Where is statistics? You might not find it underneath the couch or while preparing breakfast. It certainly isn't hiding underneath your bed or in your closet. It probably does not tell you anything about what outfit you should wear. We might need to squint hard to see statistics in action around us. However, when it is misused or misinterpreted, it can be a matter of utmost importance.
In 1999, a jury convicted Sally Clark of murdering her first two children. Rather than any amount of circumstantial evidence, the judges and juries determined their verdict based on statistics. Sally's first child died of Sudden Infant Death Syndrome (SIDS), as did her next child more than a year later. However, considering the coincidence quite suspicious, the pathologist alerted the authorities leading to Clark's arrest. With a lack of evidence, the prosecution called upon Prof. Sir Roy Meadow, an expert on child abuse. The chances of a child in Clark's household dying of SIDS was 1 in 8,453. Two children dying was inconceivable. By squaring this value, the prosecution claimed a 1 in 73 million chance of SIDS occurring twice. After two court appeals carefully scrutinized the evidence, Sally Clark is exonerated. What did the expert and prosecution get wrong?
Violation of Independence
Let's start at the 1 in 73 million chance of two children dying of SIDS. The expert witness arrived at this number by squaring 1 in 8,453. However, these events are not wholly independent of one another. Recurrence of SIDS is much more common than the 1 in 73 million chance. A Bayesian approach would create a better posterior probability distribution by adjusting for this.
The Prosecutor's Fallacy
Even if the chances are slim, so what? Remember, the 1 in 73 million statistics only refers to the recurrence of SIDS. It does not state that this occurrence is impossible, nor does it provide any information about the probability of Clark's guilt. This piece of data might not even be relevant to the case.
We do not need the probability these deaths were natural. Instead, we must know whether it's more likely that these deaths occurred naturally or through abusive circumstances. Understand the limitations of a specific piece of data without making any further references. Here, prosecutors and juries conflated guilt with the probability of a rare occurrence.
Many such cases still appear in courts, influencing juries with irrelevant points of data and arguments. There are plenty of other similar and varied examples of the criminal justice system misinterpreting statistics. When this happens, people are wrongfully convicted. While we might walk through our daily lives without acknowledging statistics regularly, understanding its applications is crucial for a functioning world. While we might not always see statistics peeking out at us from underneath our beds, it is deeply rooted within various societal institutions and hardwired into our brains. When it's misused and misinterpreted, it's easy to see the immense value provided by statistics.
Sources and Further Reading:
1. Scheurer, V. Convicted on Statistics. https://understandinguncertainty.org/node/545
2. Leung, W.C., 2002. The prosecutor's fallacy—A pitfall in interpreting probabilities in forensic evidence. Medicine, science and the law, 42(1), pp.44-50.
About Simon Spichak:
Neuroscientist and Science Communicator
2020 FameLab Ireland Winner