Stan Brown <[EMAIL PROTECTED]> wrote: : the other (about) .05*NS would not, right?
: Here's the part I don't understand: if we agree (as I think we do) : that 95% of all possible random samples lead to a 95% CI that : contains the true value of mu, how can it possibly be incorrect (as : you and others seem to say) to state that the probability of getting : mu in the 95% CI from any _one_ CI is 95%? Perhaps I'm very stupid, : but I just don't see how the statements are not equivalent. : And since I'm supposed to be teaching this stuff, I'd really like to : understand the flaw in my thinking. 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, we can talk about probability only in the context of random variables. There are no random variables in the expression P(17.6<=mu<=22.3). There are only realizations of random variables, no longer subject to probability statments. 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. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
