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...
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,…
