How do you multiply two geometric means?

[Halsey]

How do you multiply two geometric means? How do you obtain the geometric standard deviation of the result?

I have GM1 and GSD1 for a set air dust level measurements. I also have GM2 and GSD2 for a set of dimensionless "enhancement factors" to be applied against the first set. (The enhancement factor is the ratio found between contaminant concentrations in the soil to the contaminant concentrations found in air-borne resuspended dusts. I do not have the data sets, only the GMs and GSDs for them.) What is the resultant GM when you multiply the dust levels by the enhancement factors? What would be the GSD?

Any explanation is appreciated; I suspect the answer is basic but have searched many sites and a few books but found nothing that says exactly what. Clearly, I'm not a mathematician.

 

[blamocur]

Just curious: what is the context of your problem ? Is this from some class homework assignment?

 

[blamocur]

Without knowing the data sets you can still figure out the resulting GM, but not, I believe, the GSD.

 

[Halsey]

Just curious: what is the context of your problem ? Is this from some class homework assignment?

Just curious: what is the context of your problem ? Is this from some class homework assignment?

No, actual work. Apologies and I understand if this forum is limited to students; I am trying to understand the math of lognormal distributions as my company has decided our data better fits those.

I have the GM and GSD for measurements of dust in air in micrograms per cubic meter, GM and GSD for the dimensionless enhancement factors, and a soil concentration (constant) of the contaminant in ppm. I want to calculate the GM and GSD of the contaminant in air in micrograms per cubic meter.

When we used Gaussian distributions, I would multiple the means and use square root of the sum of the squares of the standard deviations to combine the errors. I am hoping the math for these is as simple.

 

[Halsey]

Without knowing the data sets you can still figure out the resulting GM, but not, I believe, the GSD.

By simple multiplication? GM for the result = GM1 * GM2?

 

[JeffM]

I do not think that this is a math question at all. The word “factor” implies that you are to multiply.

In other words, the dimensionless numbers are what you are to multiply the geometric mean and geometric standard deviation by and are not themselves statistics. They are adjustment factors. Whether the result is scientifically meaningful is a different question.

 

[blamocur]

By simple multiplication? GM for the result = GM1 * GM2?

I believe so. In fact, you can see this from the definition of GM. Or you can use the fact that the logarithm of GM is the (arithmetic) mean of the logarithms of your data elements (https://en.wikipedia.org/wiki/Geometric_mean).