Over at the Bad Astronomy weblog,

Blake Stacey

wrote the following,

which is reproduced here with permission:

Come on, we’re **scientists**, right? How about we break out the mathematics. Just for kicks, I’m gonna model Coulter as a Bernoulli process!

Assume, as a first approximation, that each statement she makes has probability *p* of being worth reading. (This could be because it is factually correct, poetically beautiful, intellectually thought-provoking, etc.) Furthermore, assume that this probability does not change significantly over time, and that one statement does not affect the others. Then out of every *N* statements, on average *Np* of them will not have been a waste of time — though in any **actual** sample of *N* statements, the number will likely be somewhat different, just as not every set of 100 coin flips will give you exactly 50 heads.

Given a sample of statements which we judge to be worthwhile or worthless, what can we say about *p,* the “behind the scenes” probability that the source will produce a worthwhile statement?

Say that we actually do the experiment: we take *N* statements from Coulter’s books, TV appearances and so forth, and we find that some fraction *q* of them were not blatant assaults upon human dignity. That is, *Nq* statements did not reek of idiocy and hate. Knowing *N* and *q*, we would like to deduce *p* to within some reasonable margin of error.

Standard scientific practice requires that we set a “confidence level“, which measures how far our results are from certainty. A confidence level of 95% means that our results will only be wrong 1 time in 20, all else being fair. You can look up the rest in Chapter 7 of Gonick and Smith’s *Cartoon Guide to Statistics*; the punchline is that the width of our “error bar” is (for 95% confidence) 1.96 times the square root of the fraction *q(1-q)/N*. The probability we want to know, *p,* will be *q* “plus or minus” that amount. Our confidence in our answer grows as the **square root** of the number of measurements we take: for a sample twice as large, our uncertainty becomes about 1.4 times smaller.

For example, if 800 out of 1000 statements are total bollocks, then *p* = 0.2 +/- 0.02.

Now all you have to do is decide how small *p* has to be before you stop listening and go do something more fun.

The real kicker is the poor sod who has to wade through all her material in order to garner the sampling. The things we do for science.

Fortunately, the Internet is vast, and there are plenty of people who have laid down their SAN to present excerpts from her books.

Let’s say that measured q=0.01; that is, in your sample, 1% of what she says is not an offense to human dignity (this would probably consist of things like “Good evening. Glad to be here” and “Thanks for inviting me”). And you want to make sure that p is within 1% of q. If my calculations and the information above are correct, you only need to analyze N=380 statements to reach this confidence level, not thousands.

And certainly not

allof her material. Gods, no. The whole point of this exercise was to mathematically calculate the point where it’s safe to dismiss her out of hand.What she says – it’s likely just for the sheeple.

Unfortunately, there is a sufficiently large pool of ignorant and gullible rejects from the stone age for this tripe to be quite harmful to society.