include the base rate for the
risk occurring.
Planning and decisions should include a process to account for
the following:
· What is the most likely outcome if you continue your current
actions?
· Are you keeping track of what happened as a result of prior
decisions?
· What are the uncontrollable factors in your situation?
· What is the range of outcomes that could result from
uncontrollable factors?
· Are you paying attention to base rates?
When you hear news about polls, health, the economy, and
potential risks, ask yourself
· Who says so?
· How do they know?
· Is the quantitative information communicated appropriately?
· Are comparisons being made on the same scale?
1

1
Randomness
and
Uncertainty
Reports
that
say
that
something
hasn't
happened
are
always
interesting
to
me,

because
as
we
know,
there
are
known
knowns;
there
are
things
we
know
we
know.
We
also
know
there
are
known
unknowns;

that
is
to
say
we
know
there
are
some
things
we
do
not
know.
But
there
are
also
unknown
unknowns
–
the
ones

we
don't
know
we
don't
know.
Donald
Rumsfeld,
February
12,
2002
What

do
randomness
and
uncertainty
have
to
do
with
clear
thinking?
Isn’t
randomness
the
antithesis
of
thinking?
It
might
be
surprising
that

there
is
an
element
of
randomness
in
most
things
we
do.
Without
randomness,
we
would
get
exactly
the
same
result
each

time
we
repeated
the
exact
same
action.
The
drive
to
work
would
be
completely
predictable,
friends
would
always
react
the
same
way,

and
sports
would
be
boring
to
watch.
Even
if
something
seems
like
it
should
be
completely
predictable,
inherent
variability
comes

into
play.
If
the
alarm
is
set
for
exactly
the
same
time
every
day,
there
are
still
bound
to
be
a
few

minutes
of
difference
between
the
time
it
goes
off
and
the
time
you
are
ready
to
leave
each
day.
Traffic
is
affected

by
any
number
of
variables;
weather,
the
number
of
other
drivers,
problems
caused
by
other
drivers
cutting
in
and
out
of

lanes,
and
road
construction.
On
any
given
day,
these
factors
may
or
may
not
affect
what
is
usually
a
fairly
predictable
trip.

While
clear
thinking
isn’t
the
result
of
randomness,
it
acknowledges
and
accounts
for
randomness
and
uncertainty
when
making
choices
and
planning

for
the
future.
2
Most
people
chronically
underestimate
the
effects
of
randomness.
Good
luck
rarely
gets
the
credit

it
deserves,
while
bad
luck
receives
too
much
blame.
When
we
make
plans,
we
often
forget
to
factor
in
variability.

Randomness
is
intrinsic
to
the
laws
of
probability,
with
which
people
also
have
trouble.
However,
it
should
be
given

its
due.
Many
times
one’s
efforts
seem
to
be
highly
effective
when,
in
reality,
external
circumstances
may
be
more
responsible
for

success.
The
converse
is
also
true
–
a
great
decision
cannot
always
compensate
for
the
effects
of
the
economy,
Mother
Nature,

or
changing
consumer
tastes.
What
are
the
benefits
of
understanding
randomness
and
uncertainty?
With
the
flood
of
information

we
are
constantly
subject
to,
we
need
to
know
what
to
believe
and
what
to
ignore
and
how
to
use
information
to
make

realistic
decisions.
Too
few
people
understand
the
difference
between
correlation
and
causality,
whether
a
new
product
or
medical
treatment
will
make

any
difference
in
our
well-‐being,
whether
we
should
risk
an
investment,
or
what
news
is
credible.
A
little
skepticism
about
claims
can

go
a
long
way
toward
developing
a
realistic
view
of
the
world.
Understanding
of
the
variability
of
the
conditions
that

shape
our
decisions
will
foster
improved
choices
and
plans.
The
ability
to
recognize
that
something
is
a
coincidence,
and
not
inherently

meaningful,
keeps
us
from
developing
false
beliefs.
It’s
important
to
know
when
information
is
reliable
and
when
it’s
not.

Choices,
both
personal
and
professional,
work
out
better
when
they
are
based
on
reality,
not
assumptions
or
misperceptions.
What
is

Randomness?
3
What
does
it
mean
for
something
to
be
“random”?
People
use
the
word
random

to
describe
events
that
are
unexpected
or
seem
to
be
unrelated
to
the
topic
at
hand
(“That
was
a
random
comment”).
The

typical
definition
is
“without
any
discernable
pattern.”
An
easy
way
to
understand
randomness
is
to
look
at
examples
from
gambling.

The
bouncing
ping-‐pong
balls
that
determine
lottery
winners
are
drawn
at
random.
Every
ball
has
an
equal
chance
of
being
selected
every

time
the
lottery
is
played,
despite
beliefs
about
lucky
numbers
or
relatives’
birthdays.
Although
the
balls
can’t
remember
which
ones

were
drawn
in
the
past,
some
people
persist
in
trying
to
find
patterns,
thinking
they
will
improve
their
chances
of
winning
the
jackpot.

