Is causal inference just statistical inference?

01/12/2025

Many researchers maintain that we can infer causal relationships just from associations found in experimental or observational data. Professor Jon Williamson (University of Manchester) suggests that this strong view of the relationship between causal and statistical inference is partly responsible for the replication crisis. Evidential Pluralism, a new approach to causal inference, may help to mitigate the crisis.

There are two views about the connection between causal inference and statistical inference: a weak and a strong view. According to the weak view, statistical techniques are useful for causal inference, i.e., for establishing and assessing causal claims. According to the strong view, causal inference is a purely statistical problem.

The weak view was common in the mid-20th Century. Austin Bradford Hill, for example, put forward nine indicators of causality, some of which invoke statistical concepts, but others of which appeal to further considerations, such as biological plausibility.

The strong view has become increasing dominant since around the 1990s. Judea Pearl, for example, developed new statistical techniques to infer causal relationships from associations in data. Independently, ‘evidence-based’ approaches to medicine and policy have become mainstream; these prioritise statistical methods, such as meta-analysis, for causal inference.

The replication crisis has emerged alongside the rise of the strong view. It is often the case that observed associations fail to replicate—this much is a part of normal science and does not in itself constitute a crisis. A more serious problem arises, however, when these associations are taken—in line with the strong thesis—to establish causal relationships. This is because, when the associations fail to replicate, established causal relationships are overturned. Causal relationships are central to the empirical sciences and if a science’s central, established claims are frequently overturned then the credibility of that science is undermined.

Many efforts have been directed towards mitigating the replication crisis. There are recommendations to carry out and publish more replication studies, to change statistical thresholds such as p-values, and to mitigate sources of bias more effectively, for example.

While these recommendations are commendable, perhaps we need to return to a more nuanced view of the relationship between causal inference and statistical inference in order to properly address the replication crisis. By adopting an approach to causal inference that accords with the weak thesis, we may be less inclined to leap from association to causation. If we are more cautious in establishing causal claims in the first place, the fact that an association fails to replicate need not overturn an established causal relationship. Normal science need not lead to crisis.

Evidential Pluralism, an emerging philosophical theory of causal enquiry, accords with the weak thesis. According to Evidential Pluralism, establishing a causal claim requires establishing not only that the putative cause and effect are appropriately correlated (the ‘correlation claim’) but also that some mechanism of action is responsible for this correlation (the ‘general mechanistic claim’). As depicted in the diagram below, the main way to test the correlation claim is to carry out an association study that repeatedly measures the putative cause and effect (possibly together with potential confounders) and uses statistical methods to estimate the magnitude of the correlation. Some association study designs can also provide indirect evidence of mechanism: randomised controlled trials, for example, are particularly informative because they can reduce the chance that any observed association is attributable to unforeseen confounding, thereby indirectly confirming the general mechanistic claim. But the general mechanistic claim can be more directly tested by hypothesising features of the mechanism complex and scrutinising mechanistic studies, which look to see whether these features are present.

 

If Evidential Pluralism is correct, causal inference requires a combination of statistical inference and mechanistic inference. Now, certain mechanistic study designs incorporate statistical methods, so mechanistic inference is not wholly distinct from statistical inference. But other study designs (e.g., qualitative study designs) do not incorporate statistical methods and can also provide valuable evidence of mechanisms, so mechanistic inference is not simply a variety of statistical inference.

Evidential Pluralism exploits a broad evidence base and does not simply infer causation directly from association. For this reason, Evidential Pluralism provides an example of the more cautious kind of framework for causal inference that is needed to mitigate the replication crisis. By being more cautious in establishing causal relationships, in line with the weak thesis, we may be able to restore confidence in science.

Jon Williamson is a professor in the department of philosophy at the University of Manchester. He has been at Manchester since 2024, before which he worked at the University of Kent. His research focusses on the philosophies of science, medicine, AI and law—especially topics connected to causality or probability.