Type I and Type II Errors › Type I and Type II Errors

In 1999, British solicitor Sally Clark was convicted of murdering her two infant sons, who had died suddenly in 1996 and 1998. The prosecution's star witness, pediatrician Sir Roy Meadow, testified that the probability of two children in an affluent family dying from Sudden Infant Death Syndrome (SIDS) was 1 in 73 million. This number, obtained by squaring the 1 in 8,543 probability of a single SIDS death, seemed to prove Clark's guilt beyond any reasonable doubt.

But the calculation was catastrophically wrong. It assumed the two deaths were independent events, ignoring known genetic and environmental factors that make SIDS more likely in families who have already experienced it. More importantly, even if the probability were correct, it confused two very different questions: "What is the probability of two SIDS deaths?" versus "Given two infant deaths, what is the probability the mother is a murderer rather than a victim of tragic coincidence?"

Clark spent three years in prison before her conviction was overturned. The court recognized what statisticians call the prosecutor's fallacy: confusing the probability of the evidence given innocence with the probability of innocence given the evidence. Sally Clark's case illustrates the devastating real-world consequences of misunderstanding error rates in hypothesis testing.

Every statistical test involves making a decision under uncertainty, and every decision carries the risk of error. Understanding these errors, their nature, their probabilities, and the tradeoffs between them, is essential for anyone who uses statistics to make decisions.