Peter Donnelly is a mathematician at Oxford University and gives a presentation about how statistics often fool juries into believing misconceptions. He begins with a simple experiment based on tossing a coin. This is meant to demonstrate that there are numerous variables involved in statistical predictions. He then demonstrates how a woman was convicted of murder based on faulty statistics. In the end he shows how many juries are fooled by misinterpreting statistics presented at trial.
Statistics and Juries
In the video "How Statistics Fool Juries," Oxford mathematician Peter Donnelly attempts to demonstrate through a number of examples how statistics, when viewed in a common manner, can be misunderstood and how this can have legal repercussions. Through a number of thought experiments, Donnelly provides the audience with examples of how seemingly simple statistics can be misinterpreted and how many more variables must be taken into account when calculating chance. Primarily he exposes the audience to the concept of relative difference, or the difference in likelihood between two possibilities in the same scenario. He then goes on to explain that without an understanding of this concept, many juries misunderstand statistics used in trials and very often convict people based on this faulty understanding.
Donnelly begins his presentation with a thought experiment involving the tossing of a coin and predicts the possibility of a certain series of results. When predicting the possibility of heads, tails, heads (HTH) or heads, tails, tails (HTT), I, like most of the audience, believed that the chance of either possibility was equal. However, I did not take into account the possibility of overlap and how HTH was more like to be achieved in an overlap. I also did not catch that the HTH could appear in clumps because of the overlapping (the third "H" in HTH is also the first "H" in the next HTH). There was also the possibility that when a HTH occurred, the third "H" could be the first "H" in a possible HTT sequence, giving that possibility a greater chance. What was important about this aspect of the video was that there were a number of factors which needed to be included when calculating the uncertainty of flipping a coin, not just two simple possibilities.
Next Donnelly gives the example of a hypothetical HIV test that was 99% accurate. However, if one took the test and received a positive result, the chance that person actually had HIV was not 99% but much less. I was surprised that in order to calculate the chance that a positive result was accurate one needed to incorporate how rare the disease was in human populations. For example if the rarity of someone actually having HIV was one in 10,000, when giving the test to a million people there would be so many false positives as to statistically overwhelm the small number who actually have the disease. If a test results in a positive then in order to calculate the chance that the positive result is correct, one must take into account the different possibilities involved. This includes such things as the statistical chance for false positives in relation to the chance that the test is accurate. When one takes all the various factors into account, the chance that a positive HIV result in a test that is 99% accurate only gives a 10% chance that the person actually has HIV, a very surprising result
Finally, Peter Donnelly discussed the concepts of "relative difference" and "uncertainty." He used an example of a woman convicted of murdering her two children and explained how statistics used in the trial were misrepresented by the prosecution and misunderstood by the jury. The prosecution's expert witness claimed that the chance of the woman's two children dying from crib death was about one in 78 million. However, this was wrong because the expert did not take into account the relative difference between two possibilities: either she killed both her children or she did not. In this case the relative difference came in the possibilities of whether the woman was innocent and she suffered an unlikely event (two crib deaths), or if she was guilty and murdered her two children. In order to statistically predict which is correct, one must take into account the relative difference, or the likelihood of each of the two possibilities in relation to each other. When this is done the chance that she is a murderer is much smaller.
"Uncertainty," as Donnelly explained, is something that everyone must deal with in their everyday lives, it is chance or the possibility that something may or may not occur. It is people's attempt to deal with uncertainty where statistics are important because statistics are a mathematical attempt to solve the problem of uncertainty. However, because there are so many variables involved in each specific case it is likely that people will get their statistics wrong by misunderstanding the variables involved and their relationship to each other. In the case of the woman convicted of murdering her two children the jury used the statistic of one in 73 million to assume that this was the chance of her being innocent. But without calculating the relative difference between the two possible scenarios, it was impossible to accurately define the uncertainty involved in the case. Juries rarely understand completely the statistics involved in legal cases and very often their verdicts are based upon these misunderstood statistics.
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