Correlations and Causal Relationships
Mark Twain said there are lies, damned lies, and statistics. Understanding mathematics
helps us interpret statistics and recognize when "facts and figures" are being misapplied
or taken out of context.
One way statistics are commonly misused is by presenting two facts and concluding that
one causes the other. For example, while I was attending Texas A&M University, the
football team won 76.4% of their games. Since I graduated, the team has won only 53.6%
of their games. Therefore, it seems that my departure from campus resulted in a 23% drop
in the football team's success (almost 3 games per year!).
Of course, my presence on campus did not affect the football team. My graduation and the
drop in the football team's winning percentage are correlated. That means they
occurred together. However, there is not a causal relationship
between the two. My absence did not cause the drop in winning percentage, they
merely happened to take place at the same time.
Just because two events happen together does not mean that one causes the other. If you
keep an eye out, you will see people trying to draw these conclusions all the time. A
recent weekend news claimed that "boosting security along the U.S.-Mexican border actually
increases the number of illegals who get here..."
The reporter spoke to an official about a large wall placed on the border within the last
12 years. The official said that the number of people coming into the U.S. illegally has
increased since the wall was constructed. It sounds like we've established a correlation
between the events, but we haven't heard any proof of a causal relationship. We haven't
seen any facts showing that the wall somehow invited more people into the country. In the
last 12 years, crime rates across the country have plummeted, but we don't hear anyone
attributing that trend to a new wall on the border.
Logical reasoning is an important part of mathematics. Now go and think mathematically.
Dec. 2005
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