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 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

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!

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.