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I have RNA counts for $4$ biological replicates and I have to combine them for further analysis.

e.g. File $$\begin{array}{c|c|c|c|c} RNA\enspace 1& 3.34 & 9.77&3.93& 1.01\\ \hline \text{RNA 2} & 0 & 38.95&0 &0 \\ \hline \text{RNA 3} & 5.99 & 3.11 &2.93 & 3.53\\ \hline \text{RNA 4}&1.40 &4.12 &1.71 & 2.43\\ \hline \text{RNA 5}&24.16 &0 & 1.22 & 0.19 \end{array}$$

Since taking the arithmetic mean may not be a true representative, I used geometric mean. But in cases where even one of the replicate has read count of zero, the GM becomes zero even when it is $38$ in another replicate. So is it ok to add $0.1$ to the whole of the matrix before taking geometric mean?

Kumar
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Kousalya Devi
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  • If by "is it ok?" you mean "Does the outcome stay the same?", the answer is no. What I would do, is to just disregard the zeros. That is, calculate the average so that you don't take them into account. – Matti P. Jul 11 '19 at 06:19
  • So what I would do is to calculate the following geometric mean: $$ GM_{\text{sample}} = \left( \prod_{i: x_i \neq 0} x_i \right)^{1/n_{\text{sample}}} $$ where $n_{\text{sample}}$ is the number of samples that are not zero. – Matti P. Jul 11 '19 at 06:46

1 Answers1

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The geometric mean is only a useful statistic measure if all the numbers are strictly greater than zero. If just excluding the zero entries make sense for the interpretation of your numbers, you can do that and then compute the geometric mean. Otherwise I would just stick with the arithmetic mean and maybe additionally show the median, the standard deviation or the number of zero entries. The best course of action here depends on what your data represents.

To see that just adding $0.1$ and the computing the geometric mean is a bad idea, ask yourself why did you add $0.1$? You could have added $0.01$ or $1$ instead. This would make a big difference for the geometric mean you get afterwards.

quarague
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