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I have the following data, where 2 properties (P1 and P2) can be either True or False

              P1      P1 
             False  True

P2:False    2646    400
P2:True     749     245

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I am trying to understand if P1 being True or False has any implication on P2. At first sight, it seems that if P1 is True, there are better chances that P2 is True. But I am sure that this is too naive.

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    $\begingroup$ Standard chi-square testing confirms association of variables overwhelmingly if it were in doubt. (I guess that many, perhaps most, statistically experienced researchers would prefer to talk of association rather than correlation here.) I don't think that any information in your question allows comment on causation. That depends entirely on what P1, P2 are. (I don't understand your precise wording in your last paragraph.) $\endgroup$
    – Nick Cox
    Commented Nov 11, 2014 at 21:49
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    $\begingroup$ One of your considerations should be what the data represent relative to the conclusions you would like to draw. If "here" means within these data, then obviously there is a relationship--albeit weak--and you can quantify it by computing proportions within your table. If "here" means some larger population the data are intended to represent, then how were the data obtained? Are they are random sample or some other kind of sample? $\endgroup$
    – whuber ♦
    Commented Nov 11, 2014 at 23:06
  • $\begingroup$ @whuber by here I meant the population from which such data are sampled. They belong to a Kaggle challenge (the one with reddit pizza) and I believe they are just randomly sampled $\endgroup$
    – meto
    Commented Nov 17, 2014 at 1:05

1 Answer 1

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  1. Is there any correlation? Using 2x2 contingency table analysis, the Phi coefficient of association is 0.14, with chi-squared = 74.08 and n = 4040. So, yes, there is some correlation (or association).
  2. Is there any causation? I don't think it will be easy to determine that philosophically, statistically, or otherwise. There is simply not enough information to know how these numbers came to be. I think you need to see if this data is observational or experimental; some people seem to believe and/or argue that you cannot make causal claims from using observational data. I think you need to pick a causal framework (one that defines what is causality) and see if the causal calculus (if any) available in that framework will allow you to draw a causal link between these two variables.

Note these sayings

  1. Correlation does not imply causation.
  2. Causation leads to correlation.

So, it seems to me, a causal relationship should manifest (or cause) a correlation relationship. But, just because you see a correlation relationship, does not mean there is a causal relationship. Kind of like (as an intuitive example), fire leads to smoke, but observing smoke may not mean there is fire.

So, I believe, you may have a causal relationship, it is not ruled out yet, because you have a correlation relationship. But it is not definitive, whether you have or do not have a causal relationship. Remember, stock prices have been shown to be correlated with moon cycles, yet, is there a causal relationship?

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  • $\begingroup$ Do you use "casual" as a synonym for "causal"? $\endgroup$
    – whuber ♦
    Commented Nov 17, 2014 at 1:15
  • $\begingroup$ No typo, it should be causal, as in cause, causation, causal. $\endgroup$
    – Jane Wayne
    Commented Nov 17, 2014 at 8:43

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