Detecting Causal Relations

Causes are difference-makers. Effect need not be universal/deterministic. Not everyone who is bitten by a cobra dies. Not everyone who dies is bitten by a cobra. But cobra bites still cause death. “Causal factor”

An apparent paradox You can’t infer causation from correlation. But, correlation is the only thing you can infer causation from. All our evidence for causation comes from correlations.

Height/weight correlation

Height/inseam correlation

Height/IQ correlation

Causation and inference to the best explanation Often, the best explanation for a correlation is that the two variables are causally linked. But it might be that: A causes B. B causes A. C causes A and B.

Causation and correlation If height correlates with weight, then weight correlates with height. As one goes up (or down), the other goes up (or down). But, weight doesn’t cause height (being heavy doesn’t make you tall).

Confound A B ? C correlates causes (A) (B) (A) (C) Motorcyclists who wear helmets have fewer fatal accidents. Helmets save lives? Helmet wearers engage in less risky behavior. (A) (C) It’s the behavior, not the helmets, that explains the fatality rates?

Confound An additional variable that: (a) correlates with one or more of the independent variables (b) serves as plausible alternate cause of dependent variable

Can’t infer causation from correlation Because there’s almost always a confound! Always be on the lookout for possible confounds.

Smoking and lung cancer Lung cancer correlates with smoking. But smoking correlates with other things: personality type socioeconomic status genetic factors number of ashtrays owned These confounding variables also correlate with cancer. How to tell whether it’s the smoking that makes the difference?

Controlled experiment “Control for” confounding variable either statistically (observational study) or experimentally (interventional study)

Observational study Control group, experimental group Ensure that control group matches experimental group in all independent variables but one. Compare cancer rates of high socioeconomic smokers vs. high socioeconomic nonsmokers etc.

Limitations Always a worry about self-selection. Whatever sorted the subjects into control vs. experimental groups might also be responsible for examined effect. Control for all variables you’ve thought of.

Interventional study “Controlled experiment” strictly speaking Randomized trials Experimenter intervenes: randomly assigns subjects to control or experimental group Sometimes infeasible, sometimes unethical

Placebo effect: just believing you’re taking a drug has some tendency to improve health. Control groups always given placebo. Double-blind experiment: even the researchers don’t know which subjects are in control, experimental group.

An apparent paradox You can’t infer causation from correlation. But, correlation is the only thing you can infer causation from. All our evidence for causation comes from correlations.

Solution Patterns of correlations do provide evidence of causation. If x really is the only variable that could explain e, then x is probably the cause of e.

Causal Narratives

Imaginative storytelling as reason for believing causal claims Plausibility of story as reason to expect that A would cause B Simple narrative: I can easily see B happening as a result of A. In more complicated cases, chain these together. A would cause B, which would cause C, which would cause D. So, A would cause D.

If we lower taxes on the rich, then they will have more money to spend, which will result in their spending more money on goods and services, and that will lead to more jobs in those industries, and then the people who work those jobs will have paychecks, which they will spend, thus creating even more jobs, and the result is that the economy will improve. So, if we lower taxes on the rich, the economy will (probably) improve.

Causal narratives are most reliable when: Simple, e.g., mechanical subject matter, (e.g., That would probably break if I stood on it.) About which we have fairly direct experience Where we don’t have other (e.g., social or political) motives to believe that narrative

Dangerously unreliable otherwise, especially when chained together. Plausible storytelling is not evidence, on par with correlation, intervention.

Causal Fallacies

Ignoring common cause Thinking A causes B when in fact C causes both A and B. e.g., Ice cream causes violent crime? No, summer weather causes an increase in ice cream sales and an increase in crime.

Confusing cause and effect Correct detection of causal relationship, but inverting causal order. e.g., Drug use and emotional instability?

Post hoc Post hoc, ergo propter hoc after this, therefore because of this. Drawing causal conclusion from temporal succession often after a single event e.g., A rain dance brings rain.

“Name one” fallacy Xs don’t cause Ys (or there isn’t good evidence for Xs causing Ys), because there’s no clear example of an X causing a Y. But, causal generalizations aren’t usually inductive generalizations, so there’s no reason we ought to be able to point out specific instances. Justifying singular causal claim is harder than justifying general causal claim.

Coincidence, confounds, and causation It is always possible that a correlation is coincidental. Causal inference is always inductive. But, coincidence is less plausible for highly significant correlations.