At 09:23 PM 11/18/02 +1000, Alan McLean wrote:
well, with any inference ... to know if you have made a decision that is correct ... one has to know the parameter ... right? if we knew that for sake of discussion ... and, we had all the possible CIs laid out in front of us ... we could know if any particular CI had snagged the parameter or notBut how do you explain that you win 95% of the time?
if it did ... you would have won ... if it did not ... you would have lost
if for cases of the mean ... sample means and intervals around them ... seems like if about 95% of the intervals snagged the parameter ... then, would you not have "won" that % of the times?
if we had used a confidence coefficient of .5 ... in the context of inferences about the population mean ... for each bet we won ... we probably would lose a bet ... in the long run, we come out about even ....
that's why we don't build 50% CIs ... or at least, i have not seen any built or ... any book advocate one
On Monday, November 18, 2002, at 11:10 AM, Elliot Cramer wrote:Alan McLean <[EMAIL PROTECTED]> wrote: : The use of the t distribution in inference on the mean is on the whole : straightforward; my question relates to the theory underlying this use. : If Z = (X - mu)/sigma is ~ N(0, 1), then is T = (X - mu)/s (where s is : the sample SD based on a simple random sample of size n) ~ t(n-1)? YES : My second question is on the matter of confidence intervals. In my : Whatever is said in the text books, this is understood by most people as : a statement that "mu lies in the interval with probability 0.95" - or : something very close to this. In effect, we define a secondary notional : variable Y which imagines that we could find out the 'true' value of mu; : Y = 1 if this true value is in the confidence interval, = 0 otherwise - : and we estimate the probability that Y = 1 as 0.95. : So my question is: how do YOU explain to students what a confidence : interval REALLY is? I treat it as a bet where on repeated samples I bet that mu is in the region. I win 95% of the time .. .. ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: .. http://jse.stat.ncsu.edu/ . =================================================================. . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
. . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
