Dawson says the same thing Everitt does.
Peter Flom <[EMAIL PROTECTED]> wrote:
Peter Flom <[EMAIL PROTECTED]> wrote:
I quoted Brian. Everitt as saying
> More complex answer: The definition of a confidence interval is
(from
> The Cambridge Dictionay of Statistics, by B.S. Everitt)
> "A range of values, calculated from the sample observations, that
are
> believed, with a particular probablity, to contain the true
parameter
> value. A 95% CI, for example, implies that were the estimation
process
> repeated again and again, then 95% of the calculated intervals would
be
> expected to contain the true parameter value. Note that the stated
> probablity level refers to properties of the interval and not to the
> parameter itself, which is not considered a random variable....."
And Robert Dawson replied
<<<
And this is wrong. The probability level refers to the method
of
generating the interval, not to the interval generated.
A valid (if, perhaps, not optimal) 95% CI method may generate
an
interval that is known to contain the true parameter value, or one
that
is known to have missed.
>>>
I am not sure that I follow you here.....Do you have an definition of a
CI which
says what you mean? Alternatively, could you provide more details?
I have found Everitt to be a reliable source; looking more closely into
this definition,
he cites Stuart & Ord (1991) Kendall's Advanced Theory of Statistics,
volume 2, 5th edition,
which I do not have.
Kotz and Johnson (1982) Encyclopedia of Statistical Sciences gives both
an intuitive
and a technical definition. Intuitively they define it as "an interval
in which one may be confident
that a parameter lies" which seems to match with Everitt's definition
They then say that "the precise
technical meaning varies considerably from this.....but the intuitive
idea is not entirely misleading". (not
a very reassuring phrase....). It is hard (at least for me) to find
their exact technical definition (although they
do give several examples), but they do say "If confidence intervals
with confidence coefficient p were computed on a large number of
occasions, then, int the long run, the fraction p of these confidence
intervals would
containt the true parameter value" which seems to me to also match
Everitt's definition.
Me, I am just a data analyst with a PhD in Psychometrics; but I am
interested in this discussion
Peter
Peter L. Flom, PhD
Assistant Director, Statistics and Data Analysis Core
Center for Drug Use and HIV Research
National Development and Research Institutes
71 W. 23rd St
www.peterflom.com
New York, NY 10010
(212) 845-4485 (voice)
(917) 438-0894 (fax)
.
.
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