In the video, Peter Donnelly Shows How Stats Fool Juries, Peter Donnelly delivers a talk on how statistics can be deceptive. After a few jokes about the social awkwardness of statisticians, Donnelly moves on to an example. He describes a scenario where you flip a fair coin until the patter HTH emerges (H being heads and T being tails). You then flip the coin again until the pattern HTT emerges. Then he asks the audience what they believe to be true:

a) The average number of flips for HTH to emerge is less than the average number of flips for HTT to emerge.

b) The average number of flips is equal for both.

c) The opposite of a) is true.

Most people in the audience answered b). The correct answer, however, is a). This is because, as Donnelly explains, the pattern HTH can repeat itself in five flips (HTHTH), where HTT cannot (HTTHT).

This is the first example he gives of how topics in statistics can often times be deceptive. He then moves on to a more relevant example (one covered in MATH 341) of the probability of having a disease given a positive test result for a test with 99% accuracy. He illustrates that while a positive test result may make it seem that there is a 99% probability that you have the disease, the true probability depends on how many people have been tested, as well as the actual probability of having the disease. If a million people are tested and there is a .01% probability of having the disease, then there will be a much larger number of false positives (9999) than people who actually have the disease (100). Furthermore, the number of the number of people tested who have the disease, only 99% of them will have a positive test result. This makes the probability that one actually has the disease given a positive test result considerably small (less than 1%).

This example relates to how statistics can be used to deceive a jury. As a matter of fact, in the wrong hands, statistics can be incredibly dangerous. This was illustrated by a true story about a pediatrician who testified against a woman accused of killing two of her babies. The pediatrician mistakenly claimed that the chances of having two infants die from Sudden Infant Death Syndrome (SIDS) is 1 in 73,000,000. One of the many mistakes made by the pediatrician was that the probability of having two children die from SIDS is independent. The woman was convicted, and was not released until her second appeal.

See the video of Peter Donnelly’s talk below: