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Re: st: Re: Confidence Interval vs Confidence in Judgement


From   Steven Samuels <sjhsamuels@earthlink.net>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Re: Confidence Interval vs Confidence in Judgement
Date   Fri, 10 Oct 2008 20:07:19 -0400

"the smaller the t-value,the smaller is the confidence interval"



That is right. The multiplier for the standard deviation for P level confidence is the (1-P)/2 percentile of the t-distribution. The lower P is, the shorter is this percentile. Suppose the degrees of freedom for t is df 50. Then the multipliers for the SD for some confidence levels from 70% to 99% are:

 foreach p of numlist .7 .8 .9 .95 .99 {
2. di "Confidence Level = " 100*`p' ". Multiplier = " invttail (50,(1-`p')/2)
  3. }
Confidence Level = 70. Multiplier = 1.0472949
Confidence Level = 80. Multiplier = 1.2987137
Confidence Level = 90. Multiplier = 1.675905
Confidence Level = 95. Multiplier = 2.0085591
Confidence Level = 99. Multiplier = 2.6777933


As you can see, a longer interval increases the confidence (probability) that the interval includes the true value. A shorter interval comes with lower confidence. Ninety-five percent CI's are so sometimes so long as to be uninformative. In such cases I would accept the trade-off of lower confidence (90%, 80%) to gain a shorter interval. Although I don't have the reference, I believe that John Tukey advocated the display of CI's with several levels of confidence. Such a display leaves the choice of confidence to the reader.

-Steve
On Oct 10, 2008, at 5:13 PM, Victor M. Zammit wrote:

The statement that I use to compute my confidence interval is the usual ttest, ie the difference between the mean of the random sample and the mean of the population, multiplied by the square root of the sample size and the product is divided by the standard deviation of the random sample.Because the result is normalised,you could infer from it the confidence interval,for
the particular degree of freedom.
The problem that I am having is that the smaller the t-value,the smaller is the confidence interval,but the higher is the confidence in your judgement
call (claim),which seems to be counter-intuitive for me.
Victor M. Zammit



-- Original Message ----- From: "Steven Samuels" <sjhsamuels@earthlink.net>
To: <statalist@hsphsun2.harvard.edu>
Sent: Friday, October 10, 2008 6:20 PM
Subject: Re: st: Re: Confidence Interval vs Confidence in Judgement


Victor, show us the statements that you are using to compute your
confidence interval.

-Steve
On Oct 10, 2008, at 12:11 PM, Victor M. Zammit wrote:

Dear Stata users,
I am reproducing a t-table,for degrees of freedom, from 1 to 30,and
after
taking 40,000 random samples of obs.,from 2 to 31,each time from an
infinite normally distributed population ,and repeated the whole
process for
10 times,my ttable has converged pretty much to that of Fisher and
Yates.
The program is very simple and I would be very glad to reproduce it
to any
one interested.
But having established the various confidence intervals associated
with the
t-values for the degrees of freedom indicates above,I am finding it
counter-intuitive, that the closer the t-value is to 0,and hence
the closer
you are to being correct in your judgement,the smaller the resulting
confidence interval.Obviously,I am confusing high confidence with wide
confidence interval.
I would like to know of other terminology that would make the
concept less
counter-intuitive.
I thank you in advance,
Victor M. Zammit

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