I have two variables A={some values} and B={some values). Each value in A is not related to the corresponding value in B. How I can find the correlation between these two variables? or how can I know if these two variables have any kind of association "relationship" between them? Just an example to make the question clear: Assume A refers to the number of daily deaths in a very big hospital (30 values within a month) and B refers to the daily number of absent doctors in that hospital (30 values within a month). Values in A and B are not sorted by the date (i.e. A[i] is not related to B[i]), so they are in different order and we want to know if they are correlated or have any kind of relationship.

I assume correlation coefficients will not work hear as each value in A does not match the corresponding value in B.

  • $\begingroup$ Why do you think that the number of absent doctors on some day $V$ would affect the number of deaths on some other day $W$? $\endgroup$ – learner Dec 20 '13 at 14:23
  • $\begingroup$ (The assumption is that few doctors may not be able to follow all cases in ICU and may lead to some deaths). Anyway, that was just an example to simplify the question. The problem is that we do not have the values of A and B obtained in the same order. $\endgroup$ – Abbas Dec 20 '13 at 14:28
  • $\begingroup$ If the example given is not the full story, I think that giving more information about your data might help us help you more. $\endgroup$ – learner Dec 20 '13 at 14:59
  • $\begingroup$ I do not think it will help but it will add more confusion. Anyway, the two variables that I am studying are (A=gene expression B=treatment response score) in a specific gene position. so we want to know if the treatments at that position lead to change in expression. (We do not know which treatment is associated to which expression value, but we have list of values). $\endgroup$ – Abbas Dec 20 '13 at 17:55
  • $\begingroup$ What is gene 'position'? $\endgroup$ – learner Dec 20 '13 at 18:42

This is not possible. Correlation doesn't work for the reason you stated. So there is no way to get the correlation.

But the same reasoning applies to whatever measure you could chose. It would change if you reshuffled the data, and, since you said the order doesn't match, then reshuffling should not matter.

  • $\begingroup$ what if I create a probability distribution for each variable and measure the distance between the two to prove some kind of association "relationship" between the two? $\endgroup$ – Abbas Dec 20 '13 at 14:19
  • $\begingroup$ That would not prove any relationship, at least, not in any way that I can see. $\endgroup$ – Peter Flom - Reinstate Monica Dec 20 '13 at 14:23

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