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Tuesday, May 30, 2023

Simpson’s Paradox Explained: The Paradox That Flips Statistics on Its Head

Simpson's paradox is fascinating but potentially misleading

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Aditya Saikrishna
Aditya Saikrishna
I am 21 years old and an avid Motorsports enthusiast.

INDIA: Statistics is a crucial tool in analysing data, but there is a paradox that can completely flip the results of statistical analysis. 

This strange paradox is known as Simpson’s paradox, and it has the power to mislead even the most experienced statisticians.

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Simpson’s paradox is a statistical phenomenon where a trend or pattern appears in different data groups but disappears or even reverses when the groups are combined. 

This phenomenon means that a conclusion drawn from the combined data may be different from the conclusions drawn from the individual data groups.

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To understand this better, let us consider a hypothetical example. A university wants to compare the admission rates of male and female applicants. 

The data shows that the admission rate for male applicants is 60%, while the admission rate for female applicants is 50%. 

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At first glance, it is apparent that the university is biassed towards male applicants, but this is not the whole picture.

Upon further analysis, it appears that male applicants tend to apply to highly competitive programmes where the admission rate is only 40%. Meanwhile, female applicants tend to apply to less competitive programmes, where the admission rate is 80%. 

When compared separately, it is clear that there is no gender bias in the admissions process. 

The paradox is that when these groups are combined, it appears to the observer that the university is biassed towards male applicants.

Simpson’s paradox arises because of a confounding variable, which is a variable that affects both the dependent and independent variables in a study. 

In this case, the confounding variable is programme competitiveness. When the data are combined, the effect of the confounding variable is lost, leading to a paradoxical result.

Simpson’s paradox can have serious consequences in fields like medicine, where it can impact the efficacy of treatments. 

For instance, a drug may appear effective when analysed across a population. However, when the analyst separates the data by age or gender, the results may show that the drug is ineffective or harmful in some subgroups.

To avoid this paradox, statisticians must be careful in their analysis and ensure that they account for the confounding variables. 

They should also pay attention to the sizes of the groups and the differences between them before drawing conclusions based on combined data.

Also Read: Time Traveller’s Dilemma: The Grandfather Paradox and its Mind-Bending Consequences


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