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8. Correlation and Causation

 

Wireless Philosophy, Fundamentals, 7:09. Original title: CRITICAL THINKING - Fundamentals: Correlation and Causation

Summary​

Paul Henne (Duke University) takes on the conflation of correlation with causation, starting from a scene between two high school students in Arizona.

Andy's sunny days​

Andy always gets an A on his math test when it is sunny outside. On one sunny day he tells Maria: "I'm going to ace this test today because it's sunny!" Maria objects that he will ace it because he studied, and that the sunshine has nothing to do with it. Andy insists that he always aces his tests when it is sunny. Maria's reply is the point of the whole video: sure, but that is because he always studies for his math tests, and it is always sunny in Arizona.

Maria is right. The two events, the sunshine and Andy's success, occur together without either causing the other. They are correlated, and Andy's reasoning from that correlation to a cause is fallacious.

More correlations​

  • Fido barks when his tail wags.
  • People with higher grades in college had higher grades in high school.
  • People who take vitamin C recover more quickly from a cold.

Each is a correspondence between events, not a causal relation. Fido's tail sometimes wags without a bark and he sometimes barks without wagging, and we may suspect a common cause for both, such as his excitement when his owner comes home.

Positive and negative correlation​

Events that frequently occur together are positively correlated: when one is present, the other often is too, as with sunny Arizona days and Andy's test results. Two events are negatively correlated when the occurrence of one makes the other unlikely; when it snows it is usually not sunny, so snow and sunshine are negatively correlated.

Headlines trade in both. "Taking vitamin C helps you recover more quickly from a cold" reports a positive correlation; "eating more nuts makes you less likely to have higher levels of bad cholesterol" reports a negative one. Someone hearing this may conclude that they will eat more nuts and be rid of their bad cholesterol, and someone else will point out that this is only a correlation. That person may be a jerk about it, but they are right: without evidence that a causal relation holds, treating the correlation as one is a mistake.

Where the causal story really lies​

Take the college and high school grades again. It is wrong to claim that high grades in high school always cause high grades in college, even though there may be individual cases where something like that happens: Jane may have earned credits in high school that transferred and contributed to her success. But most of the time what causes success in college is working hard in college courses, and at the level where we are describing a correspondence between two data sets, the causal claim is false.

When two events are correlated, then, several explanations remain in play and one of them may have been overlooked: a common cause of both events, an alternative cause altogether, or simple coincidence.

The analysis of causation and how it relates to the types of correlation is deferred to a second part; the post hoc fallacy is the related false cause fallacy.

Key takeaway​

That two events occur together, or reliably fail to occur together, never by itself shows that one produces the other. Some further evidence for a causal relation is always required before the causal claim may be made.