Take Two Samples ...

Take two samples of handwriting, practically any two samples. Make sure the two samples are made by different people. Question: If you look close enough and long enough, how probable is it that you will find the same extraordinarily rare combination of characteristics in the two samples?

Many years ago I followed exactly this procedure. I had a group of students write down the same phrase twice on two different pieces of paper and then throw their handwriting samples into a hat. I then picked two samples that I knew -- or believed -- had been written by two different people. (I think I asked the students to write their names on the back of each piece of paper with their handwriting samples on the front and I had the students do this before they knew what I was up to.) As I said just moments ago, I picked, more or less at random, two handwriting samples that had been made by different people, by different students. I then scrutinized these two handwriting samples for a while. After doing so, I found about a dozen handwriting quirks that occurred in both samples. I pointed out these similarities to the class. I then did some product rule calculations and I asked the class to do the same with the probability values (and dependencies) that they thought were appropriate. I then asked the students in the class whether they thought the two samples were written by the same person. Everyone (in a class of ca. 25) answered in the affirmative. (I had somehow managed to instruct the actual authors of the two samples to keep their mouths shut.) When I told the students that in fact two different students had produced the handwriting samples, about five students found my confession to be both astonishing and unbelievable; and despite my confession of trickery, they argued that the two sample had been written by the same person.

As I recall, statements by the two students who (I think) actually made the two samples overcame the objections of the dissenting students.

I believe I successfully tricked the class. But I can't really say that the dissenters were completely befuddled or irrational, can I?

Dreyfus redux?

My pedagogical trick would not have worked if one writer had written English and the other, Arabic. It would not have worked if one author had been 25 years old and the other, three years old. Therefore?

Improbable DNA

Jennifer Mnookin, "Fingerprint Evidence in an Age of DNA Profiling," 67 Brooklyn L. Rev. 13, 49-50 (2001)(footnotes omitted):

[I]n a 1999 case in England ... Raymond Easton was charged with burglary after authorities made a "cold hit" with his DNA in a DNA database. His DNA matched the crime scene DNA at six loci. Because there was only a one in thirty-seven million chance that a randomly selected person's DNA would match, Raymond Easton was charged with burgling a house 200 miles from where he lived. However, after Easton, who had advanced Parkinson's disease and was unable even to drive a car, offered an alibi for the night in question, the DNA was eventually tested at four more loci. This more sophisticated test showed there was no DNA match after all. All charges were dropped.

Investigating Multiple SIDs Deaths

Question for the day:

If the number of multiple SIDS ("sudden infant death syndrome") deaths within single families within some large population is exactly what one would expect if chance alone governs the distribution of SIDS, should government authorities investigate for possible wrongdoing if the only thing they know is that there were, apparently, three SIDS deaths within a single family?

Further questions:

(i) Are three such deaths within a single family ever sufficient for a criminal conviction of a person who alone had access to the children when they died?

(ii) If not, would four deaths suffice?

(iii) If not, would five or ... n deaths ever suffice?

Dice, Probability, and Law

There is more to probability than dice and games of chance. Nonetheless, I think it is probably(!?) useful to use dice to introduce law students to some basic points about probability theory. I like to use a set of large "fair" dice. (Later I will perhaps post a [true!] story about my unsuccessful attempt to buy magnetized dice.) This Monday I will also try to use the nifty applet at the following web site to make several points: Introduction to Probability Models.

Magnetized dice would be a nice way to illustrate dependent probabilities.

Repeated rolls of dice (with, e.g., the applet mentioned above) can be used, I think, to show, by analogy, some of the problems that can arise with the use of statistics about the relative (in)frequency of SIDS to prove criminal guilt or, even, with the use of such statistics to justify "just" coercive investigation by the state.