Science is largely concerned with understanding the "effects of causes" (EoC), while Law is more concerned with understanding the "causes of effects" (CoE). While EoC can be addressed using experimental design and statistical analysis, it is less clear how to incorporate statistical or epidemiological evidence into CoE reasoning, as might be required for a case at Law. Some form of counterfactual reasoning, such as Rubin's "potential outcomes" approach, appears unavoidable, but this typically yields "answers" that are sensitive to arbitrary and untestable assumptions. We must therefore recognise that a CoE question simply might not have a well-determined answer. It may nevertheless be possible to use statistical data to set bounds within any answer must lie. With less than perfect data these bounds will themselves be uncertain, leading to a novel compounding of two kinds of uncertainty. Still further care is required in the presence of possible confounding factors. In addition, even identifying the relevant "counterfactual contrast" may be a matter of Policy as much as of Science. Defining the question is as non-trivial a task as finding a route towards an answer. This paper develops some technical elaborations of these philosophical points, and illustrates them with an analysis of a case study in child protection.
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