New York City Health Atlas

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### Correlation Is Not Causation

In statistics, correlation is a measure of association between two numeric variables. The strength of correlation between two variables is represented by the correlation coefficient, represented by the abbreviation r. Correlation coefficients range between -1 to 1.

• A coefficient of 1 indicates a perfect, positive association between the variables. As variable A increases, variable B also increases the same amount.
• A coefficient of -1 is similar, representing a perfect negative association: as variable A increases, variable B decreases the equivalent amount.
• A coefficient near to or equal to 0 means that there is no association with between the two variables.

Though the correlation coefficient indicates the strength of an association, it does not provide information about whether the change in one variable is caused by the other.

For example, if the correlation between adult smoking prevalence and child poverty is 0.7—a strong correlation—we cannot say either that adult smoking causes child poverty or, inversely, that child poverty causes smoking. We only know that as one of these variables increases, the other tends to increases.