# Correlation vs. Causation - Why Correlation does not imply Causation Example

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#### ncwalker

What is the best example you use to explain why correlation does not imply causation that will reach the most non-statistical, non-mathematical people?

#### Bev D

##### Heretical Statistician
Super Moderator
Tukey's 3 requirements for causation
• consistency: more than 1 pair of independent samples, can the relationship be replicated across multiple independent events or trials
• responsiveness: The cause must explain both the good & the bad result and you must be able to turn it on & off at will at will.
• mechanism: logical reason why the factor causes changes in the response - or output factor

Spurious correlation happens everywhere...see this web site on spurious correlations

Then there are times when two things are caused by the same factor - they will appear correlated because they are - but one doesn't cause the other. This is also known as bad science. A famous example is a sociological study that showed correlation between the rate at which men were imprisoned and if their mothers smoked while the man was 'in the womb'. While smoking causes many things, it probably doesn't cause men to commit criminal acts and get caught. a follow on study tried to indict poverty as the cause, bu tthe next study revealed data showign that 'disadvantaged' youth while can be as reckless and antisocial as hihgly advantaged youth, but if yoru parents are very well of, they get you out of most of the criminal acts without jail time.

The lesson around correlation vs causation is that systems are complex and causal mechanisms have many levels of cause to effect; they are not always direct paths.

#### Miner

##### Forum Moderator
Take the case where there is a strong correlation between two variables, A & B. The following possibilities could all result in this correlation.

• A caused B
• B caused A
• A and B partially cause each other
• A caused C, which in turn caused B
• A and B are both caused by C
• A & B are under reported (i.e., only exceptions are reported)
• Pure chance

##### Lawyer
Suicides by hanging, strangulation and suffocation and the number of lawyers in North Carolina. Correlation: 0.99

#### Steve Prevette

##### Deming Disciple
Super Moderator
Actually about 20 years ago someone asked me to analyze suicide rates in counties in Washington state. The only outlier (per capita rate) was the county at Port Angeles WA. Must be either economic depression due to loss of logging industry, or just the weather, was my guess.