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Simpson’s Paradox in Aggregated Market Share Data

Article Quant Q&A · Author: Gianluca G
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Summary

The document presents a market share puzzle: two company areas each maintain their share over time, yet the company’s aggregate share falls. It identifies the pattern as Simpson’s paradox, in which a trend visible within separate groups can reverse after the groups are combined. The central lesson is that group level results do not necessarily predict the direction of an aggregate result.

The explanation is conceptual and points to the paradox’s broader statistical examples, but it supplies no underlying figures or detailed breakdown of the company’s areas. In practical analysis, changes in the relative sizes or weights of the groups can affect the aggregate and create the reversal. The note therefore serves as a caution when interpreting aggregated market or performance statistics: examine subgroup composition alongside within-group trends before drawing conclusions. It does not offer a worked numerical example or a method for diagnosing a particular dataset.

Key ideas

  • Simpson’s paradox occurs when a trend within groups reverses in the combined data.
  • Stable market share within business areas can coexist with declining total company share.
  • Changes in how much each group contributes can influence the aggregate result.
  • Analysts should check group composition before interpreting combined statistics.

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Full text
# Why combining market share behaviours brings a different conclusion


# Why combining market share behaviours brings a different conclusion












Please check the following dummy example to explain the paradox.

Both areas in the company keep the same market share during the years, but at the end company lost share in the market!

Math is 100% correct, both Areas worked well and reached their goal, but need to clarify why this happens (in simple words without using math).

## Answer by David Duarte (score 2, accepted)

https://quant.stackexchange.com/a/51008

This is known as the Simpson's Paradox in Statistics, which occurs when groups of data show one particular trend, but this trend is reversed when the groups are combined together.

Check the wikipedia page for some examples.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.