We have written here before about DNA in several posts.
DNA is a very power tool is used correctly. It can free the falsely accused. It can also be used to condemn a man to death. Often times it is incorrectly reported and its value and relevance can also be extrapolated to beyond what the result truly means. This is frequently referred to as The Prosecutor’s Fallacy.
We probably see a headline that promotes this type of incorrect interpretation of DNA at least once a week. It probably says reads like this:
DNA evidence says means there is only 1 chance in 9 quadrillion that a person other than the suspect left the semen.
The prosecutor might argue: “The chance is 1 in 9 quadrillion than someone (anyone) other than the suspect left the stain.” In other words, the prosecutor’s fallacy is the assumption that the random match probability is the same as the probability that the defendant is the source of the DNA sample. This is incorrect.
The most correct statement would be “The chance is 1 in 9 quadrillion that some (particular) person other than the suspect would leave a stain like the actual stain.”
A good explanation can be summed up as follows:
Let’s assume the DNA profile found at the crime scene—and the matching DNA of the suspect—is expected to occur once in every million people. The correct statement of probability arising from these facts is, “If the suspect is innocent, there is a one-in-one-million chance of obtaining this DNA match.” The fallacy is to reverse these clauses, and state, “If the DNA matches, there is a one in one million chance that the suspect is innocent.” To understand the logical fallacy, imagine the statement, “If it’s Tuesday, it must be a school day.” The reverse is not true—there are other school days besides Tuesday. Source:DNA Profiling – Statistics And The Prosecutor’s Fallacy – Suspect, Innocent, Match, and Crime – JRank Articles http://medicine.jrank.org/pages/2161/DNA-Profiling-Statistics-Prosecutor-s-Fallacy.html#ixzz1gBawrV1z
Further reading on a similar topic includes: Bayesian Based Metrology and DNA. A very good article on CODIS based or CODIS like searching can be found here: Are the F.B.I.’s Probabilities About DNA Matches Crazy?