Optional: Causes

• we’ve seen lots of diagrams, and the word cause has come up a bit more

• define cause - y listens to x (if you change x, y will change)

  • i.e., somewhat interventional (if we intervene on x, what happens to y?)
  • counterfactual (in a world where x was A instead of B, what would y be like?)

• statistical estimates are never more than associations

• our assumptions about the design/dgp/theory are what (sometimes) allow us to more confidently infer an estimate to be representative of causal effect

• diagrams show our causal assumptions

• silly examples

• two columns. RCT vs simple confounding. two diagrams

• whether estimates represent “the amount y changes if we intervene on x” depends entirely on if we’re right in how we drew those diagrams.

  • depends on if we got arrows right way round
  • depends on if we measured and adjusted for all relevant confounders
  • depends on if we can assume no issues like non compliance in RCTs

• IFF we’re right, then estimates we get out of statistical machinery like lm will be unbiased estimates of how much y changes in response to a change in x

  • we’ll never really know if we’re right. we can test certain implications (e.g., conditional independences), but no result will ever tell us if we’ve correctly identified x->y

• so we can never “test” causality.

• causality isn’t something that is separate from traditional stats, or some fancy methods we can do that suddenly allow us to say “[estimate] is the causal effect of x on y”

  • there are fancy methods for better adjustment of confounding variables, but obviously the identification of what those confounds are is not something statistics can tell us.
  • causal quartet

• it is the logical antecedent to statistical inference