Cognitive Biases I
Optional Reading
Today’s lecture is based
primarily on:
“How We Know What Isn’t
So,” Chapter 1.
By Thomas Gilovich, a
psychologist
Patterns
Pattern Recognition
Seeing patterns in your
data is a good thing, and
humans are natural
pattern finders.
Watson & Crick discovered
the structure of DNA by
recognizing the “fuzzy X”
pattern it left when
bombarded with X-rays.
Pattern Recognition
But sometimes we see
patterns when there’s
really nothing to see.
Consider this famous
photograph from 1976 by
the Viking I spacecraft.
Look! A face on the
surface of mars!
Pattern Recognition
But sometimes we see
patterns when there’s
really nothing to see.
But this was what we
were seeing…
Jesus Tree
Jesus Toast
Jesus Sock
Why do we see extra patterns?
Our brains are very good at finding patterns
when they exist, and this is important.
But part of our success comes by seeing
patterns everywhere, even when they don’t
exist, including in random data.
The Clustering Illusion
I flipped a coin (really!) 20 times in a row. ‘X’ is
Queen Elizabeth II and ‘O’ is the lion with the
crown. Here is what I got:
XXXXOOXOOXXOOXOOXOOO
That doesn’t look random. But it is. The coin
lands the same as the previous toss 10 times
and different from the previous toss 9 times.
The Clustering Illusion
Ask anyone who watches
basketball whether this is
true:
“If a player makes a shot,
they’re more likely to
make the next; if they
miss a shot, they’re less
likely to make the next.”
The Clustering Illusion
Most people will say ‘yes, of course’. But it’s not
true, they’re subject to the clustering illusion.
Gilovich, Vallone & Tversky (1985) analyzed
records of made and missed shots, and they
found:
The Clustering Illusion
• Players who made a shot, on average, scored
on the very next shot 51% of the time.
• Players who missed a shot, on average, scored
on the very next shot 54% of the time.
• Players who made two shots in a row, scored
on the very next shot 50% of the time.
• Players who missed two shots in a row, scored
on the very next shot 53% of the time.
Representativeness
INVENTING EXPLANATIONS
Split-Brain Patients
Split-brain patients are
individuals who have had
their corpus collosum
severed (the part of the
brain by which the left
half of the brain
communicates with the
right half of the brain).
Split-Brain Patients
The right eye sends
information to the left half
of the brain and left eye
sends information to the
right half of the brain.
Split-Brain Patients
Speech is controlled by
the left half of the brain. If
a split brain patient is
shown something only to
her left eye, she cannot
describe it. That
information goes to the
right half of her brain, and
it can’t communicate with
the left.
Confabulation
Researchers performed the following
experiment on split-brain patients.
They presented two pictures, one only to their
left eye (right brain, non-verbal) and one only to
their right eye (left brain, verbal).
Confabulation
Presented to left eye (right
hemisphere of brain):
Presented to right eye (left
hemisphere of brain):
Confabulation
The patients were then asked to point to
another picture (out of several others
presented) that went together with the ones
they were presented with.
Pointing is a non-verbal task, so it can be
accomplished by both the right and the left side
of the brain.
Confabulation
Subjects chose this picture to go
with the snow:
Subjects chose this picture to go
with the chicken:
Confabulation
But then the subjects were asked:
“Why did you pick the shovel?”
To answer the question, the subjects needed
their left brain (verbal), but the left half of the
brain did not see the snow picture.
Confabulation
In response, subjects would say things like:
“Oh, that’s easy. You need a shovel to clean out
the chicken shed.”
That is not why they picked the picture. But they
weren’t lying– they thought that was why they
picked it!
Confabulation
The human mind doesn’t just see patterns
where there is only randomness. It also freely
invents reasons and explanations to “make the
world make sense.”
When we encounter random data, we see a
pattern that isn’t there. And we explain why
there should be a pattern. This can make our
bad beliefs difficult to abandon.
REGRESSION TO THE MEAN
Variables
From the point of view of statistics, any measure
that can take on different values is a variable.
So for example, height is a variable, since people
can be different heights. Profit is a variable,
since companies can have different profits.
Spiciness is a variable since different foods can
be more or less spicy…
Perfect Correlation
We say that two variables are perfectly
correlated when knowing the value of one
variable allows you to know the value of the
other variable with certainty.
For example, the area of a triangle whose base
is 5 (one variable) is perfectly correlated with
the height of the triangle (another variable).
Imperfect Correlation
Two variables are imperfectly correlated when
the value of one influences the value of the
other.
For example height of parents (one variable) is
imperfectly correlated with height of children
(another variable). Tall parents have tall
children, on average, and short parents have
short children, on average.
Regression to the Mean
Whenever two variables are imperfectly
correlated, extreme values of one variable tend
to be paired with less extreme values of the
other.
Tall parents have tall children, but the children
tend to be less tall than the parents. Students
who do very well on Exam 1 tend to do well on
Exam 2, but not as well as they did on Exam 1.
Regression to the Mean
This is true of any two imperfectly correlated
variables.
Companies that do very well one year on
average do well the next year, but not quite as
well as the previous. Students who do well in
high school on average do well in college, but
not as well as in high school.
Regression to the Mean
“Regression” just means going back, and
“mean” means average. “Regression to the
mean” is just a fancy way of saying going back to
average.