Many
people
don’t
know
what
randomness
looks
like.
If
someone
were
asked
to
pick
a
random
number
between

1
and
50,
few
would
select
1
or
50,
even
though
those
numbers
are
as
likely
as
something
more
“random-‐sounding”
like
19
or

37.
If
we
flipped
a
coin
repeatedly
and
saw
the
patterns
HTHTHTHT,
HHHTTT,
HHHHHT,
TTTTTT,
and
HHTHTT,
most
people
would

say
the
last
one
is
random,
but
the
others
aren’t.
The
truth
is
that
they
are
all
equally
likely,
because
each
coin

toss
is
an
independent
event
–
the
coin
doesn’t
remember
what
the
outcome
of
the
last
flip
was.
Even
though
we

eventually
expect
an
equal
number
of
heads
and
tails
from
repeated
flips,
it
takes
many,
many
flips
to
get
this
kind
of

result.
This
is
due
to
the
“law
of
large
numbers.”
Simply
put,
the
law
of
large
numbers
says
that
as

the
number
of
trials
(flips
of
a
coin,
dice
rolls,
spin
of
a
roulette
wheel,
pulls
of
a
slot
machine
lever,
etc.)
increases,

the
more
likely
the
average
result
will
be
the
expected
value
(in
this
case,
50%
heads
and
tails).
While
a

long
series
of
trials
will
converge
on
the
expected
value,
short
series
4
seldom
do.
Most
people
know
that

there
is
supposed
to
be
a
50:50
chance
of
heads
or
tails,
but
relatively
few
understand
that
this
is
the
long-‐run
outcome.

When
there
is
a
streak
of
several
heads
or
tails
in
a
row,
it
seems
surprising.
One
phenomenon
that

sports
fans
wholeheartedly
believe
in
is
the
“hot
hand.”
This
is
the
idea
that
an
athlete
is
on
a
winning
streak
(or

conversely,
a
losing
streak).
The
usual
explanations
point
to
momentum
or
the
confidence
from
one
success
leading
to
another
success.

From
a
probability
perspective,
a
hot
hand
implies
that
when
a
player
scores,
the
probability
that
he
or
she
will
score
on

the
next
try
should
be
higher
than
average.
Psychologists
Robert
Vallone
and
Tom
Gilovich
wondered
whether
the
hot
hand
could

be
documented,
so
they
analyzed
the
shooting
records
of
each
player
on
the
Philadelphia
76ers
for
48
games.
Much
to
the
dismay

of
players,
coaches,
and
fans,
they
found
no
evidence
of
a
hot
hand
for
any
player.
The
reaction
to
this
finding
was,

and
continues
to
be,
disbelief.
However,
think
back
to
the
coin-‐flipping
example;
remember
that
a
series
of
flips
doesn’t
usually

alternate
between
heads
and
tails,
even
though
the
average
over
the
long
run
is
50:50.
In
a
short
series,
a
streak
of

heads
or
tails
may
not
look
random,
but
it
is.
It’s
the
same
with
the
hot
hand.
Great
players

make
more
shots
than
average
players,
but
the
likelihood
that
he
or
she
will
make
the
next
shot
isn’t
a
function
of
the

last
shot.
Since
people
are
generally
not
very
good
at
recognizing
randomness,
and
the
idea
that
momentum
and
confidence
affect

performance
is
very
appealing,
the
myth
of
the
hot
hand
rings
true
despite
reality.
The
“gambler’s
fallacy”
is
another
common
belief.
When

someone
is
betting
on
a
random
outcome,
like
a
particular
number
on
a
roulette
wheel,
a
common
5

misperception
is
that
the
longer
he
or
she
goes
without
winning,
the
more
likely
the
desired
number
is
to
come
up.
The

problem
is
that
each
spin
is
independent
and
the
roulette
wheel
has
no
memory.
Luck
doesn’t
self-‐correct.
The
same
is
true

for
slot
machines,
the
lottery,
and
just
about
any
other
kind
of
gambling.
Thinking
that
they
are
due
to
win
on

the
next
spin,
or
the
one
after
that,
or
maybe
the
one
after
that,
gamblers
keep
betting,
often
ending
up
with
significant
financial

losses.
What
do
these
examples
have
to
do
with
everyday
life?
You
don’t
have
to
be
a
gambler

to
encounter
problems
caused
by
misunderstanding
randomness
or
probability.
Believing
that
success
will
continue
based
on
prior
success
can
lead
to

overconfidence
and
less
careful
decision
making.
Continuing
to
make
risky
decisions
in
an
expectation
that
a
win
is
due
is

wishful
thinking.
There
are
three
main
areas
in
decision
making
where
understanding
randomness
will
help
you
make
better
choices
and
plans:

• Understanding
cause
and
effect
• Developing
more
accurate
expectations
about
future
outcomes
• Being
a
smart
consumer
of
information

Understanding
Cause
and
Effect
Many
athletes
swear
by
pre-‐game
rituals
to
give
them
an
edge,
from
lucky
shirts
to

a
specific
way
to
tie
shoes
to
special
foods.
Michael
Jordan,
famed
Chicago
Bull
basketball
player,
always
wore
his
University
of

North
Carolina
uniform
shorts
under
his
Chicago
uniform.
These
rituals
may
give
athletes
a
boost
of
confidence,
but
do
they

really
cause
better
performance?
6
On
a
more
serious
note,
a
number
of
parents
in
the
U.S.
refuse
to
vaccinate

their
children
against
childhood
diseases
such
as
measles
and
whooping
cough.
The
basis
for
this
practice
was
a
now
widely

discredited
paper
by
Andrew
Wakefield,
a
British
doctor
who
claimed
that
childhood
vaccination
caused
autism.
He
subsequently
lost
his

medical
license
for
falsifying
data.
Still,
some
Hollywood
celebrities
helped
spread
the
idea
that
vaccines
contain
harmful
ingredients
that
cause
autism,

giving
legitimacy
to
the
anti-‐vaccination
trend
in
the
eyes
of
some
parents.
Despite
wide
agreement
in
the
medical
community
that

there
is
no
link
between
vaccines
and
autism,
many
parents
persist
in
refusing
vaccinations
for
their
children.
Vaccination
provides
“herd
immunity”

