This blog is a companion to my website Common Mistakes in Using Statistics. I intend to use it to announce updates to that site and to comment on other things related to statistics that come to my attention. I hope it will be of interest to the following categories of people:

- Teachers of statistics (especially those, such as myself, who come from backgrounds other than statistics)
- Undergraduates and early graduate students in statistics
- Users of statistics (especially people who read research using statistics)

I’ve been reading your text “Common Mistakes…” and have a question:

I’m guessing that mathematicians feel certain that the law of large numbers will guide convergence to the expected value. Is there a proof of why LOLN is true? or is it a phenomenon? the Bernoulli’s discussions I’ve read seem kind of circular (something’s true b/c it’s true). Tom Stoppard wrote “rosencrantz & gildernstern are dead” just to poke fun at LOLN, but what he is suggesting is just as plausible. BTW: thanks for the website and blog. good to read. ever run across inexpensive deep thoughts books about statistical thiniking? Best. Jim Watts

I won’t hazard speaking for all mathematicians, but doubt that those who have really thought about the Law of Large Numbers feel certain that it will guide convergence to the expected value. For one thing, convergence can sometimes be very, very slow. In fact, some mathematicians study just how fast or slow convergence can be in certain specific situations (and it may be quite different in situations that might look very similar).

There are (at least) two versions of the Law of Large Numbers, one called the Weak Law of Large Numbers and the other the Strong Law of Large Numbers. They differ in just what is meant by “convergence. I won’t go into details, but if you’re interested in more detail, the Wikipedia article on the Law of Large Numbers has some.

As for “inexpensive deep thoughts books about statistical thinking” — not sure what you consider “deep thoughts”, but for “inexpensive,” I’d suggest looking for some old editions of books by David Moore, David Freedman, or Philip Good.