Monday, January 8, 2018

The confidence interval fallacy

Statisticians have a concept called the p-value that is crucial to most papers in science and medicine, but is widely misunderstood. I just learned of another similarly-misunderstood concept.

Statisticians also have the confidence interval. But it does not mean what you think.

The Higgs boson has mass 125.09±0.21 GeV. You might see a statement that a 95% confidence interval for the mass is [124.88,125.30], and figure that physicists are 95% sure that the mass is within that interval. Or that 95% of the observations were within that interval.

Nope. It has some more roundabout definition. It does not directly give you confidence that the mass is within the interval.

Statistician A. Gelman recently admitted getting this wrong in his textbook, and you can learn more at The Fallacy of Placing Confidence in Confidence Intervals.

Some commenters at Gelman's blog say that the term was misnamed, and maybe should have been called "best guess interval" or something like that.


  1. Roger, write a textbook. It's lucrative and you can get it right!

  2. Hey MD Cory, what happened to your blog and Twitter? Where can I read your output now?

    1. Why prostitute my mind? I should start charging. By the way, The Cult of Statistical Significance by Stephen Ziliak & Deirdre McCloskey is a great book on the problem with Fischerian vs Gossetian statistics.