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?