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I am looking at a scientific paper in which a single measurement is calculated using a logarithmic mean

'triplicate spots were combined to produce one signal by taking the logarithmic mean of reliable spots'

Why choose the log-mean?

Are the authors making an assumption about the underlying distribution?

That it is what...Log-Normal?

Have they just picked something they thought was reasonable... i.e. between a a mean and a geometric mean?

Any thoughts?

kjetil b halvorsen
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Stephen Henderson
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    maybe a reference to the paper could help ? – robin girard Jul 27 '10 at 14:52
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    Slightly related question: http://stats.stackexchange.com/questions/298/in-linear-regression-when-is-it-appropriate-to-use-the-log-of-an-independent-var/ – Shane Jul 27 '10 at 14:53
  • You may find this paper of interest, which discusses the log mean and how it refines the 'arithmetic mean - geometric mean' inequality: http://www.ias.ac.in/resonance/June2008/p583-594.pdf – Tony Breyal Jul 27 '10 at 15:03

2 Answers2

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Are the authors making an assumption about the underlying distribution?

You are making an assumption whether you choose to use it or whether you choose against using it. For Power Law distributions it usually makes sense to look at the logarithms.

Christian
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In the case of log-normally distributed data .... the geometric mean is a better measure of central tendancy than the arithmetic mean. I mean I would guess they look at the paper and have seen a log-normal distribution.

Spots ... makes me think its referring to probes from a microarray .. in which case they do tend to do log-normally distributed (can't find the reference though sorry).

Nathan Harmston
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