Too Many Probabilities: Statistical Evidence of Tort Causation

Judges and lawyers first encountering statistical evidence want to believe that scientific standards are tougher than legal standards. A court will reject an assumption that there is no causal connection between an act and an injury if the evidence makes causation "more likely than not." A scientist will reject an assumption that there is no relationship between two variables only if there is less than a five percent probability that the statistical evidence showing a relationship is due to chance. The law appears willing to accept no more than a forty-nine percent chance of error while science appears willing to accept no more than a five percent chance of error. This perception is incorrect, but hard to change. It is a matter of such serious concern to statisticians and scientists that they often raise the issue, but lay people seldom understand it. This article offers those uninitiated into the statistical guild several reasons to look behind the probabilities when evaluating scientific evidence. This article describes three types of statistical results as reflecting the "belief probability," the "fact probability," and the "sampling error probability." The belief probability relates to evidentiary requirements imposed by the law, and the fact probability relates to the facts relevant to legal cases. These two probabilities are directly related to the civil law evidentiary requirement that the proponent of a claim must prove that the other's act is more likely than not a cause of harm. By contrast, the sampling error probability is a characteristic of statistical science. Appreciating the distinctions among these probabilities facilitates an understanding of the relationship between the preponderance of the evidence standard and the probabilities reported by statisticians.