Does Ice Cream Cause Drowning?

Does Ice Cream Cause Drowning?

In AP Statistics, we are learning about correlation—a mathematical measure of the relationship between two variables. When two variables are correlated, we can use the value of one to reasonably predict the value of the other. We can find examples of correlation everywhere. Here’s an example dear to my heart—for those of us who drink coffee each morning, there is a correlation between caffeine intake and reported energy level. When we have our daily caffeine fix, we tend to report high levels of energy. When we miss our morning coffee, we typically report low energy levels. In this case, caffeine intake and perceived energy levels are correlated because a change in one variable biologically causes a change in the other.

It is therefore natural to assume, every time we see a relationship on paper between two variables, that one variable explains the other. This is a dangerous statistical fallacy known as confusing correlation with causation. There may be a mathematical pattern between two quantities, but that pattern does not mean that a change in one causes a change in the other.

An example: there is a correlation between ice cream sales and rates of drowning. When ice cream sales are high, rates of drowning are high. When ice cream sales are low, deaths by drowning are far less common. Do ice cream sales, then, cause people to drown?

Of course not. It turns out that a separate variable—time of year—affects both ice cream sales and rates of drowning. During the summer, it is hot and sunny, so people buy ice cream to cool down. People also swim and visit the beach more during the summer, and thus there are more swimming-related accidents. Ice cream sales and drowning therefore have a clear mathematical relationship despite the fact that neither variable has any effect on the other.

Correlation and causation are easily confused. Our minds are trained to find simple, easily-articulated patterns, so we often look at the relationship between two variables in a vacuum, forgetting that in the real world, quantities are affected by a multitude of different factors. The next time you read that two values are connected to one another mathematically, remember that real-world quantities are produced by a tremendously complex system of different influences. The correlation you see does not automatically imply causation.

Todd Bryant
Mathematics Instructor