Berkson’s Paradox – a Statistical Illusion

By: Michael Mo

Once in a while, Twitter blows up with the story of a high school dropout who became a multi-billionaire. Before long, people would start saying things like “university is useless!” or “School is useless!” in the comment section. Their “argument” is that Ivy League graduates are struggling to find jobs while high school or university dropouts are building successful businesses around the world. There are two simple methods to rebut this absurd claim: you could either tell them to look in the mirror and see how that face compares to an Ivy League graduate, or you could educate them on Berkson’s Paradox.

Berkson’s Paradox

Berkson’s Paradox is the counterintuitive relationship between two traits in statistics. At its root, this false observation is based on the incorrect assumption that “cause” is related to “effect” and bias in data collection. Let’s take the high school dropout as an example.

We first assume that how successful a person becomes have nothing to do with their education level. Therefore, we will not find a relationship between education and success when we examine the general population (shown in figure 1).

However, we are generally not surprised about the fact that less-educated people find less success. We have thereby neglected a fair proportion of the population in our data collection (shown in figure 2).

As a result of the bias in our data collection, we end up seeing 100% of less-educated people finding success (Figure 3 – green shade) but only a fraction of highly-educated people finding success (Figure 4 – green shade). This is why education seems to make people less successful in life.

Another example of Berkson’s Paradox is the phenomenon “all handsome men are players” (Figure 5). Once again, we can put the visual appearance of a person on the x-axis and the loyalty of a person on the y-axis. Since none of the ugly and unloyal people will attract the opposite sex, we only observe those who are dull but loyal. On the other hand, both loyal and unloyal handsome men attract the opposite sex. As a result, people conclude that unloyalty is a trait that only belongs to handsome men.

An Idea to Take Note Of…

Berkson’s Paradox epitomizes how a narrow mindset would lead to absurd conclusions in life. So before using statistics to support your claim, think to yourself, “Have I collected enough data? Have I opened my perspective wide enough?”