–
if
the
majority
of
a
population
is
immune
to
a
disease,
it’s
much
less
likely
to
spread
widely.
In
populations
where

the
anti-‐vaccination
movement
is
strong,
diseases
such
as
measles,
mumps,
whooping
cough
and
chicken
pox
are
on
the
rise.
For

most
healthy
individuals,
these
illnesses
cause
minor
discomfort
for
a
few
days.
However,
for
those
with
a
compromised
immune
system

or
infants
too
young
to
be
vaccinated,
these
illnesses
can
be
severe
or
even
fatal.
How
can
we
determine
whether
vaccination
causes

autism?
If
you
have
ever
taken
a
statistics
course,
you
will
have
heard
“Correlation
does
not
imply
causation.”
Correlation

is
a
measure
of
the
relationship
between
two
variables,
such
as
total
revenue
and
the
amount
of
money
spent
on
advertising
or
time

spent
exercising
and
cardiovascular
health.
Correlation
is
necessary
to
demonstrate
causal
relationships,
but
it’s
not
enough.
Two
variables
can

be
highly
correlated
such
that
an
effect
is
present
when
a
possible
cause
is
present
and
an
effect
is
absent
when
a

7
possible
cause
is
absent.
That’s
because
other
variables
might
be
responsible.
For
example,
deaths
from
drowning

are
highly
correlated
with
ice
cream
consumption.
When
ice
cream
consumption
is
high,
deaths
by
drowning
are
high.
When
ice
cream

consumption
is
low,
deaths
by
drowning
decrease.
Would
water
safety
be
improved
if
the
ice
cream
supply
were
restricted?

Do
people
go
back
into
the
water
too
soon
after
eating
ice
cream?
In
this
case,
the
answer
is
obvious.
There

is
a
correlation
between
deaths
by
drowning
and
ice
cream
consumption
because
both
swimming
(and,
unfortunately,
drowning)
and
eating
ice
cream

occur
more
frequently
in
hot
weather
and
less
frequently
in
cold
weather.
To
assess
whether
a
causal
relationship
exists
between

two
variables,
we
need
information
about
each
variable.
Let’s
look
at
the
relationship
between
vaccination
and
autism.
The
variables

are
whether
or
not
a
child
is
vaccinated
and
whether
or
not
the
child
is
diagnosed
with
autism.
According
to
the
Center

for
Disease
Control,
the
current
prevalence
of
autism
in
the
U.S.
is
about
1.5%
among
children
aged
3
to
10.
With
a

sample
of
100,00
children
of
whom
10%
are
not
vaccinated,
this
is
what
we
would
expect
to
see.

Vaccinated
Not
Vaccinated
Autism
1,350
150
No
Autism

88,650
9,850
Total
90,000
10,000
8
The
number
of
autism

cases
is
proportional
to
the
number
of
children
in
each
group.
There
are
more
autism
cases
in
the
vaccinated
group
because
there

are
9
times
as
many
children,
not
because
they
were
vaccinated.
If
vaccinations
did
cause
autism,
our
table
should
look
more

like
this.
Vaccinated
Not
Vaccinated
Autism
90,000
0
No
Autism

90,000
10,000
Of
course,
there
might
be
cases
of
autism
unrelated
to
vaccination,
and
not

every
vaccinated
child
would
end
up
with
an
autism
diagnosis,
so
these
numbers
are
an
exaggeration.
But
the
general
pattern
would

look
like
this.
Here’s
what
you
need
to
determine
cause
and
effect:
Cause
Present
Cause
Not

Present
Effect
Present
Yes
No
Effect
Absent
No
Yes
If

the
possible
cause
is
present,
it
should
lead
to
the
effect
the
majority
of
the
time,
and
it
should
seldom
lead
to
cases

where
there
is
no
effect.
If
the
possible
cause
is
absent,
there
should
not
be
an
effect,
and
most
of
the
time,

absence
of
the
possible
cause
should
mean
no
effect.
Why
do
people
falsely
believe
that
one
thing
causes
another,
when
in

reality
there
is
no
relationship?
Essentially,
they
only
look
at
one
cell
of
the
table
above
–
the

9
cell
for
Cause
Present
and
Effect
Present.
When
two
events
happen
close
together,
people
sometimes
think
the
first
one
caused

the
second
one.
They
forget
to
check
whether
other
causes
account
for
the
effect
or
whether
the
effect
ever
happens
without

the
possible
cause.
Interestingly,
even
pigeons
can
be
conditioned
to
act
“superstitious”
by
providing
food
at
predictable
intervals

that
have
nothing
to
do
with
the
bird’s
behavior.
(Pigeons
are
usually
trained
by
receiving
food
after
they
perform
a
specific
task.)

