Title: What assumptions do we need to make to infer cause from correlation?
Course: UGQuants (SSPS) > Section: Causality

What assumptions do we need to make to infer cause from correlation?

How can we start to investigate whether a relationship between two variables is evidence of a causal process at work?

Imagine we have a pair of variables, with X being what we think is the independent or predictor variable and Y the dependent or response variable. In this example imagine that X takes two values (e.g it might be a variable describing whether a respondent is male or female).

The only assumption we need to be able to make is that the two or more groups we are comparing with different values for X are alike in all other respects, and this breaks down into two more detailed assumptions: that prior variables have been controlled and intervening variables have been controlled. A prior variable is a variable that has a causal relationship with our X variable. An intervening variable is one that has a causal relationship with our Y variable. There may also be ensuing variables, but since these will not affect the relationship between X and Y, we can safely ignore these just now.

The diagram below illustrates a simple causal path diagram. It is usually helpful to keep the logic of how we think of a possible relationship between variables as clear as possible by setting it down diagramatically, with circles or ovals representing variables and arrows between them representing what we hypothesise to be the direction of cause and effect. The diagram below summarises the situation that we usually confront. We have two variables of interest, X and Y. However, our task is to work through variables that might be prior to or intervening in, the relationship between X and Y.