Friday, January 15, 2016

What Are the Chances, Part 3

Let’s begin with a little, 9-question survey.  You know, one of those fun, little questionnaires that can tell you everything from whether you’ll be a successful brain surgeon to the best color for your doorbell button.

What I’d like you to do is to estimate the chance that each of events described below will occur in 2016.  Don’t worry if you do not know much about the topic, just give your best guess.  You can use proportions, e.g., any number between 0.0 and 1.0, where 0 means there is no chance of this event; 0.50 means there is a 50-50 chance; and 1.0 means that this event will definitely happen.  And of course, you can use any number in between those, like 0.27345196, when there is a 27.345196% chance of the event.

OK, here are the nine events:

  1. The NCAA will sanction at least one Power 5 football school because one or more football players receive some type of banned compensation.
  2. Donald Trump will win the Republican nomination for President of the United States.
  3. The cost of food in the US will increase slower than the overall rate of inflation.
  4. The US Stock Market will continue its volatility, while the overall economy grows slowly.
  5. The NCAA will relax its rules on pay for college athletes, paving the way for them to receive compensation through either endorsements or academic benefits other than scholarships.
  6. Prices on produce will increase significantly, as strong US weather fluctuations from an El Nino pattern hurt production.
  7. Donald Trump will continue to make provocative political statements right up to the day he becomes the Republican nominee for President.
  8. Oil production from shale will slow, allowing gas prices to increase significantly.
  9. Overall, the US economy will show slow growth for the year.

Got your answers written down?  Ok, let’s score them.

First, compare your answers for events number 2 and 7.  Did you rate the chance of 7 greater than 2?  Sorry, but that’s not possible.  Event 2 says that Trump wins the Republican nomination.  Event 7 says he wins AND he continues to make provocative statements.  The chance that both of these happen must be equal to or less than the chance that either one of them happens alone.

Now, compare events 4 and 9.  Did you rate the chance of 4 greater than 9?  Again, by the same logic, that is not possible.  Both 4 and 9 involve the chance that the economy grows slowly, but 4 adds the requirement that stock market volatility also continues.

There is no guarantee that I wrote these questions correctly – I don’t have the resources to pre-test questions.  But in fact, researchers have found many examples like these where the chance of two things happening is rated higher than the chance of one of them alone.  The reason – the combined events seem more “representative.”  And events that seem more representative seem more likely, even if they are not.  So, a statement such as “the US Stock Market will continue its volatility, while the overall economy grows slowly” may seem like what we get year after year, but it is still less likely than just slow growth alone.

So, what do you do with your individual results?  If you got one or both comparisons wrong, your doorbell should be black.  Otherwise, pick whatever color you want…

Happy writing,

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