# Comparing three groups for one variable when two of the groups' values are zero

I'm trying to compare three groups but the fact that two of theml only show values of zero is giving me a hard time. Specifically, I'm comparing the production of a metabolite (M3G) by three cell lines. the results are as follow :

Line 1 : mean = 0 SEM = 0, n=10
Line 2 mean = 0, SEM = 0, n=10
Line 3 : mean = 2.89, SEM = 0.23, n=10


Here are the values for cell line 3 :

> 3,52 4,37 2,51 2,71 2,48 2,09 2,73 2,92 2,80 2,66


All the values for cell lines 1 and 2 are 0.

What test should I use to compare these cell lines ? I've been trying to find an answer and came up with a thread recommending a one-sample t-test, but I have three groups... I'm not sure what to do as I'm no expert in statistics ! For my other analyses (comparing groups with means different from zero), I usually use Mann-Whitney : is this applicable here ?

## 1 Answer

The one-sample t-test would presumably show that cell line 3 has a non-zero production of the metabolite. If you are sure that the other 2 lines have 0 production, then your problem is solved. Two lines have no production, and the third does.

In practice, however, a value of "0" typically means below the limit of detection. A limit of detection of 2 units would be consistent with your data. In that case you would have to know more about how the detection method handles samples that are close to that limit, both in terms of the mean value reported and the variability in the values that might be reported.

• Hi, thanks for the answer ! My method of detection is L-MS/MS (HPLC coupled to tandem mass spectrometry) so it's more or less the most sensitive apparatus available right now. I don't really understand what you mean by "a limit detection of 2 units" ?? Thanks :) – Neuron May 30 '15 at 19:44
• Something mention : My data are actually an extrapolation of the results to the total content of the metabolite : the signal detected by the LC-MS/MS was 10 times lower (I inject only 10µL out of 100, and the values obtained are in pmoles). – Neuron May 30 '15 at 19:52
• From your comments, your raw LC-MS/MS numbers are evidently 0.352 pmol, 0.437 pmol, etc. My point about the limit of detection of "2 units" then becomes: what would happen if you injected 0.2 pmol in your 10 ul? Would you see a signal? Even if this is the most sensitive technology, how sensitive is it? What's the lowest amount you can distinguish from a true 0 value? – EdM Jun 1 '15 at 13:08