Correlation vs Connection

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…from CheLabWiki, an online resource for chemical-engineering laboratories located at www.chelabwiki.org; Site Revision #844; 6 January 2009.

Community Portal → Data Analysis → Correlation vs Connection

Be aware that even when you have established the existence of a correlation, you have not necessarily established a complete causal connection. The typical possibilities are these:^[1]

(a) Your correlation between

x

and

y

might be the result of chance. Even with 1% significance, there is still one experiment out of 100 in which chance causes the apparent correlation. This eventuality is most common with small amounts of data, that is, when the number of measured points

N

< 10.

(b) Even when the correlation is real, there may not be a causal connection. For example, two clocks may strike at the same time (correlation), but this does not mean that the striking of one caused the striking of the other. To establish a causal connection you must develop and test a chain of events or circumstances that connect effect to cause. The incentive to seek such chains of logic may be bolstered by knowing that a correlation exists.

x

and

y

are correlated and causally connected, the value of a linear or rank-order correlation coefficient does not tell us whether

x

causes

y

y

causes

x

. We need additional information. Usually the information is temporal: part of the distinction between cause and effect is that the cause happens before the effect. This seems simple, but there are situations in which the temporal order of events is obscure. Examples include biological activities at the molecular and cellular levels.