Correlation, Causation & Controlled Experiments

The strength and direction of a *linear* association between two variables, from −1 to +1 — association only, never mechanism. A strong non-linear pattern (like a ring) can still give r ≈ 0, so always look at the scatter plot.

1) X causes Y; 2) Y causes X (reverse causation); 3) a confounder Z causes both; 4) coincidence or a selection artifact.

When the arrow runs the other way than assumed. Example: people who exercise are less depressed — exercise may lift mood, or depression may sap the energy to exercise.

A third variable that causes both X and Y, creating a correlation between them. Ice cream sales and drownings both rise because of summer. Old coffee studies looked bad for the heart because heavy coffee drinkers were also smokers.

Coin-flip assignment balances the two groups on average for everything — age, diet, genetics, income, optimism — including confounders nobody has ever measured. Any difference beyond chance traces back to the treatment.

Many conditions improve on their own (regression to the mean) and people respond to being treated at all (placebo effect). Without a control you can't tell treatment effect from either.

Single-blind: the subject doesn't know which arm they're in. Double-blind: the experimenter doesn't either, so they can't unconsciously nudge measurements or encourage one group.

Stating the hypothesis and analysis plan before collecting data stops researchers from quietly testing twenty outcomes and reporting only the one that hit p < 0.05.

A selection effect: if a study only samples hospital-admitted patients, two unrelated diseases can look anticorrelated simply because having both makes admission more likely.

Before accepting the causal arrow, spend a minute trying to invent a confounder. If one comes to mind easily, the authors had better have addressed it.