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.
The Simpson paradox origin story
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
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).
- 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.
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