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.
Aspect | Explanation |
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Definition | Simpson’s Paradox, named after British statistician Edward H. Simpson, is a statistical paradox where a trend or association observed within subgroups of data can reverse or disappear when the subgroups are combined. In other words, what seems true for individual parts of the data may not hold when the data is analyzed as a whole. |
Key Concepts | 1. Subgroup vs. Aggregate: The paradox revolves around the distinction between examining data within subgroups (i.e., disaggregated data) and analyzing the data as a whole (i.e., aggregated data). |
2. Causality vs. Association: Simpson’s Paradox highlights the difference between a causal relationship and a statistical association. An apparent association between variables may not imply causality when considering the entire dataset. | |
Causes | 1. Heterogeneous Subgroups: Simpson’s Paradox often occurs when subgroups within the dataset have significantly different characteristics or sample sizes. These differences can lead to skewed results when aggregated. |
2. Hidden Variables: Sometimes, there are unobserved or unaccounted-for variables that influence both the grouping and the outcome, resulting in the paradoxical reversal of trends. | |
3. Weighted Averages: Aggregating data with unequal sample sizes can give disproportionate weight to certain subgroups, affecting the overall trend. | |
Examples | 1. Medical Studies: Simpson’s Paradox is commonly encountered in medical research. A treatment that appears to be less effective in a subgroup may be more effective when considering the entire patient population. |
2. Educational Outcomes: Test scores within different schools or districts may suggest that one school performs better, but when considering all schools together, a different conclusion may emerge. | |
3. Sports Statistics: A baseball player may have a higher batting average in different seasons or against different teams, but the overall average for all seasons may be lower. | |
Consequences | 1. Misleading Interpretations: Failing to recognize Simpson’s Paradox can lead to incorrect conclusions and potentially poor decision-making based on aggregated data. |
2. Inaccurate Policies: In areas like healthcare or education, misinterpreting data can result in the implementation of policies that are ineffective or even detrimental. | |
3. Loss of Insights: If analysts focus solely on aggregated data, they may overlook valuable insights that exist within subgroups. | |
Mitigation Strategies | 1. Data Disaggregation: Consider analyzing and reporting data at both the subgroup and aggregate levels to gain a comprehensive understanding. |
2. Identifying Confounding Variables: Carefully examine potential confounding variables that might influence the relationship between the variables under study. | |
3. Transparent Reporting: When presenting data, clearly communicate the presence of Simpson’s Paradox, especially if it could impact decision-making. | |
4. Expert Consultation: Seek input from statistical experts or data analysts to ensure the validity of your interpretations, especially when working with complex datasets. | |
Conclusion | Simpson’s Paradox serves as a reminder of the nuances and potential pitfalls in statistical analysis. It underscores the importance of considering data from multiple angles and being cautious when drawing conclusions based on aggregated information. By understanding and addressing the paradox, analysts and decision-makers can make more informed choices and avoid misinterpretations. |
The Simpson paradox origin story
As Tom Grigg explained exceptionally well, the Simpson paradox took its name from Edward Hugh Simpson thanks to a technical paper in 1951.
Yet it was made famous 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 were 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.
The admissions were biased toward women in four of the six departments analyzed.
But, as women applied to departments where fewer applicants were selected when the data 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 about 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, as when the data is combined, it’s easy to mistake a correlation for 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 overrepresented audience, not because it’s more aligned with your audience but because you’re misreading the data.
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).
Quantitative vs. Qualitative Research
Dealing with data is extremely hard.
It’s one of the hardest things in business.
And as most businesses now have a lot of data available, it’s easy to fall into the trapping of misusing it.
For that, it’s critical to establish project business processes, whereas it gets clear to the internal team when to use quantitative vs. qualitative data or both.
Quantitative research, if used in the proper context, can be incredibly effective.
Companies like Amazon have learned how to balance that with qualitative research.
Indeed, quantitative data is extremely helpful to improve business processes.
However, it’s critical to know when human judgment needs to kick in, when some qualitative data is available that completely flips things upside down.
