#rstats I occasionally write Clearing Up the Confusion documents on various statistical issues; see the .md files in http://github.com/matloff/regtools/inst. My topic for this evening will be probabilistic interpretation of confidence intervals. 1/

This topic arose from a recent thread involving Deborah Mayo @learnfromerror and Opher Donchin @opherdonchin. The question at hand: Say we have data and form a 95% confidence interval for, say, a mean. Can we say P(CI contains the true mean) = 0.95? 2/

As a frequentist (which Deborah is, not sure about Opher), the answer is Yes -- provided we define the meaning of P( ) properly. 3/

I explained my meaning -- the only one possible for a frequentist -- by giving an example of a coin flip: I flip a coin in the next room, out of your view. What is P(heads)? From my point of view, it's 0 or 1, but from yours it's 0.5. 4/

Opher's response, if I understood him correctly, was that P(heads) is undefined in this setting. (No specific reply from Deborah yet.) But of course it IS defined. We do this every day. 5/

Consider the famous Monty Hall problem, for instance. Before Monty gives a hint, from the contestant's point of view, P(door A has a car) = 1/3, even though from Monty's point of view it's 0 or 1. 6/

Or, think of the Super Bowl, with a coin flip determining who gets the first kickoff. Instead of calling the flip in the air, say the flip is done secretly beforehand, with full certification etc. The team calling the flip can still do so, and it still will be fair. 7/

It's the same situation for the CI. 8/8