Re: how does one calculate confidence values for geometric means

[JE McGimpsey]

I'm cross-posting this to the microsoft.public.excel.worksheet.functions
group (since it isn't Mac specific), in the hope that one of the stats
gurus can do a better job answering this than I can...

 

[Jerry W. Lewis]

Depends on what you assume about the distribution of the data. If you
assume the data are lognormal, then you should take logs of the X values
calculate the arithmetic mean and usual Student's t confidence intervals
(say LCL to UCL) on the log scale, then back transform the results to
the original scale. Thus exp(LCL) to exp(UCL) is a 95% confidence
interval for exp(average(ln(data))) = geomean(data) for lognormal data.

Jerry W. Lewis, PhD

 

[Jerry W. Lewis]

Sorry, I read the question, but didn't look at the data. The data are
interval censored. That is a much more complicated problem.

You could do a maximum likelihood analysis. If you assume that the
underlying continuous variable is from a lognormal distribution, then
the contribution to the log likelihood of the observation in A1 is
=LN(NORMDIST(LN(A1),$D$1,$D$2,TRUE)-NORMDIST(LN(A1/2),$D$1,$D$2,TRUE))
assuming that a titer of 512 is interpreted as "the true value lies
between 256 and 512". Here D1 initially contains average(ln(data)) and
D2 initially contains stdev(ln(data)). In another cell (say D3) use a
formula to sum the individual contributions to the log likelihood. Then
use Solver to maximize D3 by changing D12, to get the maximum
likelihood estimates for the mean and standard deviation of the assumed
continuous (unobserved) underlying log data. With logs of the posted
data, I get an MLE of 7.575 for mu and 0.833 for sigma vs. 7.922 and
0.873 ignoring the censoring

Jerry