Causation is sometimes treated probabilistically. Rather than committing a 100 percent to the effect in our causal predictions, we might say that there is a certain chance of the effect occurring, given the cause. But what do we mean by this? It depends. First, it depends on what we take causation to be. Second, it depends on what we take probability to be.
Say we test a treatment and find that it has an effect in 40 percent of the patients. Based on this information we might infer that there is a 0.4 chance that the treatment will have an effect on a particular patient. There are at least three ways to interpret this claim.
1. Credence: The practitioner might think that causation only happened in the 40 percent that had an effect, while no causation happened in the remaining 60 percent. To say that there is a 0.4 chance that the treatment will have an effect then only means that there is a 0.4 chance that the prediction is correct. This is a purely epistemological notion of probability since it only concerns the limitation of our causal knowledge.
2. Frequency: The practitioner might think that the treatment raises the probability of the effect, and that this probability is given by the distribution of outcomes over a sequence of trials. In each patient who gets the treatment, it will then be thought to have the exact same effect, namely 0.4. This is an ontological notion of probability in which the probability is given by a statistical average within a sub-group.
3. Propensity: The practitioner might think that there is something intrinsic to the treatment, a property or a disposition, that gives it a tendency towards a certain type of outcome. But since everyone has a different set of properties or dispositions, the treatment won’t raise the probability of the effect to the same degree in all the patients. This is an ontological form of probability, where probability is thought to exist in reality in virtue of things’ intrinsic properties.
Why does it matter how we interpret statistical data? First of all, frequencies don’t automatically transfer to propensities. This is a common criticism of evidence-based medicine, which uses statistical methods and large scale population data to generate causal knowledge about some statistical average patient. In some cases the statistical average doesn’t even have a single instance, such as the woman with 1.8 children. So when a practitioner tells a patient they have a certain probability of getting better from a treatment, at least they should specify what they mean by probability.