Statistical theatre: misinterpretation of quantitative evidence in the courtroom

The increasing use of quantitative evidence in legal proceedings reflects a broader shift towards data-informed forms of proof. Statistical analyses, probability estimates, and forensic calculations are frequently presented as objective indicators of truth; however, their evidential value depends not on the mathematics itself, but on how the relationships they describe are interpreted. This paper examines the misinterpretation of quantitative evidence in courtroom settings, arguing that numerical outputs are often treated as conclusions rather than as components of structured inference. Focusing on conditional probability, the prosecutor’s fallacy, base rate neglect, witness testimony, and DNA evidence, the paper demonstrates how common errors arise from a failure to engage with the conditional and relational nature of probabilistic reasoning. Consistent with earlier work highlighting the interpretive limits of quantitative evidence, the analysis of key cases, including the Sally Clark case and People v Collins, together with contemporary examples drawn from forensic science and algorithmic decision-making, demonstrates how numerical evidence can assume persuasive authority that exceeds its probative value when underlying assumptions are not made explicit.Building on established scholarship concerning the persuasive authority of numerical evidence, expert testimony, and probabilistic reasoning in legal decision-making, this paper proposes the Statistical Theatre Model to describe situations in which quantitative evidence acquires persuasive force independent of its inferential value.The paper further considers cognitive and institutional factors that contribute to these errors and argues that improvement lies not in increased mathematical complexity, but in greater conceptual clarity. In addition to identifying common interpretive failures, the paper proposes practical reforms to improve the communication and evaluation of quantitative evidence by experts, lawyers, judges, and jurors. In doing so, it highlights the importance of aligning the presentation of quantitative evidence with the interpretive demands of legal decision-making. Statistical evidence must remain a tool of inference rather than an unwarranted source of certainty.