Mill’s Methods
Mill’s Methods are five techniques proposed by John Stuart Mill for inferring causal factors from patterns of presence and absence across cases.
Why use these without an experiment?
They formalize the Principles of Agreement and Difference into operational rules you can apply when you cannot run a controlled experiment.
Agreement: if cases of effect Y share only one common antecedent X, then X is probably a cause
Five people get food poisoning at a buffet. The only food they all ate was the shrimp.
Difference: if a case where Y occurs and a case where it doesn’t differ in only one antecedent X, then X is probably a cause
Two identical lab mice; one gets the drug, one does not. The treated mouse develops the response.
Joint Method: combine the two; X present whenever Y occurs and absent whenever Y does not. Strongest of the comparative methods.
Residues: subtract the parts of an effect already explained by known causes; the leftover must be due to the remaining factor
A planet's orbit deviates from predictions; known pulls explain most of it but not all. The residue led to the discovery of Neptune.
Concomitant Variation: when variation in X reliably tracks variation in Y, X is probably causally connected to Y. The formal basis of Correlation as evidence.
As average study hours per student rise, average grades rise.
Limitations
- All five rely on having identified the right candidate factors; hidden confounders can still trick you
- Method of Agreement is especially weak; two cases share many properties you did not list
- The methods support ampliative inferences, not deductive proof
- Modern controlled experiments are essentially the Method of Difference, made rigorous via randomization and controls