Giorgio Delgado

Statistical Illusions

February 10, 2014

As humans, we tend to be bad statisticians. This may not seem like a significant issue at first, but what people don't realize is that life's decisions often involve statistical inference. Quite often we are left making the wrong decision based on human intuition.

Consider this example, curtesy of Kahneman and Tversky (1982):

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which of the two outcomes is more likely?

Because linda is portrayed as someone who is likely to be a feminist, people will jump to the conclusion that the second outcome is more likely, which in fact is actually a wrong assertion. The reason the second outcome is less likely to occur is because it requires the existence of two independent events. One event on its own is more likely than two unrelated events happening at the same time.

Policy makers may correlate two things (just like we correlated Linda with feminism), and as such, make the wrong decision about legislation.

Lazy Minds:

Another problem with the human psyche is that we subconsciously seek the path of least resistance. If we feel that thorough contemplation is not required, we will immediately assume the first thing that comes to our mind is true.

Here's an example from Daniel Kahneman's book, Thinking Fast And Slow:

A bat and a ball cost $1.10

The bat costs a dollar more than the ball

How much does the ball cost?

Again, a certain number came to your mind immediately (most people come up with $0.10). Because the puzzle in question seems easy and intuitive, we assume that second thought is not required. But if you think it out, you will realize that $0.10 is the wrong answer. The correct answer is $0.05.

Most of us would like to believe that we are rational people, with logic presumably surrounding all our decisions. These are just two of the many circumstances that will cause us to make the wrong decision.