A great friend and colleague of mine from Maryland recently had a trial involving mitochondrial DNA (mtDNA) that was used to “not exclude” his client as the donor of a particular hair found within the duct tape used to fashion a home-made silencer used to kill a lady.

Leaving the use of mtDNA alone for a moment which will be the addressed at a later date and focusing instead of on the use of loaded language.

The purported “loaded” language that was going to be used in the Courtroom was going to be as follows:

The mtDNA sample excludes 99.94% of the world’s population

Ok, but what does that really tell us?  Not too terribly much without the method or the method validation.  Let’s assume that the government’s method is correctly applied and is valid.  Let’s also ignore any sort of uncertainty in the measure that would recognize the fact of full Type I and Tye II error such as percent false positive.  99.94 percent of the world’s population still leaves 4,018,352 people or the population of all but 22 states of the union including Maryland which was where the trial occurred.  So, even using the government’s own numbers the government could not exclude as a donor of the unknown the entire population of the state where the trial was occurring.

However, another way to look at it is from the building of a true expanded uncertainty budget using Bayesian-based metrology.

Bayesian-based metrology involves the interplay of prior probabilities and the examination of Type I and Type II error.

Type I error, also known as an “error of the first kind“, an α error, or a “false positive“: the error of rejecting a null hypothesis when it is actually true. Plainly speaking, it occurs when we are observing a difference when in truth there is none, thus indicating a test of poor specificity. An example of this would be if a test shows that a woman is pregnant when in reality she is not. Type I error can be viewed as the error of excessive credulity.

Type II error, also known as an “error of the second kind“, a β error, or a “false negative“: the error of failing to reject a null hypothesis when it is in fact not true. In other words, this is the error of failing to observe a difference when in truth there is one, thus indicating a test of poor sensitivity. An example of this would be if a test shows that a woman is not pregnant, when in reality, she is. Type II error can be viewed as the error of excessive skepticism.

Persecutors love to use the ridiculous numbers than can come about with DNA testing where the state scientist comes into court and opines that the Random Match Probability error that the donor of the unknown is anyone else other than the accused is one in 55 quadrillion.  However, these numbers are not based upon expanded uncertainty measurements and are presented without the use of Bayesian Based Metrology.  If Bayesian Based Metrology was employed the number would be far, far less.  Just say no to fuzzy math.