The
pigeons
engage
in
behaviors
like
whirling
around
or
flapping
their
wings
in
a
certain
way
–
whatever
they
were
doing

when
the
food
first
arrived.
They
look
as
though
they
believe
their
behavior
caused
the
food
to
appear
and
continue
to
repeat

the
specific
behavior
so
the
food
will
keep
coming.
When
people
hold
strong
beliefs,
they
are
likely
to
see
causality
when

there
is
only
coincidence.
In
the
case
of
superstitious
sports
stars,
a
good
performance
coincides
with
a
lucky
shirt
(or

meal,
socks,
etc.).
When
the
athlete
seeks
a
reason
for
the
performance,
attention
falls
on
the
shirt.
Superstitions
like
this
are

harmless,
but
when
mistaken
beliefs
about
causality
affect
public
health
and
policy
decisions,
we
are
worse
off.
In
business

settings,
there
are
numerous
occasions
when
it’s
important
to
know
whether
two
variables
have
a
causal
connection.
Do
training
programs
improve

employee
performance?
If
more
funds
are
allocated
to
the
social
media
budget,
will
brand
image
improve
in
proportion
to
the
extra

spending?
Does
increased
customer
satisfaction
really
increase
sales?
Many
online
firms
conduct
A/B
testing
to
determine
10

whether
one
variable
has
a
causal
relationship
with
another.
Too
often,
businesses
don’t
have
the
luxury
to
conduct
those
real
world

experiments
and
must
work
with
the
data
that
are
available.
In
these
cases,
it’s
important
to
look
at
all
the
information
that

bears
on
the
question,
not
just
that
which
supports
the
idea
of
a
causal
relationship.
Expectations
about
the
future

Will
the
future
be
like
the
past?
It’s
human
nature
to
wonder
what
will
happen
in
the
future.
Most
of

us
end
up
basing
our
predictions
on
our
prior
experiences,
or
those
of
people
we
know.
When
thinking
about
how

you
will
do
on
a
final
exam,
it’s
natural
to
think
about
how
well
you
did
on
the
midterm.
If
you
have

an
exceptionally
good
meal
at
a
restaurant,
you
look
forward
to
sampling
it
again.
How
could
randomness
be
part
of
predicting
your

performance
on
an
exam
or
the
quality
of
a
restaurant
meal?
If
you
aced
the
midterm,
shouldn’t
you

expect
to
ace
the
final?
You
may
well
ace
the
final,
but
making
that
prediction
just
on
the
basis
of
your

midterm
score
is
a
mistake.
Performance
on
exams,
quality
of
restaurant
meals,
stock
prices,
race
times,
heights
of
siblings,
download

speeds,
and
almost
anything
else
that
can
be
measured
are
a
combination
of
an
average
performance
plus
some
random
variation.

Performance
varies
from
one
time
to
the
next,
so
a
truly
exceptional
performance
(either
positive
or
negative)
is
unlikely
to
be
followed
by

another
that
is
equally
exceptional.
This
is
due
to
a
phenomenon
called
regression
to
the
mean.
The
basic

principle
is
that
over
time,
extreme
values
are
followed
by
more
moderate
values.
11
Simply
put,
scores
typically
return

to
their
long-‐run
average.
That
doesn’t
mean
extreme
values
can’t
be
followed
by
other
extreme
values,
just
that
it’s
unlikely.
With

no
additional
information,
the
average
value
is
the
best
prediction.
If
a
student
consistently
aces
all
exams,
his
or
her
average

performance
is
pretty
high
and
the
student
may
well
ace
the
next
one.
For
more
typical
students,
an
exceptionally
high
or

low
score
will
likely
be
followed
by
something
closer
to
his
or
her
usual
score.
If
a
restaurant
meal
is
exceptional,

it’s
more
likely
that
the
next
one
won’t
stand
out
as
much
unless
the
average
quality
is
very
high.
An
easy

way
to
understand
this
is
to
think
about
peoples’
heights.
This
is
actually
where
the
idea
of
regression
to
the
mean
originated,

with
British
scientist
Francis
Galton
in
1886.
He
noted
that
very
tall
people
usually
had
tall
children,
but
at
least

some
of
them
were
shorter
than
their
parents.
Very
short
people
usually
had
short
children,
but
at
least
some
of
them
were

taller
than
their
parents.
If
the
children
of
tall
people
were
always
taller
than
their
parents,
eventually
their
descendants
would

be
extremely
tall.
The
same
holds
for
short
people.
Without
regression
to
the
mean,
the
range
for
adult
human
height
eventually

might
go
from
1
foot
to
12
feet,
or
even
more
extreme
sizes.
Regression
to
the
mean
should
be
taken
into

account
when
making
plans
and
predictions.
One
of
several
factors
contributing
to
the
2008
recession
was
an
unrealistic
belief
that

housing
prices
only
went
in
one
direction
–
up.
Had
that
been
the
case,
the
risky
loans
made
to
homebuyers
with
bad

credit
and
few
resources
would
have
been
secured
by
continually
appreciating
assets.
Instead,
as
was
inevitable,
home
prices
fell.

