Quidnunc: From the Latin quid, "what", and nunc, "now." It describes a person who is always asking "What Now?," i.e. an inquisitive person.

 

I pass this along without comment: "Exactly 73% of the statistics you hear every day are made up on the spot." - Gillian Madsen

More on Benford’s Law:  On July 2, 2009, the article The Rise and Flaw of Internet’s Election-Fraud Hunters by Carl Bialik appeared in the Wall Street Journal. There are discussions of the use of Benford’s Law statistics as a tool in looking for fraud in election results and references to the sources of these discussions. Of particular interest is the discussion of second digit statistics. While the second digit statistics won’t behave the same as first digit statistics when the data set is multiplied by an arbitrary number (scale factor), they can also be useful in looking for artificially constructed or distorted data sets.

This link (rewritten on 3/9/10) is a short note referencing an excellent discussion of Benford’s law, showing some of the calculations and an explanation of why Benford statistics show up so often in nature: File: Benford Coeffs rev II.pdf

Monty Hall, again: In chapter 1 I discuss the Monty Hall game problem. On April 8, 2008, the New York Times reported that proper statistical analysis throws some doubt on a whole slew of "cognitive dissonance" reports in the psychology literature and uses the Monty Hall game to explain the issues. This article has the most succinct explanation of the Monty Hall problem choices I've seen: "....when you stick with Door 1, you'll win only if your original choice was correct, which happens only 1 in 3 times on average. If you switch, you'll win whenever your original choice was wrong, which happens 2 out of 3 times.The article examines an experiment where monkeys had to make a choice between 2 of their 3 favorite M&M colors, and were then offered a second choice of the remaining 2 colors. Most of the monkeys then chose the color that had not been offered to them on the first choice. The psychological interpretation was that the monkeys were reinforcing their rejection of the color they didn't choose the first time. The article points out that this interpretation is only correct if you assume that the monkeys had no hierarchy of preferences going into the game.

The parallel to the Monty Hall problem is that if you assume the monkeys had a hierarchy of preferences, then the first choice reveals some information which then changes the odds going forward. The impact of this issue to the entire literature of cognitive dissonance is then debated.

Regression towards the Mean: Never mentioning this term in the book was an oversight. The concept was covered in pieces in several places in the book and I'd like to tie these pieces together. Assume you have, say, 1,000 people, each flipping a coin 100 times. You would expect to see an average of about 50 heads. In other words, about 500 people would get 50 or more heads. Suppose that you take these 500 people and had them flip their coins another 100 times. Again, you'd expect to see an average of about 50 heads. The fact that these (500) people had gotten at least 50 heads on their first 100 flips wouldn't affect the results of the second set of flips. This is the most extreme case of "regression to the mean."

Now, let's measure the heights of 1,000 men. We'd probably get something like a bell-shaped (normal) distribution. If we were to take the tallest 500 men and re-measure their heights, we'd obviously get the same results as in the first measurements for these men. There has been absolutely no regression to the mean.

Lastly, let's measure the heights of the children of these tallest 500 men (once the children have grown to full height). Assuming that there is indeed a genetic propensity for tall people to have tall children, we'd expect to see a distribution of heights with an average higher than the average height of the original 1,000 people, but shorter than the average height of the original 500 tallest people. This is regression towards the mean.

A factor which can muddy up these types of experiments unless you look carefully is discussed in Chapter 8. Consider your basic coin flip gambling game (heads - you give me a dollar, tails I give you a dollar). If you played with another person and just kept records on a sheet of paper, you'd expect to neither win or lose in the long run. However, if you start out with, say, $25 to gamble and must quit if you get down to having $0 ("wiped out"), then someone who is lucky enough to win several games early has more money to play with and therefore has less of a chance of getting wiped out in some certain number of games going forward than someone who wasn't this lucky. In other words, if you repeat the 1,000 person coin flip experiment above but include the category of "getting wiped out" after, say, a $25 net loss, don't expect a simple regression to the mean of (in this case) $0 for the profits.

A good article on regression towards the mean can be found in Wikipedia.

Probably Not: Quidnunc