I know Hoekstra says it’s wrong, but #5 is fairly standard shorthand for “The interval [0.1, 0.4] was produced using a procedure such that, if we were to repeat the procedure over and over, then 95% of the time the confidence intervals produced would contain the true value of q.” It’s in most introductory stats books, presumably as a convenient way to point toward the correct interpretation.
The full statement you wrote is correct, but Hoekstra et al.'s point is that the shorthand is confusing: the statement refers to the returned boundaries and not to the procedure. So in spirit, it's not totally wrong as shorthand, but logically speaking, it's fallacious.
Now, I agree that this sort of statistical pedantry is often unhelpful. But I find it useful to point out how we've invented a cookbook of statistics where at least 95% of the chefs are confused about their recipes.
Why is #4 not correct? Is there an intuitive explanation? How is it different from the quote above: "95% of the true value of q would lie inside the interval C(X)"
I agree it's confusing! It's because "q" itself isn't a probabilistic entity. At least in the weird frequentist framework which confidence intervals come from (the Monte Carlo Algorithm framework), q is a deterministic quantity so assertions about p(q) don't make sense.
Isn't the question whether a coin is biased ill-posed in the first place. The coins that I've seen are certainly not perfectly symmetrical P(heads) might be close to 0.5 but it is most certainly a tiny bit off.
So we already know that the coin is biased and there really is no need to do any kind of statistical analysis.
Your argument for 5-nines confidence sounds awfully like the one CERN et al use for '5 sigma' - ie at this point one can stop arguing about pure statistical issues (and move on to arguing about systematics ...)
I know Hoekstra says it’s wrong, but #5 is fairly standard shorthand for “The interval [0.1, 0.4] was produced using a procedure such that, if we were to repeat the procedure over and over, then 95% of the time the confidence intervals produced would contain the true value of q.” It’s in most introductory stats books, presumably as a convenient way to point toward the correct interpretation.
The full statement you wrote is correct, but Hoekstra et al.'s point is that the shorthand is confusing: the statement refers to the returned boundaries and not to the procedure. So in spirit, it's not totally wrong as shorthand, but logically speaking, it's fallacious.
Now, I agree that this sort of statistical pedantry is often unhelpful. But I find it useful to point out how we've invented a cookbook of statistics where at least 95% of the chefs are confused about their recipes.
but Tampa would have been kicking the extra point in an indoor stadium, surely the probability of a successful kick is higher indoors? 😜🤣
Love it. The point estimate is higher and but the error bars are wider.
Why is #4 not correct? Is there an intuitive explanation? How is it different from the quote above: "95% of the true value of q would lie inside the interval C(X)"
I agree it's confusing! It's because "q" itself isn't a probabilistic entity. At least in the weird frequentist framework which confidence intervals come from (the Monte Carlo Algorithm framework), q is a deterministic quantity so assertions about p(q) don't make sense.
Isn't the question whether a coin is biased ill-posed in the first place. The coins that I've seen are certainly not perfectly symmetrical P(heads) might be close to 0.5 but it is most certainly a tiny bit off.
So we already know that the coin is biased and there really is no need to do any kind of statistical analysis.
Right, I sort of talk about this in today's blog. The probabilistic null hypotheses are often very suspect.
Your argument for 5-nines confidence sounds awfully like the one CERN et al use for '5 sigma' - ie at this point one can stop arguing about pure statistical issues (and move on to arguing about systematics ...)