Hello Joeu2004:

Thank you for all of this additional information and detailed explanations.

Interestingly enough, your formula gave me a closer value to the target test
value than Harlans. My programmer says it may have to do with the log
function in some way.

You may not consider yourself an expert in the legal sense, but I'm pretty
sure your explanations and formulas would hold up anyplace. Thank you so
much for your time and efforts!

Warm regards,

Bob Allen

"joeu2004" wrote:

On Dec 5, 12:35 pm, BobA5835
wrote:
Our young programmer told me this as a further explanation
[....]
The largest positive number in Excel is 9.99999999999999 * 10^307

That is the largest positive constant that you can enter. The largest
postive value as a result of computation is a little more than
1.7976931348623157E+308, which is displayed as 1.79769313486232E+308.

Yes, the equal sized Groups do produce a numerical Value equal to the Value
of the Geomean in an 'n' of 273 data points. Hence my second question to a
mathmatician: Are these actually the same Value?

First, considering the constraints of your data (up to a value of 15,
if I understand your first posting correctly), I think you would have
to settle for groups of 262, not 273. 15^262 is about 1.367E+308, but
15^263 overflows. You might know that your average data point less
than 15; you said you computed the geomean of 273 data successfully.
But I think it would be risky to depend on that. It's a judgment
call.

As for the mathematical question, it has already been answer: yes,
the geomean of k geomeans of n data each is equal to the geomean of
k*n data [1]. But remember that n must be the same for all "sub-
geomeans". If you choose 262 for n, the total number of data must be
a multiple of 262(!!).

joeu2004: Thank You for a second workable formula ditto on showing it to my
programmer.

Harlan's formula, using AVERAGE, is equivalent and arguably cleaner.
You can use exp/ln or 10/log. Frankly, that's the form that I always
use. I don't know why I chose not to use AVERAGE in my formula.
Brain fart!

"You don't need to be a mathematician." Well, actually, you do in this
case. I'm asking for an expert opinion. We are in a regulated industry.
I'm a biologist, not a mathematican.

I would not qualify as an "expert mathematical opinion" in a court of
law.

HTH.


-----

Endnotes:

[1] Proof. For simplicity, G(...) means GEOMEAN(...).

G( G(y[1,1],...,y[1,n]), ... ,G(y[k,1],...,y[k,n]) )

=( G(y[1,1],...,y[1,n]) *...* G(y[k,1],...,y[k,n]) ) ^ (1/k)

=( (y[1,1]*...*y[1,n])^(1/n) * ... * (y[k,1]*...*y[k,n])^(1/n) ) ^ (1/
k)

= ( y[1,1]*...*y[1,n] *...* y[k,1]*...*y[k,n] ) ^ (1/n) ^ (1/k)

= ( y[1,1]*...*y[1,n] *...* y[k,1]*...*y[k,n] ) ^ (1/n*k)

=G(y[1,1],...y[1,n], ... ,y[k,1],...,y[k,n])