For instance, companies like Amazon have launched successful projects, like reviews, Kindle, Prime, and third-party stores, which were absolutely the result of human judgment rather than quantitative understanding.
Indeed, if Amazon was going to look into these endeavors with a quantitative mindset, it would have never undertaken them as they did not make sense from a quantitative standpoint.
Yet, the intuitive understanding of how those things that might seem negative from a first-order effect standpoint (losing profits in the short-term) might make complete sense from a second-order effect standpoint (becoming way more successful in the long run).
Understanding the implications of second-order effects is something that qualitative understanding and human judgment together can do.
Whereas quantitative data can be extremely useful to improve, in the short-term, business processes to make them way more efficient, which also, in the long-term, if properly used can create a competitive moat for the business.
For instance, going back to Amazon’s example, the company processes like inventory management and order fulfillment are part of its core strategic advantage, and they are driven by quantitative data!
Case Studies
- Healthcare:
- Scenario: A hospital wants to determine which treatment is more effective for a certain illness. At first glance, Treatment A seems to have a higher recovery rate than Treatment B. However, when data is broken down by severity of illness, Treatment B is more effective for severe cases, while Treatment A is more effective for mild cases.
- Simpson’s Paradox: The aggregate data suggests Treatment A is better, but a more detailed analysis shows that Treatment B is better for severe cases.
- Sports:
- Scenario: A baseball player, Player X, has a higher batting average than Player Y in both the first and second half of a season. However, when combining the two halves, Player Y has a higher overall batting average.
- Simpson’s Paradox: Individual performance in each half of the season does not necessarily predict overall performance.
- Economics:
- Scenario: A country’s unemployment rate decreases both this year and the previous year. However, when looking at the two-year period as a whole, the unemployment rate has increased.
- Simpson’s Paradox: Annual data may show positive trends, but longer-term trends might reveal a different story.
- Education:
- Scenario: Students from School A score higher on math tests than students from School B in both 9th and 10th grades. However, when combining scores from both grades, students from School B have a higher average.
- Simpson’s Paradox: Performance in individual grades doesn’t necessarily predict overall academic performance.
- Real Estate:
- Scenario: City A has seen a decline in house prices in both the east and west sectors. However, overall, the city’s house prices have increased.
- Simpson’s Paradox: Individual sectors of the city might show a decline, but the overall city might see an increase due to factors in smaller unexamined areas.
- Environment:
- Scenario: Factory A reduces its carbon emissions in both 2020 and 2021. Factory B increases its emissions in both years. However, when the total emissions of both years are combined, Factory A has a larger increase in emissions than Factory B.
- Simpson’s Paradox: Individual yearly reductions can be overshadowed by larger overall increases when data is combined.
- Transportation:
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.
Key highlights
- Definition of the Simpson Paradox: The Simpson Paradox is an effect in statistics and probability where a trend appears in clusters of data but disappears or reverses when the data is combined, leading to biased overall effects.
- Origin and Famous Case: The paradox is named after Edward Hugh Simpson and gained fame when statistician Peter Bickel analyzed UC Berkeley’s admission data, revealing biases in gender representation.
- Occurrence in Business and Marketing: The Simpson Paradox can hide in business and marketing analyses, leading to mistaken correlations for causation and overspending on misinterpreted data.
- Impact of Hidden Variables: Hidden variables, known as “lurking variables,” affect combined data, causing spurious associations and disrupting cause-effect relationships.
- Importance of Proper Data Analysis: Proper data analysis and understanding when to use quantitative and qualitative research can mitigate the effects of the Simpson Paradox in business decision-making.
- Balancing Quantitative and Qualitative Research: Companies like Amazon have demonstrated the importance of balancing quantitative data with qualitative understanding and human judgment for more effective decision-making.
- Strategic Implications: Understanding the implications of second-order effects and combining qualitative understanding with quantitative data can create competitive advantages and long-term success in business.
Connected Thinking Frameworks
Convergent vs. Divergent Thinking
Law of Unintended Consequences
Read Next: Biases, Bounded Rationality, Mandela Effect, Dunning-Kruger Effect, Lindy Effect, Crowding Out Effect, Bandwagon Effect.
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