Comments on: Do you understand what a “95% confidence interval” means?

By: K.D. Kong

K.D. Kong — Sat, 16 May 2020 18:09:41 +0000

Got 3 right (inside my range), was close on a couple more. Good exercise and very informative on swag’s and modeling.

By: Maxico

Maxico — Sun, 10 May 2020 05:01:10 +0000

Sounds like a fallacy. If I’m 100% confident I don’t know the answer, how can I give a 95% estimate? Or the opposite, if I know something with 100% confidence, how can I scale it back to 95%? I got the point, but the video spent most of the time talking about nonsense and a very dumb exercise.

By: Aretae

Aretae — Sat, 09 May 2020 21:49:30 +0000

I love Doug’s Book. I’ve been a huge fan since around the time we e-met.

By: Bob Sykes

Bob Sykes — Sat, 09 May 2020 12:13:47 +0000

Wm. Briggs has a blog and a book and many refereed papers where he rants on about the stupidity of correlation coefficients, p-values, and confidence limits:

http://wmbriggs.com

By: John K.

John K. — Fri, 08 May 2020 23:00:08 +0000

Regarding confidence intervals: in reality, the meaning of any confidence interval is undefined for any real-life result whatever. We cannot say whether our particular mean µ falls within the calculated confidence interval at all, let alone whether it falls within it “with 95% confidence.”

The mathematical meaning of the confidence interval is only defined in the case of doing the same experiment an infinite number of times, and then calculating each of those experiment’s confidence intervals. ALL the meaning is contained ONLY in the infinite set. There is NO mathematically-definable meaning even for the ‘infinity-minus-one’ confidence interval.

To repeat: We have no way of knowing whether or not any actual result we obtain falls within the calculated confidence interval. This is in fact admitted in comprehensive textbooks, though the implication is conveniently obfuscated. For example: “Therefore, we cannot say that there is a 95% chance that the parameter µ will fall within a particular 95% CI. However, we can say the following: Over the collection of all 95% confidence intervals that could be constructed from repeated random samples of size n, 95% will contain the parameter µ.” Rosner B. Fundamentals of Biostatistics. Fourth Edition, 1995. p. 162.

Dr. Rosner said it out loud: ALL the meaning in the term “confidence interval” is contained ONLY in the infinite set — and zero in any confidence interval we can actually calculate based on real data.