In statistics, the Simpson Paradox happens when a trend clearly shows up in clusters/brackets of data. But it disappears or at worse it reverses when the data is grouped and combined. In short, the Simpson paradox shows that when the data moves from clusters to combined data, it hides several distributions, which end up creating a biased overall effect.
As Tom Grigg explained extremely well, the Simpson paradox took its name from Edward Hugh Simpson thanks to a technical paper in 1951.
Yet it was made popular when another statistician, Peter Bickel, was called – in 1971 – to analyze the admission data at UC Berkley’s suspected gender bias.
As the story goes, the university feared a lawsuit, so they had the data analyzed by Bickel.
When the data was combined it really gave the impression that more males had been selected over women.
In fact, of the total male applicants, 44% were selected and of the total female applicants 35% were selected.
Yet when the data were analyzed by the department, it showed something completely different.
In four out of the six departments analyzed, the admissions were biased toward women.
But, as women applied to departments where fewer applicants were selected when the data got combined it gave an impression of bias toward male applicants.
Understanding the Simpson paradox
A good example is Nassim Taleb’s video on the topic.
While this is related to vaccine data, it can be easily translated into business as we’ll see.
As Taleb explained in relation to the vaccine data.
When the data are grouped under the same umbrella, after having been analyzed in clusters and homogeneous groups, it suddenly gives an opposite effect.
It’s like the data not only doesn’t give the same result when analyzed in brackets, but it gives the reverse effect.
This is what happens when the Simpson paradox messes up the statistics data.
Why? Intuitively, when data, before compared under brackets, get combined it disperses, thus making that worthless for the initial scope.
In the case, of the vaccine, because many people over 60s were vaccinated, and a few people under 20s were vaccinated, when the data gets combined it’s skewed toward the mortality of people over 60s, thus creating a bias, and.
Beware of the Lurking variable
To keep things short, hidden variables in the combined spurs the overall analysis, making it worthless.
This is known as a “lurking variable” or a variable that affects the data at the point of creating a “spurious association” (in short, the cause-effect relationship ceases).
The Simpson paradox in business
The Simpson paradox can hide in many of the business and marketing analyses out there, as when the data is combined it’s easy to mistake a correlation with causation.
Take the case of, as explained by adexchanger.com, for instance, when deciding on a programmatic campaign, when looking at the data for gender only, it shows how the male budget has seemingly more conversions, thus skewing the data toward males.
Yet from an age analysis, you figure that females between 18-24 have higher conversion rates.
If you don’t understand this bias, it’s easy to overspend on an audience that is overrepresented not because it’s more aligned with your audience, but rather because you’re reading the data in the wrong way.
And as you can imagine, this can have substantial consequences on your bottom line (money wasted on ineffective campaigns, and lost revenues as you’re not targeting the right audience).
Key takeaways
The Simpson paradox is an effect that in statistics and probability can create biased analyses. In fact, when present the data combined from an analysis gives a reverse effect compared to the data analyzed in buckets.
The Simpson paradox can create biased analyses also in business and marketing creating overspending toward the wrong audience.
The Simpson paradox also makes it much harder to make decisions in business when doing statistical analysis.
As highlighted by German psychologist Gerd Gigerenzer in the paper “Heuristic Decision Making,” the term heuristic is of Greek origin, meaning “serving to find out or discover.” More precisely, a heuristic is a fast and accurate way to make decisions in the real world, which is driven by uncertainty.
Bounded rationality is a concept attributed to Herbert Simon, an economist and political scientist interested in decision-making and how we make decisions in the real world. In fact, he believed that rather than optimizing (which was the mainstream view in the past decades) humans follow what he called satisficing.
Second-order thinking is a means of assessing the implications of our decisions by considering future consequences. Second-order thinking is a mental model that considers all future possibilities. It encourages individuals to think outside of the box so that they can prepare for every and eventuality. It also discourages the tendency for individuals to default to the most obvious choice.
Lateral thinking is a business strategy that involves approaching a problem from a different direction. The strategy attempts to remove traditionally formulaic and routine approaches to problem-solving by advocating creative thinking, therefore finding unconventional ways to solve a known problem. This sort of non-linear approach to problem-solving, can at times, create a big impact.
Moonshot thinking is an approach to innovation, and it can be applied to business or any other discipline where you target at least 10X goals. That shifts the mindset, and it empowers a team of people to look for unconventional solutions, thus starting from first principles, by leveraging on fast-paced experimentation.
The concept of cognitive biases was introduced and popularized by the work of Amos Tversky and Daniel Kahneman in 1972. Biases are seen as systematic errors and flaws that make humans deviate from the standards of rationality, thus making us inept at making good decisions under uncertainty.
The Dunning-Kruger effect describes a cognitive bias where people with low ability in a task overestimate their ability to perform that task well. Consumers or businesses that do not possess the requisite knowledge make bad decisions. What’s more, knowledge gaps prevent the person or business from seeing their mistakes.
Occam’s Razor states that one should not increase (beyond reason) the number of entities required to explain anything. All things being equal, the simplest solution is often the best one. The principle is attributed to 14th-century English theologian William of Ockham.
The Mandela effect is a phenomenon where a large group of people remembers an event differently from how it occurred. The Mandela effect was first described in relation to Fiona Broome, who believed that former South African President Nelson Mandela died in prison during the 1980s. While Mandela was released from prison in 1990 and died 23 years later, Broome remembered news coverage of his death in prison and even a speech from his widow. Of course, neither event occurred in reality. But Broome was later to discover that she was not the only one with the same recollection of events.
The bandwagon effect tells us that the more a belief or idea has been adopted by more people within a group, the more the individual adoption of that idea might increase within the same group. This is the psychological effect that leads to herd mentality. What is marketing can be associated with social proof.
Gennaro is the creator of FourWeekMBA, which reached about three million business students, executives, and aspiring entrepreneurs in 2021 alone | He is also Head of Enterprise Sales for a high-tech startup, which he helped grow at a double-digit rate since the onset | In 2012 Gennaro earned an International MBA with emphasis on Corporate Finance and Business Strategy.