Imperfect Correlation
If I flip a fair coin and ten times in a row it lands
heads each time, it will not “regress to the
mean” and land tails more than heads to
balance things out.
Since it’s a fair coin, it is most likely to land
heads half the times and tails the other half.
Future tosses of a coin are independent of past
ones. Fair coins land, on average, 50% heads and
50% tails.
Imperfect Correlation
Regression to the mean happens when we have
two imperfectly correlated variables X and Y, and
X takes on a very extreme value. Then we expect
Y to take on a less extreme value.
But coin flips are not imperfectly correlated.
They are not correlated at all. Past coin flips do
not influence future coin flips.
On Average
It’s important to note that sometimes,
regression to the mean doesn’t happen (or
doesn’t happen immediately).
Tall parents can have children who are even
taller than they are. But the average height of
children born to tall parents is lower than the
average height of the parents. On average,
things regress to the mean.
Not Causal
It’s also important to note that regression to the
mean is not a causal relation between variables.
If I give an exam, there will be some random
variation– some measure of “luck.” Imagine that
I’m going to give an exam with 5 questions on it.
I give all the students 10 questions to study, and
for each exam, I randomly select 5 of those 10
questions for the exam.
What the Students Study
Now imagine that each student studies only 5 of
the possible questions. So each student knows
the same amount– half of the material.
Intuitively, each student “deserves” the same
grade.
Giving the Exam
But now imagine that I give an exam, randomly
selecting 5 questions. On average, students will
know the answers to 2.5 of the questions, since
on average they know half of the material.
But some students will be “lucky”– I will pick
only the questions they studied, and they will
get 5/5. Other students will be unlucky: I will
pick only the questions they didn’t study.
Everyone else will be in the middle.
Regression to the Mean
But if I give a second exam, we will see regression
to the mean. The lucky students on the first exam
probably won’t be the lucky ones on the second.
The same goes for the unlucky students.
So the lucky students on exam #1 will get worse
grades on exam #2 (on average), and the unlucky
students on #1 will get better grades on #2 (on
average). Their grades regressed to the mean (2.5).
Real Life
This isn’t exactly how real life works, but the
idea is the same. Every exam is a random
sampling of the questions the professor could
have asked, and each student knows some of
the material. On any given exam, sometimes you
will be lucky, sometimes the exam will give your
“true” score, and sometimes you will be unlucky.
But since luck is random, usually lucky people
won’t be lucky twice: they’ll be average the
second time, and will regress to the mean.
Regression Fallacy
The regression fallacy involves attributing a causal
explanation to what is nothing more than
regression to the mean.
If you feel very bad when you wake up hung over,
you will likely feel better in an hour. If you eat a
greasy meal when you wake up, and feel better in
an hour, you might commit the regression fallacy
and assume your meal made you feel better.
The Sports Illustrated Jinx
Some people believe in
the “Sports Illustrated
jinx”: when you appear on
the cover of Sports
Illustrated, you do very
poorly in your sport.
The Sports Illustrated Jinx
For example, while this
was the cover of SI in
February, Jeremy Lin shot
1-for-11 in a game where
the New York Knicks lost
to the Miami Heat 102-88.
The Sports Illustrated Jinx
And when this was the
cover of SI, Lin’s team
snapped a 7 game winning
streak when they lost at
home in New York to the
New Orleans Hornets.
Regression to the Mean
But there is no SI jinx. This is just regression to
the mean.
You get on the cover of SI when you are the best
athlete in all sports (in America) during the
previous week. Your performance this week is
imperfectly correlated with your performance
last week. You’re unlikely to be the best athlete
in all sports two weeks in a row!
Traffic Survey
Suppose that the government conducts a survey
of traffic intersections to find out which had the
most accidents in the past month. At every
intersection where there was a large number of
accidents, the government installs cameras.
Next month they do a survey again and notice
than on average there are fewer accidents at the
locations where cameras are installed.
Government Claims
The government claims:
Claim: Installing the cameras reduced the
number of accidents.
Regression Fallacy
The government might be right. But this also
might be the regression fallacy.
The variables “traffic accidents this month” and
“traffic accidents next month” are imperfectly
correlated. Intersections with lots of accidents
this month will likely have lots next month;
intersections with few this month will likely have
few next month.
Regression to the Mean
If you have two imperfectly correlated variables,
and one of them (“traffic accidents this month”)
takes on an extreme value, the other will have a
more moderate value. So the intersections that
were the worst this month will be, on average,
bad-but-less-bad next month. The will, on
average, improve– simply through regression to
the mean.
The Regression Fallacy
The regression fallacy is attributing a cause (the
cameras the government installed) to an effect
(the decrease in accidents at the intersections
that had the most accidents last month) that is
really just regression to the mean.
Note
None of this means the cameras didn’t work!
To truly test whether cameras work, you must
install them at a random sampling of
intersections– good and bad ones. If accidents
then go down on average, you can be confident
the cameras worked. We’ll talk more about
random samples later in the course.
Reward and Punishment
We can see how people might become
convinced that punishment works better than
reward.
You punish someone when they do something
exceptionally bad. Even if the punishment does
nothing, we expect their behavior to regress
back to normal. So it will look like punishment
works.
Reward and Punishment
We can see how people might become
convinced that punishment works better than
reward.
You reward someone when they do something
exceptionally good. Even if the reward does
nothing, we expect their behavior to regress
back to normal. So it will look like rewards make
them behave worse.