Hidden Common Cause

If two things are shown to be (strongly) correlated, it is tempting to assume that one causes the other (see PostHocErgoPropterHoc and CorrelationImpliesCausation). But often there simply is a HiddenCommonCause for both. This will invariably cause a correlation between both.

Not to be confused with SpuriousCorrelation? (if you have a sufficiently large number of studies, statistics says, that a few will find correlations, that are - well - random).

Example:

• Listening to music when young correlates with being better at maths.

Without further information one is tempted to read it as:

• Listening to music when young makes you better at maths.

But the truth may or may not be:

• Parents nurturing their children let them hear music and provide other interesting stimulus which leads to (among other things) to being better at math.

Other examples:

• Shark attacks and consumption of ice-cream are positively correlated
• Average number of storks on a roof in Denmark with the number of children in the household

If you think, that these are bad examples or SpuriousCorrelation?, don't be fooled. These is a HiddenCommonCause and it is revealed below the spoiler.

I would say these are better examples because the common cause is less obvious. It depends on what you're trying to show I suppose. If the answer is too obvious people will simply reject it as unrealistic, and that they claim wouldn't be fooled by "real" examples.

And the answers are at the bottom of this page ...

• Salary rises with size of shoe (it does). The reason is not that income lets your feet grow or your large feet allow you to kick asses. It's just plain, that men earn more than women and women have smaller feet. Thus the HiddenCommonCause is gender.
  • And age. Five-year-olds have small feet and don't earn very much. This is a far bigger factor than gender.
  • And height - tall people have been shown to make more money (at least in the US) than short people.

See FallaciousArgument

Spoilers follow:

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• Shark attacks and ice-cream consumption are linked by hot weather. More people swim, more people get attacked.
• The common factor with the storks and children is the size of the house - specifically, the area of the roof.