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I want to perform a non parametric test (Mann-Whitney) for my experiments that is briefly quantification of viral load (Real Time Polymerase chain reaction). My final result is the amount of RNA copies per microliter (i.e. 1e10 copies per microliter). I log transform these values in order to better represent the data (graphically). My question is: for the statistic matters, should I run the statistical test with the log-transformed data or with the raw data?

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    $\begingroup$ Wilcoxon-Mann-Whitney operates on ranks. and ranks are the same under any monotonic transformation. So, there is no issue here. Naturally, or even decimally, logarithms could be desirable (essential?) for useful graphics. $\endgroup$ – Nick Cox May 15 '17 at 7:28
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Most of the RNA-Seq analysis I know operate on the log-scale, because transcriptome abundance could be quite large (you have 1e10).

For example, we do differential analysis on the log-scale, we plot MA-plot on the log-scale, we create scatter-plot between two samples also on the log-scale, we create gene expression matrix on the log scale ......

You should consider conduct your analysis on the log-scale.

EDIT:

Sorry, I didn't see you asked for the Mann-Whitney test. The test is done on ranks, thus it should work with both ways. I'd still do it on the log scale for consistency.

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  • $\begingroup$ Good advice, but doesn't address Mann-Whitney detail. $\endgroup$ – Nick Cox May 15 '17 at 7:30
  • $\begingroup$ @NickCox Sorry, I missed it was stated in the question. $\endgroup$ – SmallChess May 15 '17 at 7:30

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