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# Calculating geometric mean for real-time PCR

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### #1 tyrosine

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Posted 23 May 2011 - 01:27 AM

Hi all,

I have a question regarding qRT-PCR data analysis. I performed a PCR run with my target gene and two endogenous controls (GAPDH and B-ACTIN) and was going to determine the relative expression by using the comparative Ct method (i.e. find difference in Ct values between target and control, then normalising it to a calibrator). After reading heaps of papers about using multiple controls, I realised that it is not as easy as just taking the mean Ct values of both controls and normalising my target genes to that (I guess this is what you would call an 'arithmetic mean').

All these papers mentioned using a geometric mean value instead, how do I calculate it?

For example, if I have GAPDH Ct values of 17.17, 17.26, 16.95 and B-ACTIN values of 20.92, 20.95, 20.92, do I multiply each of the numbers by themselves, add them, then nth root the final value? And once I have done that, I divide the mean Ct of my gene of interest to get a relative value? Do I need to calculate a geometric mean for that?

Please help, I have read the quintessential papers (Hellemans (2007) and Vandesompele (2002)) but I am still really confused!

### #2 pito

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Posted 23 May 2011 - 01:53 AM

In maths the geometric mean value is simple the Nroot of the product of your numbers.

Example: 6, 7 and 8 are your numbers, then the geometric mean value would be: ³root of (6x7x8).

I am not sure if they used this, but in maths its like this.

(see the attachement)

#### Attached Thumbnails

Edited by pito, 23 May 2011 - 01:54 AM.

If you don't know it, then ask it! Better to ask and look foolish to some then not ask and stay stupid.

### #3 Trof

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Posted 23 May 2011 - 02:46 AM

pito, on 23 May 2011 - 01:53 AM, said:

I am not sure if they used this, but in maths its like this.
Yes, that's it.
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### #4 tyrosine

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Posted 23 May 2011 - 02:56 AM

Thanks for your input. I understand how to calculate geometric mean, but I would like to know if the way I applied it to normalization of gene expression is correct.

### #5 Trof

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Posted 23 May 2011 - 03:15 AM

It's in Hellemans (2007).

This equation:

The ugly thing below the line is the geometric mean of relative quantity values of all reference genes. You take the efficiency (E) of each reference and power to delta Ct (Ct calibrator - Ct sample) for each of them and calculate the relative quantity (you do the same for the gene of interest). Then you make geometric mean of the relative quantity of references. Then you divide the relative quantity of GOI with the geometric mean of reference genes.

I'm not very good in mathematical english, so I hope you can understand this.
Our country has a serious deficiency in lighthouses. I assume the main reason is that we have no sea.

I never trust anything that can't be doubted.

### #6 tyrosine

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Posted 23 May 2011 - 03:50 AM

Hi trof,

Of course! Thanks for pointing that out. I went straight to the formula section at the end of the paper (because I was impatient) and didn't read the start! The formula you posted made so much sense, basically just a regular rt-pcr quantification formula except for the reference gene calculations. I don't know how I didn't see it the first time. Thanks!!!!!