12
Because
so
many
risky
loans
had
been
made,
a
cascade
of
bad
debt
severely
impacted
the
economy.

A
similar
phenomenon
is
the
“Sports
Illustrated
effect,”
where
some
people
believe
a
team
that
appears
on
the
cover
of
Sports
Illustrated
will

be
jinxed
and
perform
worse
following
the
cover
feature.
Similarly,
the
performance
of
CEOs
who
appear
on
the
cover
of

Business
Week
often
declines
following
the
cover
story.
Does
this
publicity
really
affect
performance?
It’s
much
more
likely
that
the
events

that
prompted
the
athletes
and
executives
to
be
featured
on
magazine
covers
were
outliers
and
their
performance
returned
to
historic
averages

after
the
magazine
covers
appeared.
The
problem
with
over-‐specified
plans
When
we
think
about
the
future,
we
often
engage
in

daydreaming
about
what
we
think
our
lives
will
be
like
when
we
finish
graduate
school,
have
a
new
job,
move
to
a

different
part
of
the
country,
or
whatever
other
event
we
hope
will
actually
happen.
The
more
detail
we
add,
the
more

real
it
seems.
Daydreaming
about
the
details
of
your
future
life
is
fun,
but
it
shouldn’t
be
the
basis
of
planning.

While
details
make
your
daydreams
seem
more
real,
the
more
detail
you
add,
the
less
likely
it
is
that
those
details

will
be
correct.
This
may
seem
counterintuitive,
but
the
reason
lies
with
a
simple
rule
of
probability.
The
probability
of

two
independent
events
co-‐occurring
is
always
lower
than
the
probability
of
either
individual
event.
Probabilities
are
always
between
0
and

1:
a
probability
of
0
means
the
event
will
never
happen
and
a
probability
of
1
means
that
it
is
certain
to
happen.

To
determine
the
joint
probability
of
two
events
co-‐
13
occurring
(e.g.,
taking
a
specific
job
in
a
specific
city)

you
multiply
the
individual
probabilities.
So
if
you
have
a
20%
chance
of
being
hired
for
a
specific
job
and
a
30%

chance
of
finding
a
job
in
a
specific
city,
the
probability
of
both
happening
is
6%.
Every
time
a
detail

is
added,
the
joint
probability
is
reduced.
We
will
see
more
about
the
probability
of
multiple
events
in
later
chapters.

So,
how
should
people
think
about
the
future?
Do
we
need
to
be
statisticians
before
we
can
start
making
good
plans?

Should
uncertainty
strike
fear
into
our
hearts?
Absolutely
not.
The
most
important
thing
to
remember
is
that
there
is
variability
around

future
events.
Rather
than
making
plans
depend
on
a
specific
outcome,
we
need
to
try
to
figure
out
a
likely
range

of
outcomes.
Remember
that
trends
rarely
continue
in
a
single
direction
indefinitely.
Investment
firms
always
include
the
statement,
“Past

performance
does
not
guarantee
future
results.”
It’s
true
well
beyond
the
domain
of
stock
prices.
Rather
than
evoking
fear,
accounting

for
uncertainty
will
lead
to
plans
that
are
more
realistic
and
flexible.
The
best
way
to
account
for
uncertainty
is
to

first
establish
what
is
known
and
what
is
unknown,
then
develop
estimates
for
the
likelihood
of
different
situations.
With
the

combination
of
what
is
known
and
what
is
estimated,
different
contingency
plans
can
be
developed.
This
may
seem
a
bit
formal,
but

for
important
decisions
it’s
worth
taking
the
time
to
be
as
accurate
as
possible.
Following
some
significant
intelligence
failures,
such
as

the
prediction
that
weapons
of
mass
destruction
would
be
found
in
Iraq
prior
to
the
Gulf
War,
the
Intelligence
Advanced
Research

Projects
Activity
funded
research
into
how
to
improve
14
predictions.
In
response,
psychologists
Philip
Tetlock
and
Barbara
Mellers
developed

the
Good
Judgment
Project
to
understand
the
characteristics
of
people
who
were
good
at
predictions
and
what
might
make
them
even

better.
The
key
factors
turned
out
to
be
training
in
basic
probability
theory,
education
about
cognitive
biases,
and
working
in
a

team
that
included
both
specialists
and
generalists.
Keeping
track
of
results
and
forming
teams
of
“superforecasters”
led
to
accuracy
that

was
almost
double
that
of
people
with
no
training.
Being
a
smart
consumer
of
information
More

than
60
years
ago,
Darrell
Huff
published
a
small
book
titled
How
to
Lie
with
Statistics.
The
purpose
of
the
book
was
to

help
people
understand
how
statistics
in
the
news
and
advertising
could
be
technically
correct,
but
misleading,
depending
on
the
purpose
of

the
news
report
or
the
ad.
This
slim
volume
had
dozens
of
printings
and
ultimately
over
half
a
million
copies
were
purchased.

The
examples
Huff
used
were
tied
to
1950s
era
concerns,
but
decades
later
the
underlying
message
is
still
important.
We

hear
statistics
about
government,
sports,
political
races,
traffic
accidents,
crime
and
a
myriad
of
other
topics.
Are
we
in
a
recession
or

a
recovery?
How
can
the
unemployment
rate
go
up
when
more
new
jobs
are
being
created?
The
news
is
full
of

reports
about
purported
causes
of
cancer,
heart
disease,
and
other
health
issues.
Advertising
makes
promises
that
products
will
make
us

more
attractive,
energetic,
and
slimmer.
Should
we
eat
dark
chocolate
for
its
antioxidants
or
avoid
it
because
it
might
contribute

to
obesity
and
diabetes?
Should
we
run
for
cardiovascular
health
or
walk
to
avoid
joint
damage?
Do
we
need
to

buy
a
standing
desk
to
avoid
the
effects
of
too
15
much
sitting?
We
often
forget
that
news
programs

shape
their
programming
to
maximize
ratings
and
advertisements
are
designed
to
influence
our
spending,
not
to
help
us
make
good
decisions.

