Politics and Numbers: Don't Abuse the Denominator

Business analysis graphs and charts
Business analysis graphs and charts

Politics and numbers make for strange bedfellows. This seems counter-intuitive as modern politics is actually loaded with numbers from polling to policy analysis. To illustrate, I ask you to consider the case of the humble denominator.

In a recent editorial, the Wall Street Journal called out the numbers fueling Donald Trump's stump speeches about immigrants. As the editorial explained, you can make a group look bad just by your choice of the denominator, which happened when the number of households was used as the denominator to calculate rates of welfare use among immigrants. Because immigrant households tend to be larger than average, using households as the denominator instead of the actual immigrant population provided a misleading statistic.

Electoral politics, whether we like it or not, is a team sport that includes a lot of trash talking through comparative statistics. Rates, proportions, and percentages are the tools--they are the metrics used to judge one group against another. These statistics always include a numerator and a denominator. The numerator is usually where the action is: the number of deaths, the number of people in poverty, or number enrolled in Medicaid. The denominator, on the other hand, provides the context--the point of comparison, like the total population or the total number of households. Denominators have no shame. They will do whatever you ask them to do. The denominator, in the wrong hands, can be a bit unruly.

The trouble begins when you choose the denominator in a way that privileges one group over the other. You can do this in two ways. First, by choosing a denominator that varies widely among groups, you can create the impression of a difference when there may be none. Second, you can choose a denominator that is not the right dance partner for the numerator and emphasize a difference that may not be real. It's pretty subtle, and that's probably why it is such a useful tool in shaping opinion.

I live in the Midwest, so I understand the importance of good bratwurst. Let's use bratwurst consumption to illustrate the first problem. Let's say you want to claim that people who live in the state of Illinois eat more bratwurst than people in Wisconsin because you have to claim something in a year when the Bears aren't doing so well. In this case, the number in the numerator is the total number of bratwurst eaten (don't ask me where you get that number from), and then you slyly use the number of households in each state as the denominator. The people in Wisconsin might seriously object to the comparison, and they might be right--average household size in 2007-2009 in Wisconsin was smaller than in Illinois. So even if Packers' fans eat the same amount of bratwurst at a tailgate as the Bears' fans, there are still fewer of them to eat brats in each household. In a hypothetical example, two people eating four brats per household gives you a Wisconsin brat rate of eight brats per household. In Illinois, where the household size might be three, you get three people eating at the same rate, which gives you a brat rate of 12 per household. Does this mean Packer fans are eating sushi instead? Nope. It means the denominator is just wrong for this type of interpretation. It should be the number of persons and not the number of households for this kind of comparison. The people of Illinois may eat more brats overall, but this doesn't mean that an individual resident does. To say a Bears fan eats more brats, you need it to be a per capita rate. As I said, it is easy to make a denominator do unconscionable things even in silly circumstances. (Bratwurst domination rises to the level of "unconscionable" in these parts.)

What about when the numerator and denominator are not dancing well together? This happens when the events in the numerator can't happen to everyone in the denominator. A good example is divorce rates. What happens when you use the number of divorces per capita as a measure of the quality of married life in different states? Divorces can't officially happen to people who have never been married. A rate actually should contain the number of events in the numerator and the population at risk of the event in the denominator. Then a comparison between states will tell you something about the state of marriage or the risk of divorce. You can calculate the number of divorces per capita if you wish, but it can be a bit misleading if you use it to understand what happens to marriages.

Here is an example. In 2009, Pew did a report on marriage and divorce by state, and it reported on the percent of men and women currently married and currently divorced. One of the lowest figures is in the state of New York, where only 7 percent of adult men were divorced in 2009--which doesn't really square with stereotypes gleaned largely from our favorite "Sex and the City" episodes. On the flip side, 12 percent of adult men in Montana are divorced--what's going on out there in the West? The answer lies in another piece of data that was reported. Only 49 percent of men were currently married in New York in 2009 while 55 percent were currently married in Montana. This suggests that the men in Montana are the marrying kind and, thus, more vulnerable to divorce. It doesn't really tell us that New York is a better place to be married than Montana. You really have to look at the divorce rate to figure that out.

Is there always a right way and a wrong way to use a denominator? No. The rate or proportion is as innocent as its denominator. What matters is how it is interpreted. For the brat rate, if you are in the grocery business and you sell goods to households, you do want households in the denominator so that you stock your stores differently in Wisconsin than in Illinois. The proportion of divorced persons per state might tell you something about the availability of a future mate or whether it is a good place to be a divorce lawyer. The conclusions you cannot draw safely are that Bears fans eat more brats than Packers fans and that your marriage is safer in New York than Montana.

Political comparisons that rest on statistics that are not correctly constructed can contribute to a feeling that the whole enterprise of numbers and politics is untrustworthy. Denominators, in particular, are vulnerable to manipulation. When numbers arise in politics or in life, always remember the acronym--WITD (What's In The Denominator?).