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Confounding

Also known as: confounder, lurking variable, common cause.

A third factor that influences both the supposed cause and the outcome, creating or hiding an association between them.

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Definition

Confounding occurs when a third factor influences both the thing you think is a cause and the outcome, creating or hiding an association between them. Comparing groups that differ in that factor then credits the supposed cause with an effect that belongs to the third factor.

In plain terms

Ice-cream sales and sunburn rise together because both follow the sun. In business data the classic case is selection into a treatment: sellers put video on the products that already sell well, so products with video outsell those without, whatever video does.

Ways to deal with it: randomise who gets the treatment (which breaks the link to the third factor); compare within groups that are alike on the confounder (stratification, matching, adjustment); or draw the assumed causal structure and reason about it. A confounder that was never measured cannot be adjusted for, which is why design beats after-the-fact statistics.

Example

1,000 products; 200 are “popular” and 800 are not. Sellers add a video to 150 of the popular ones and 50 of the others. In truth the video changes nothing: popular products sell 60 a week, the rest 15.

GroupProductsAverage weekly sales
With video200 (150 popular, 50 not)(150 × 60 + 50 × 15) / 200 = 48.8
Without video800 (50 popular, 750 not)(50 × 60 + 750 × 15) / 800 = 17.8
Within popular products, with vs without video60 vs 60: no difference
Within other products, with vs without video15 vs 15: no difference

Overall, videos seem to give a 2.7-fold boost. Within each kind of product they give none: the entire gap comes from which products were given videos.

Common misunderstandings

  • “Statistics can always remove a confounder.” Only measured ones; unmeasured confounders stay, which is why randomisation matters.
  • “Adjusting for more variables is always better.” Adjusting for the wrong variable (one that is itself an effect of the treatment) can create bias.
  • “Confounding is the same as measurement error.” It is a problem of what produced the groups, not of how precisely they were measured.
  • Correlation vs. Causation

    Correlation means two quantities move together; causation means changing one would change the other. Data alone cannot tell which, or whether a third factor drives both.

  • Simpson's Paradox

    A trend that appears in every subgroup can reverse or vanish when the groups are combined, because group sizes differ and the grouping is linked to both choice and outcome.

  • Selection Bias

    The units in your data differ systematically from the group you want to describe, because of how they were chosen or kept. Results hold for the selected group only.

References

  1. Sander Greenland, James M. Robins, Judea Pearl. Confounding and Collapsibility in Causal Inference . Statistical Science, 1999. DOI: 10.1214/ss/1009211805
  2. Judea Pearl. Causality: Models, Reasoning, and Inference . Cambridge University Press, 2009. ISBN 978-0521895606.