Alan Neustadtl replied to Dan Weitzenfeld:
> This is an interesting issue. Blalock (Social Statistics 1960, p.
> 210) provides the following discussion about confidence intervals:
> "Several words of caution are necessary in interpreting confidence
> intervals. The beginning student is likely to use vague phrases such
> as, "I am 95 per cent confident that the interval contains the
> parameter", or "the probability is .95 that the parameter is in the
> interval." In so doing one may not clearly recognize that the
> parameter is a fixed value and that it is the intervals that vary from
> sample to sample. According to our definition of probability, the
> probability of the parameter being in any given interval is either
> zero or one since the parameter is or is not within the specific
> interval obtained. ...one's faith is in the procedure used rather
> than any particular interval. We can say that the procedure is such
> that in the long run 95 per cent of the intervals obtained will
> include the true (fixed) parameter."
[...]
It might be worth pointing out that Iversen (1984) - amongst many
others - has argued, repeatedly in this case, that using the
terminology of probability when estimating and interpreting confidence
intervals is only possible after the generation of Bayesian
statistical models. Indeed, he also argues that they are
computationally equivalent yet conceptually different: the 0.95
statistic is founded as a measure of uncertainty about the point
estimate; the 95% statistic is seen as a "long-run relative frequency"
(p38). Confusingly, he mentions the word 'probability' for both
classical and Bayesian approaches here, but he gives a even clearer
definition between the two on p31.
Wood (2005) produced a rather nice primer on bootstrapping CIs that
may be of assistance here, and it should be freely available on the
Interweb.
--
Clive Nicholas
[Please DO NOT mail me personally here, but at
<[email protected]>. Thanks!]
Iversen GR (1984) "Bayesian Statistical Inference", Sage University
Paper on the QASS 07-043, Thousand Oaks: Sage.
Wood M (2005) "Bootstrapped Confidence Intervals as an Approach to
Statistical Inference", O rganizational Research Methods 8(4): 454-70.
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