Many
of
us
glaze
over
at
the
mention
of
statistics.
But
statistics
enables
us
to
summarize
information
in
order
to

learn
about
the
world.
Statistics
is
a
tool
to
understand
whether
a
change
has
happened
or
not,
whether
variables
are
related;
a

way
to
detect
a
signal
in
the
noise
of
randomness.
Unfortunately,
someone
with
an
agenda
can
easily
“lie
with
statistics”
to

mislead
us.
We
don’t
have
to
look
too
far
for
examples.
During
the
lead-‐up
to
the
Brexit
vote,
in
which

Britain
voted
to
leave
the
European
Union,
the
Vote
Leave
group
repeatedly
claimed
that
the
United
Kingdom
sent
£350
million

every
week
to
the
European
Union.
This
was
true
–
but
something
was
missing.
The
European
Union
refunded
about
two-‐thirds
of

that
amount,
so
the
net
figure
was
actually
£100
to
£125
million.
A
recently
published
study
reported
in

the
Wall
Street
Journal
(8-‐29-‐16)
was
titled
“Eating
Fruit
While
Pregnant
May
Boost
Your
Baby’s
Intelligence,”
with
a
subtitle
of
“Infants

whose
mothers
ate
more
fruit
were
smarter
one
year
after
birth,
a
preliminary
study
shows.”
Fruit
is
part
of
a
healthy
diet,

so
this
news
is
not
exactly
earthshaking.
However,
the
claim
that
the
fruit
eaten
during
pregnancy
is
the
reason
for

a
baby’s
higher
intelligence
is
stretching
what
the
scientists
found.
Researchers
looked
at
cognitive
development
scores
for
688
infants
and
related
the

scores
to
data
from
a
survey
the
mothers
completed
during
pregnancy.
The
finding
was
that
there
was
16

a
statistically
significant
relationship
between
self-‐reported
fruit
consumption
and
a
composite
of
the
scores
on
the
Bayley
Scales
of
Infant
and
Toddler

Development
at
age
one.
Test
scores
are
not
the
same
as
intelligence,
and
the
increase
in
scores
was
2.38
points

per
serving
of
fruit,
well
within
the
standard
deviation
of
the
Bayley
Scale,
which
has
a
mean
of
100
and
standard
deviation
of

15.
The
authors
of
the
research
study
were
careful
to
state
that
these
results
are
preliminary
and
that
cognitive
development

scores
at
one
year
don’t
predict
cognitive
development
scores
at
the
age
of
three.
The
journalist
made
a
claim
in
a
catchy
headline

about
intelligence,
but
the
researchers
were
talking
about
test
scores
at
age
one,
not
intelligence,
which
is
a
much
more
complex

concept.
Questions
to
Ask
There
are
a
few
things
to
keep
in
mind
when
someone
is
using
statistics
to

support
a
point
of
view.
In
How
to
Lie
With
Statistics,
Darrell
Huff
characterized
these
issues
in
a
chapter
titled
“How

to
Talk
Back
to
a
Statistic.”
Who
Benefits?
First,
does
the
sponsor
of
the
research
have
a
reason
to

favor
one
side
of
the
argument?
Here
are
two
examples
from
nutritional
research
where
this
question
needed
to
be
asked.

The
California
Walnut
Commission
sponsored
a
study
that
found
eating
walnuts
improved
the
health
of
people
at
risk
for
diabetes.
Another

study
found
that
Concord
grape
juice
improved
driving
performance
and
spatial
memory
among
mothers
of
pre-‐teens
included
an
author
who
was

an
employee
of
a
major
grape
juice
17
provider.
It’s
entirely
possible
that
these
findings
are
legitimate,
but
in
many

cases,
studies
that
are
funded
by
organizations
with
a
vested
interest
in
the
results
tend
to
show
more
positive
findings
than

studies
funded
by
neutral
organizations.
How
Do
They
Know?
What
Sample?
A
second
issue

to
consider
is
the
nature
of
the
sample.
Two
factors
matter
here:
the
size
of
the
sample
and
how
the
people

in
it
were
selected.
When
a
sample
is
large,
the
data
it
provides
is
more
likely
to
be
true
of
the
population

the
sample
represents
because
of
the
law
of
large
numbers.
When
the
sample
is
small,
you
really
can’t
draw
solid

conclusions
from
the
data.
Problems
with
sample
selection
occur
for
a
number
of
different
reasons.
The
ideal
sample

is
one
that
accurately
represents
the
population
of
interest.
Finding
a
truly
random
sample
to
answer
a
pollster’s
survey
is
difficult.

If
you
select
people
from
a
telephone
directory,
you’ll
miss
the
growing
number
of
those
who
only
use
cell
phones.

