Re: Unusual formulae for confidence intervals

Reef Fish wrote:

Why was it that NO ONE challenged or commented about my
comment on the use of (n-1), n, and (n+1) as the THREE most
commonly used denominators for S^2, for reasons of ESTIMATION
criteria? Answer: probably none of the discussant know about
that one. :-)

The use of "n+1" is certainly peculiar to those who don't use it,
but
there is nothing "peculiar" about it for those who understand that
"unbiased estimate" and "maximum likelihood estimate" are just
TWO of the main THREE criteria in statistical POINT estimation!


Well, I thought it was just a misinterpretation of what was in the
original post ...
where I think (subject to my own possible misinterpretation and
without looking back) the "S" in question was meant itself to be a
sample variance (of some form) and not an unscaled sum of squares, and
that the expression was meant to be used to decide a sample size to
estimate a mean with a given precision, in which case a factor of 1/n
would be usual (with a factor of 1/(n-1) contained in the calculation
of the sample variance). I couldn't see why 1/(n-1) would appear in
the formula given except perhaps as some form of allowance that would
be better done using percentage points of a t-distribution.

Of course the use of (n-1), n, and (n+1) as possible denominators for
S^2 (where this is the sum of squared errors) should be well-known. I
don't know whether there are any simple results available from the
theory which would cover the type of two-stage sampling being
contemplated here to say how one might use an initial sample to choose
the size of a second sample in some "optimal" way.

David Jones


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