In science (and when developing hypotheses more generally), it is very common to come across situations where a variable of interest (let’s call this the dependent variable, “Y”) is strongly correlated with at least two other variables (let’s call them “A” and “B”). Here are some examples:
- If you’re a psychology researcher investigating possible causes of depression (Y), you may have trouble disentangling the effects of poor sleep quality (A) and anxiety (B), both of which tend to be correlated with depression.
- If you’re a health researcher investigating the causes of diabetes (Y), you may have trouble disentangling the effects of high carbohydrate intake (A) and obesity (B).
- If you’re investigating the causes of high life satisfaction (Y), you may have trouble disentangling the effects of friendship quality (A) and mental well-being (B).
In all these examples, we know that at least two of the variables (A and B) are related to the main variable (Y), but the really tricky question is to figure out what all the possible causal relationships are between the three. For instance, does A cause B, which causes Y, does Y cause both A and B, or is there some other explanation?
In the pdf below, I sketch out 45 possible explanations to consider in situations where there are two variables that both correlate with a third variable of interest.
First of all, there are the types of causal relationships one often expects, where A and B both cause Y in simple ways (either directly or through each other):
Even if A and B really do cause Y, they could be interconnected to each other in complex ways:
It also could be the case that only A or only B causes Y, with the other variable only appearing to cause Y due to a confounding effect:
It’s also possible that Y is actually one of the causes rather than merely being caused by A and B:
Then there are situations where there is a critical other variable (or set of variables – represented as a “?” below) that are integral to the causal structure:
Finally, there are situations where Y is caused by A or B (or both), but Y also causes A or B (or both), resulting in a cyclic relationship:
Here’s a link to my pdf showing most of the possible relationships.
If you want to read about other challenges associated with untangling causality in the real world, you can read another post about this here.
I first created this diagram on April 19, 2021. I made minor edits to the diagram and wrote this piece with assistance from Clare Harris. This piece first appeared on my website on November 22, 2023.
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