<- file 95cirefs.html ->

Please clarify "confidence intervals".

=======================Steven Goodman, 20 Feb 1995========ssc Message-ID: <Pine.SOL.3.91.950220222627.21490B-100000@welchlink.welch.jhu.edu> From: STEVEN N GOODMAN <sgoodman@WELCHLINK.WELCH.JHU.EDU> Subject: 95% CIs - a philosophical twist > Date: Mon, 20 Feb 1995 15:47:26 +0000 > From: Leslie Daly UCD <LDALY@IVEAGH.UCD.IE> > Subject: Re: More Clarification Requested W.R.T. Confidence Interval > > I have a difficulty with the form of the arguments against the > interpretation of a 95% CI being interpreted as 'a 95% probability > that the interval will contain the unknown parameter'. I know that > the parameter is not a random variable, but the argument usually says > that the parameter is either inside or outside the interval and > therefore the probability is either 1 or 0. > If I have 5 green marbles and 5 red marbles in a bag, the probability > of drawing a red is 0.5. If however I have drawn the ball (but not > looked at it) can I not still say the probability that the ball in my > hand is red is 0.5. If I can say it why won't it hold for the CI too > since the ball is either red or green, with a probability of red > being 0 or 1.!!! If I can't make that probability statement about > the unlooked-at ball in my hand - why not? Is not the essence of > probability statements to quantify uncertainty? > Leslie Daly, Email: LDALY@IVEAGH.UCD.IE Everybody on the list may be sick of this issue (I notice that the innocent originator of the discussion was surprised at what he had wrought, and bowed out), although there is a reason it seems endlessly fascinating. The question of the meaning of probability in the individual case is a deep one in the philosophy of inference, and has never been resolved. As (I believe) Vic Barnett sums up the statistical implications of this issue, the central problem (and challenge) for frequentist inference is how the properties of a procedure apply to the outcomes of that procedure. They are not transferable, as several commentators on this issue have already pointed out (e.g. 95% of time, interval = -inf to +inf, 5% = null set: this is a procedure with 95% coverage, which does not apply to either outcome). To make the properties of a procedure apply to a single outcome, we must appeal to issues outside the realm of pure ("long range") empiricism, i.e. we will find ourselves essentially constructing Bayesian priors, whether we call them that or not. Anyway, to get back to the original point, the meaning of probability in the individual case can be endlessly discussed, but will not be resolved (or "explained") on this list, because it has not been resolved in many volumes of writing on this issue. For people interested in the issues, they might consider looking at the Barnett book on Comparative Stat Inference (Wiley?) that I mentioned, the books by Ian Hacking, Steve Stigler, or Ted Porter on the history of probability/statistics, or some of the foundational writings of DeFinetti, Savage and Jeffreys. One of my favorites is Lorraine Daston's "Classical Probability in the Enlightenment" (Princeton, 1988). To discuss this subject in a purely statistical (i.e. non-philosophical) and ahistorical context is to endlessly spin our wheels (as evidenced by the 1-2 weeks of discussion without discernable progress). Also, to characterize the issue as simply one of Bayesianism vs. Frequentism is to strip the debate of its richness. Bernoulli, DeMoivre, Laplace and Poisson agonized about this very issue centuries before the jargon or methods of modern statistics. Steve Goodman * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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