Why should business care about Simpson’s Paradox?
Chances are you’ve never heard of Simpson’s paradox, but it matters. In sum, Simpson’s paradox—sometimes referred to as the “reversal paradox”—says that how we choose to analyze a data set may cause us to draw opposite conclusions. For instance, in the 1980s, there was a study about the most effective way to treat kidney stones, using existing outcome data. When looking at the outcomes for all patients, procedure A showed better results. However, when scientists cut the data by stone size, they found that for all stone sizes, procedure B was better. To make matters worse, there is no boundary to Simpson’s paradox. If researchers had cut the data by gender or height or BMI or whatever, they could have seen reversal after reversal after reversal.
Fortunately, if you can design an experiment, you don’t run into this problem. But there are many studies that would be unethical. We often hear about drugs, for instance, that have not passed all of the FDA’s gates for safety and efficacy but still are administered to patients. Unfortunately, these are all instances where the patient’s alternative is death. But imagine a condition like depression, where there are lots of alternatives. And imagine that we wanted to study the effectiveness of a treatment on mild to moderate depression—so that the alternative to failure of the intervention is not catastrophic. The new pill, however, has a 1 in 1000 chance of causing slow, painful, but certain death. It would be unethical to study this drug in a randomized controlled trial (RCT), which is considered to be the gold standard of research. Because we have alternatives, including doing nothing, that are better than dying a slow painful death, we are in a situation where we have to use existing data to figure out how to treat mild to moderate depression.
So, in the real world, where we have strong ethical controls on experiments, we will always be confronted with Simpson’s Paradox and no way for our data to tell us how to slice it up so that we’re assured that procedure A truly is better than procedure B.
In business, we’re even in a worse situation. We really have only data about the past. Other than what’s called A/B testing—where a company sends out two mailers with different fonts or text to entice potential customers to sign up for their credit card, or a website feeds people many different looks/feels to see which keep people on the site longest—we are stuck with using existing data to try to draw conclusions about the right way to proceed in the future. But Simpson’s Paradox tells us that quite literally, we can never be sure in advance whether we have analyzed our marketing, financial, and other data in the right way or not.
But there is good news. First, Judea Pearl of UCLA has worked out a calculus of causality, with tools to model it. That is, there is a way to use information from the past to tell us what causes what. We don’t have to sweat Simpson’s Paradox, we can know from past data whether procedure A or procedure B will (or is more likely) to produce our desired outcome. Second, if we do not need to make something happen in the real world, then data analysis—which will give us nice correlations—is good enough. Put another way, if we don’t need to cause people to buy a product, no problem. However, if we want to figure out how to get people to buy our product or use our service, we either need to have special intuition or we need to understand what causes someone to buy our product vs. all other options.