With
the
prevalence
of
caller
ID,
many
people
won’t
answer
the
phone
unless
they
recognize
the
caller.
If
your
survey
is
online,

you
miss
the
population
that
doesn’t
use
the
Internet.
There
are
many
reputable
polling
organizations
that
take
pains
to

sample
respondents
and
report
statistics
properly.
Gallup,
Pew
Research,
Harris
and
NORC
(National
Opinion
Research
Center)
all
apply
sophisticated
approaches

to
sampling
and
analyzing
opinion
data,
so
you
can
be
confident
in
what
organizations
like
these
report.
18

Which
Average?
There
is
a
joke
about
Microsoft
founder
Bill
Gates
walking
into
a
bar
and
everyone
in
the
bar

being
happy
because
their
average
income
just
went
up
dramatically.
Technically,
a
scenario
like
that
would
be
true
(about
the
average,
not

necessarily
the
happiness)
–
if
the
mean
is
the
average
that
you
use.
Income
distributions
are
almost
always
positively
skewed,

meaning
that
there
are
some
individuals
whose
income
is
high
enough
to
distort
the
mean
in
a
positive
direction.
If

the
distribution
weren’t
skewed,
the
mean
would
be
very
close
to
two
other
average
measures
–
the
median
and
the
mode.
The

median
is
the
number
that
divides
the
distribution
in
two,
so
that
half
of
the
people
make
less
than
the
median
and
half

make
more.
Medians
are
usually
used
to
report
income,
housing
prices
and
other
government
statistics
because
they
aren’t
sensitive
to
extreme

values
like
Bill
Gates’s
income.
The
mode
is
the
most
frequent
value
in
a
distribution
and
isn’t
used
as
commonly
as

means
and
medians.
You
would
use
a
mode
if
you
wanted
to
figure
out
which
item
(or
flavor
or
size)

was
the
most
popular.
So,
when
you
hear
a
news
story
that
reports
average
income,
prices,
scores
on
educational
tests,
or
any

of
a
host
of
other
topics,
keep
in
mind
which
average
is
being
reported.
What’s
Missing?
When

a
new
medical
study
comes
out,
we
are
often
warned
that
the
risk
of
contracting
a
disease
is
increased
by
50%
among
people

who
fit
a
certain
profile
or
promised
that
a
new
drug
will
reduce
the
time
required
to
recover
from
an
illness
by

19
20%.
What
is
left
out
is
what
is
called
the
“base
rate;”
how
many
people
are
affected
by

the
disease
or
how
long
people
are
typically
sick.
For
example,
Tamiflu
is
widely
prescribed
for
the
flu
because
it
cuts

the
duration
of
the
illness
by
20%
when
taken
within
36
hours
of
symptoms.
The
flu
will
make
most
people
miserable,
but

the
misery
usually
lasts
about
5
to
7
days
without
medication.
Tamiflu
reduces
the
duration
by
20%
-‐
to
about

4
to
6
days
(from
123
hours
with
a
placebo
to
98
hours
with
the
drug,
according
to
a
2015
study).

Since
1997,
direct
to
consumer
advertising
for
pharmaceuticals
has
become
widespread
in
the
U.S.
Although
ads
must
include
disclosures

about
possible
side
effects,
they
rarely
discuss
the
risks
and
benefits
of
drugs
in
a
transparent
way.
Most
ads
mention

benefits
as
a
relative
risk,
such
as
a
50%
reduction
in
developing
a
disease.
What
is
missing
is
absolute
risk,
without
which

you
can’t
tell
whether
the
50%
reduction
is
meaningful.
Does
the
50%
reduction
mean
that
only
100
of
1000
people
would

develop
the
disease
compared
to
200
of
1000
without
the
drug?
Or
does
it
mean
that
only
1
of
1000
people

would
develop
the
disease,
compared
to
2
of
1000
people
without
the
drug?
The
50%
reduction
in
relative
risk
is
correct
in

both
cases,
but
the
extent
of
the
absolute
risk
is
different
by
two
orders
of
magnitude.
You
can’t
really
get

an
idea
of
the
risk
unless
you
know
the
base
rate.
That’s
why
(from
a
marketing
perspective)
many
pharmaceutical
ads
mention
benefits

only
in
relative
terms
without
including
information
about
the
absolute
risk.
Does
the
picture
tell
the
true
story?

20
Many
arguments
are
made
using
information
presented
in
charts.
Well-‐
constructed
charts
convey
information
more
quickly
than
tables

and
make
it
easy
to
understand
relationships
that
otherwise
might
be
difficult
to
discern.
Unfortunately,
charts
are
susceptible
to
the

same
kinds
of
manipulation
as
statistics.
Can
you
tell
what’s
wrong
with
the
following
chart?
It
documents
gun
deaths
over

time
in
Florida,
with
a
special
emphasis
on
2005,
the
year
the
“Stand
Your
Ground”
law
was
passed.
The
vertical

axis
starts
at
1,000
rather
than
zero,
so
what
you
might
normally
interpret
as
a
decline
when
the
law
was
enacted
in
2005

is
actually
a
steep
increase.
This
chart
drew
media
attention
because
it
was
so
misleading.
There
are
many
ways

charts
can
mislead.
As
in
this
example,
axes
can
be
misleading,
especially
when
they
start
at
a
number
other
than
zero.

Pie
charts
are
often
used
inappropriately
(they
should
only
be
used
to
indicate
proportions
within
a
whole),
and
sometimes
add
to

more
than
100%.
Some
figures
on
infographics
represent
more
21
of
a
difference
between
items
than
is
warranted,
because

the
area
of
the
figures
varies
in
two
dimensions
when
the
numbers
they
represent
vary
only
in
one.
When
someone

has
a
point
of
view
they
are
trying
to
sell
you,
be
sure
to
look
at
how
they
are
presenting
the
data.

