Meaningless Statistics

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Once again the Minnesota Department of Transportation is putting the word out that drunk drivers cause 1 in 4 traffic deaths. I begin with this example of a meaningless statistic, not because it is especially egregious, but because it exemplifies what makes statistics meaningless.

Of course, it is not entirely meaningless. We all have a gut feeling that drunk drivers do not drive 1 out of 4 miles driven in America. We strongly suspect that the vast majority of our fellow travelers are not drunk even at 1:00 AM. So it doesn’t take much thought to realize that 1 out of 4 traffic deaths is out of all proportion to the number of miles drunk drivers actually drive. In fact, the National Highway Traffic Safety Administration estimates that drunk drivers drive 1 out of every 140 miles driven on America’s highways. So drivers doing only 1/140th of the driving are responsible for 1/4th of the fatalities. That’s 35 times the expected number.

But most people seeing the signs have no idea what the context is. They do not know what fraction of miles driven are driven drunk. Statistically speaking there is no difference between “Drunk drivers cause 1 in 4 traffic deaths” and “Sober drivers cause 3 in 4 traffic deaths.” Yet the latter statement seems to make a case for drinking before driving! The lack of context is what empties the statistic of its meaning.

In the same way, there is an oft-quoted statistic that women earn $0.77 for every $1.00 men earn that also suffers from lack of context. (Apparently in 2015 the pay gap went down $0.02. Women now earn $0.79 on average for every $1.00 men earn.) The pay gap is an aggregate of all the income women earn compared to all the income men earn. It is commonly used as evidence of continuing sexism in corporate America. But as evidence it fails because there are so many other factors involved. Missing from the statistic are a lot of facts. For example, men work more hours than women. Women also tend to be over-represented in care-giving and hospitality occupations, which do not pay as well as more male-dominated occupations. This may be due to cultural sexism, but it’s hard to see what actions businesses or governments could take to close whatever portion of the gap is due to this kind of income difference. The truth is most companies in America already have policies prohibiting gender discrimination.

Statistics always present an aggregate view of data. That is what makes statistics valuable. However, aggregating data always also loses some information. The reports on which popularized statistics are based are usually careful to include methodology and context and indicate other possible interpretations of the data. But when the statistic shows up in Facebook meme or a highway sign, all that context is lost. The power of statistics is in simplifying complex data into a few numbers. We understand by simplifying. We should not, however, mistake our understanding for a grasp of the truth.

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