Jerry Dallal <[EMAIL PROTECTED]> wrote in sci.stat.edu:
(responding to my request for clarification)
>Your language is imprecise, which allows for wiggle room. Your statement
>may or may not be correct. It is incorrect to talk about the probability
>that a particular realization of a confidence interval contains the
>parameter of interest. For example, it is incorrect to say, for example,
>that P(17.6<=mu<=22.3) = 0.95. In a frequentist context,
>[snip...] There are only
>realizations of random variables, no longer subject to probability
>statments.
Thanks for the explanation. I think I begin to see the issue; let me
make an analogy to see if I understand your point.
Take a golf course, and divide it into a grid of 1-meter squares.
Consider one particular square. Then before the golfer swings at the
ball, there is a probability that the ball will land in that square.
(The probability might be found by historical experience; obviously
it would not be calculated a priori!) But after the ball has come to
earth, it is either in that square or not; there is no longer any
sense to talking about the probability. Is that what you are saying?
Coming back to the CI, I think you are saying that once a particular
confidence interval is selected, either it definitely contains the
true population parameter or it definitely does not. But once the
CI is selected it is no longer meaningful to talk about the
probability that it contains the population parameter. We can say,
"Well, the process by which we found this CI does bracket the mean
95 times out of 100", but we can not make a probabilistic statement
about this particular confidence interval.
Is that more or less it? (I'm trying to steer here between simply
repeating your precise language to my students, most of whom I think
would be lost by it, and using unacceptably imprecise language.)
>Have another look at the example involving the 50% CI for theta in the
>U(theta-1, theta+1) distribution that I posted earlier. It shows how it's
>possible to have 50% CIs that *must* contain the parameter of interest.
I confess I kind of buzzed past it on first reading. As I ponder it
in light of your recent explanation I think I now understand.
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA
http://OakRoadSystems.com/
"My theory was a perfectly good one. The facts were misleading."
-- /The Lady Vanishes/ (1938)
.
.
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