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From |
"Alan Neustadtl" <alan.neustadtl@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Bootstrapping Conf Intervals - what do they mean? |

Date |
Tue, 3 Jun 2008 15:54:45 -0400 |

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 <dan.weitzenfeld@emsense.com> 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 > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Bootstrapping Conf Intervals - what do they mean?***From:*"Clive Nicholas" <clivelists@googlemail.com>

**References**:**st: Bootstrapping Conf Intervals - what do they mean?***From:*"Dan Weitzenfeld" <dan.weitzenfeld@emsense.com>

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