<I know that this question is not new but I haven't seen the answer yet.>
the correct answer probably is 'that depends...'
<Is it correct to work with the log-data and then make the antilog of the
confidence interval limits?.>
in general, under log and-or exponential transforms, variances do not
transform correctly, but percentiles do.
under different assumptions about how the errors arise you can derive
different types of asymptotic confidence intervals.
typical approaches for finding c.i.s for geometric means are
1) using some distributional assumption such as the data has a log-normal
distribution.
logging the data (as you said), finding a normal c.i. for the mean of the
logged data, and
1a)transforming the percentiles. in general, this gives no estimate of
standard error but you may not need it. also, if you are transforming the
empirical distribution to get the percentiles,
you will be limited in the alpha you can use (or have to form a random
c.i.).
1b) making assumptions that allows you to transform the variance, such as
the data has a log-normal distribution.
note: if you assume that your data, X, is log-normal(mean=mu, standard
deviation-sigma), then sigma, the standard deviation of ln(X), provides a
measure of dispersion of X/exp(mu) in the sense that
[exp(-1.96*sigma),exp(1.96*sigma)] is a 95% c.i. for X/exp(mu). so under
the assumption of log-normal X, the anti-log of the standard normal c.i.
provides a c.i. for X.
(actually, this note is probably all you wanted)
2) using a taylor linearization.
if X is your random variable, and GM(X) is the geometric mean of X, then:
GM(X) approximately= E(X) - var(X)/[2E(X)]
your english seems fine, but i would recommend that you talk to a spanish
speaking statistician at your university.
do you have a theory as to how your errors arise?
do you need an estimate of variance or only the confidence interval?
can you treat you data as an i.i.d. sample?
do you think your data is log-normal?
do you think a taylor approximation is a really fun way to get an estimate?
a few things you might need to think about.
i'm sure i got a few things wrong in here but the list is good at correcting
me and, as i said, you should really ask someone about this.
good luck with your problem.
bob
-----Original Message-----
From: Jaume [mailto:jaguado@medicina.ub.es]
Sent: Friday, May 24, 2002 5:53 AM
To: S-News (E-mail)
Subject: [S] geometric mean
I know that this question is not new but I haven't seen the answer yet. How
could I compute the standard deviation of the geometric mean with S-Plus?.
Is there a function to do it? Is it correct to work with the log-data and
then make the antilog of the confidence interval limits?.
Thank you.
PD: this is my first post. Spanish undergraduate student. So sorry about my
english.
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