“Mathematics is the Art of Giving the Same Name to Different Things”
Chicago’s Booth School of Business is discussing some new research about the ways in which we misinterpret data. — the results of which explain why the Henri Poincare quote above has some truth to it.
In sum, we tend to overestimate the likelihood of something happening when the likelihood is framed as a statistical probability, and underestimate the odds of it happening when the likelihood is framed as a percentage-point difference.
The authors of the paper ran this experiment in contexts that included political polling and sports betting. If you tell people that the Warriors have an 84% chance to beat the Wizards, they are much more likely to think the Warriors will win than if you tell them the Warriors are 10-point favorites. (Even though being a 10-point favorite and having an 84% chance to win are the same)
Similarly, before the 2016 election….people who saw that Hillary Clinton had a 74% chance to defeat Trump were more confident about her chances than people who saw that she was estimated to receive 53% of the vote – even though the 74% number was extrapolated from the poll that put her at 53% of the vote.
(Nate Silver has harped on this constantly at his fivethirtyeight website and he is absolutely right. Although he also echoes the arrogance of many statistical modelers, who seem to insist that as long as you say something has even a 1% chance of happening, you can always crow that you were “correct,” no matter what the actual outcome is.)
The findings intuitively make sense – in these examples the statistical probability is the larger number so we probably shouldn’t be shocked that the larger number seems more powerful. But if nothing else it is a warning about how one conveys information, especially numerical data.