Applications
The
benefits
of
understanding
the
basics
of
randomness,
uncertainty,
and
probability
are
similar
in
both

personal
and
managerial
settings.
You
will
be
at
a
significant
advantage
because
the
evidence
is
that
far
too
few
people
understand
these

topics,
even
those
who
are
educated.
You
will
be
less
susceptible
to
questionable
claims
and
better
able
to
assess
possibilities.

Your
plans
will
account
for
uncertainty
and
be
more
realistic.
There
are
two
major
types
of
benefits
associated
with
understanding

randomness,
probability
and
uncertainty.
The
first
is
greater
clarity
in
your
thinking.
The
second
is
that
you
will
be
able

to
make
plans
more
successfully.
Both
benefits
apply
to
personal
and
business
life.
Clarity
The
ability
to
discern

when
something
is
random
or
not
is
helpful
when
you
are
trying
to
understand
why
things
happened
and
whether
a
causal
relationship
exists.

When
you
see
a
true
causal
relationship,
your
actions
will
be
more
effective
and
you
will
be
able
to
avoid

problems.
When
you
know
something
is
random,
you
can
stop
wasting
time
trying
to
change
it.
You
won’t
be
fooled
into

thinking
something
will
succeed
just
because
there’s
been
a
long
string
of
misses.
22
When
you
understand

the
principle
of
regression
to
the
mean,
you
will
have
more
realistic
expectations
about
future
events.
Spectacularly
good
and
spectacularly

bad
events
can
occur
to
anyone,
but
they
are
unlikely
to
be
repeated
and
shouldn’t
be
taken
as
an
indication
of
how
future

events
will
unfold.
Investors
who
do
the
best
tend
to
be
the
ones
who
don’t
react
on
the
basis
of
day-‐to-‐day
swings

in
the
market.
Instead,
they
recognize
that
outliers
occur
on
both
the
positive
and
negative
side
and
focus
on
the

long-‐term
return.
The
less
fortunate
investors
are
those
who
check
their
portfolios
daily,
reacting
to
what
is
essentially
random
noise.

Understanding
which
events
are
meaningful
and
which
are
just
noise
requires
a
skeptical
eye.
Inclusion
of
base
rates
helps
you
understand

whether
a
risk
or
benefit
is
significant
or
not.
Statistics
are
so
easily
distorted
that
it’s
worth
your
while
to
consider

the
source
and
ask
the
basic
questions:
• Who
says
so?
• How
do
they
know?
• Are
they

comparing
apples
to
apples?
• Do
they
have
an
interest
in
a
particular
interpretation?
Planning

Planning
involves
making
choices
about
what
we
will
do
in
the
future
on
the
basis
of
what
we
expect
the
state
of
the

world
to
be
in
the
future.
The
problem
is
that
the
future
is
uncertain,
except
as
Benjamin
Franklin
famously
noted,
“…
in

this
world
nothing
can
be
said
to
be
certain,
except
death
and
taxes.”
What
we
want
to
be
true
in

23
the
future
doesn’t
necessarily
have
an
impact
on
what
will
happen.
If
you
don’t
smoke,
eat
wisely,
and

stay
fit,
you
will
be
more
likely
than
not
to
enjoy
a
long
and
energetic
life,
but
there’s
no
guarantee.
You
may

want
to
win
the
lottery
and
quit
your
job,
but
the
probability
remains
1
in
292
million,
so
you’ll
likely
need
to
find

an
alternative
for
retirement.
Rare
events
do
happen,
but
they
are
by
definition
rare.
How
can
understanding

randomness
and
probability
help
in
planning?
If
your
plans
depend
on
economic
conditions,
competitors’
responses,
and
consumer
demand,
you
are

already
well
aware
that
the
past
doesn’t
predict
the
future.
Certainly
the
present
and
recent
past
provide
a
baseline
to
initiate
planning,
but

how
can
you
go
beyond
looking
at
the
past
and
present
to
predict
the
most
likely
future?
As

mentioned
above,
regression
to
the
mean
should
be
taken
into
account
when
trying
to
determine
whether
trends
are
likely
to
continue.
Extreme

results
are
most
often
outliers,
so
unless
you
can
identify
the
specific
causes
and
can
expect
those
causal
factors
to
continue

to
impact
your
business,
you
are
better
off
with
a
more
moderate
forecast.
If
you
are
experiencing
phenomenal
success,
how
much
of

it
can
be
attributed
to
you
or
your
firm’s
actions
and
how
much
can
be
attributed
to
external
factors?
Similarly,

if
you’ve
had
a
disastrous
year,
can
you
identify
the
causes?
Was
it
something
over
which
you
had
control?

To
make
good
predictions,
you
need
to
distinguish
those
aspects
of
your
life
or
your
business
that
you
can’t
control.

For
each
of
these,
what
is
most
likely
to
happen?
How
much
variability
exists?
For
example,
if
you
are
a

manufacturer,
what
factors
affect
your
supply
chain
and
how
likely
are
they
to
occur?
The
2011
earthquake
and

24
subsequent
tsunami
in
Japan
led
to
massive
shortages
in
the
automotive
supply
chain.
These
shortages
affected
not
only
Japanese

carmakers,
but
an
estimated
350,000
–
400,000
fewer
vehicles
were
produced
in
the
US
due
to
parts
shortages.
While
it
isn’t

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