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.
