# Calculating CV for intra-assay ELISA

Sorry if this is in the wrong thread.

I have to calculate CV for intra-assay ELISA sample OD's. My problem is that i'm finding people are using sample standard deviation in their CV formula, though from what i understand as intra-assay CV reflects variability within the same assay run that to me should be considered as a whole data set and therefore population standard deviation should be used.

Am i correct in my assumption or am i missing something?

As far as I am concerned the intra-assay CV is the average of individual CVs found in an assay.

So let's assume you have a data set of 40 samples, and for each sample you have 2 replicates (results), like the one below. You would first calculate the mean for each sample, so in the sample above that would be: $$\frac{0.132 + 0.128}{2} = 0.130$$

Then you would calculate the standard deviation for each sample, so going back to our example above, the standard deviation for sample 1 would be as follows: $$\sigma=\sqrt{\frac{1}{2} ((0.132-0.130)^2 + (0.128 - 0.130)^2)}=\frac{1}{500}=0.002$$

Next you would calculate the Coefficient of Variation, so in our case:

$$CV = \frac{\sigma}{\bar{x}}\times100=\frac{0.002}{0.130}\times100\approx1.6%$$

Afterwards you would repeat the aforementioned procedure for each sample.

In the end you would calculate the average of all individual CVs, so: $$CV_{intra} = \frac{\sum_{i=1}^{40} CV}{40} \approx 5.2%$$

I have stolen the example from Salimetrics, I think this document explains inter-assay and intra-assay CV very nicely.

Please note: The usefulness of inter and intra-assay CVs are somewhat disputed, as this Wikipedia article mentions.

• Thank you for your reply, i have read this. They have 2 result sets, so it's possible to calculate the CV for each individual sample, i generally only have one. It's probably fine to use Sample Standard Deviation in their formula as they are calculating the individual sample CV from a whole data set. As i have only one set to work with i need to calculate the CV from the data set as a whole, which is why i think i should be using Population Standard Deviation in my CV formula rather than Sample Standard Deviation for my scenario instead. Though everyone seams to use Sample SD regardless. – user3796133 Mar 28 '18 at 23:57
• I guess it really depends what you want to measure with the CV. It sounds to me, seeing that you have only one result per sample, that an intra-assay CV is not the measure you are looking for. Going by what you have said it sounds like you simply want to calculate the CV for your entire data set and that seems to make sense. I think it then becomes more of a question what it tells you about your data and that really depends on your study design and what you test for.. – Johnny Mar 29 '18 at 7:57