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."
Based on this I believe that after 10,000 samples have been produced
(simulating a sampling distribution) 95 per cent of your samples
produced a point estimate within your population confidence interval.
Whether your sample captures the fixed parameter or not is still a
question, yet, if it is in this range it likely does.
Considering single samples (not simulated sampling distributions)
Blalock continues "You should be careful not ti imply or assume that
the particular interval you have obtained has any special property not
possessed by comparable intervals that would be obtained by other
intervals." (p. 211)
Best,
Alan
On Tue, Jun 3, 2008 at 3:09 PM, Dan Weitzenfeld
<[email protected]> wrote:
> Hi Folks,
> I'm grappling with what the results of Bootstrapping can tell you.
> Let's say I bootstrap from my sample 10,000 times, calculating a given
> statistic, giving me the detail I need to use the 2.5% and 97.5%
> percentiles to construct a 95% confidence interval.
> What does that *mean*?
> Am I 95% confident that the true value of that statistic is within the
> interval? If so, doesn't that require 100% confidence that my sample
> is an accurate representation of the underlying population?
> Thanks,
> Dan
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