# correct mean of replicates

Gottfried Griesmayr griesmayr at salzburg.co.at
Tue May 4 05:26:45 EST 1999

```How to calculate correctly the mean of replicates in an immunoassay?

We are used to calculate first the mean of the measurement values of all
replicates of a sample (e.g. mean of OD measured with the ELISA reader),
then  we calculate the concentration of this sample based on the mean (e.g.
using a standard curve). The concentrations of individual replicates are
Others calculate concentrations only for the individual replicates and
report the mean of replicate concentrations to be  the sample
concentration.

This two ways end up with identical results, as long as the concentration
axis and calibration curves are linear and there is a linear relation
between measurement values and concentration. But it is obviously not the
same when we are dealing with a logarithmic concentration axis!
If we take simply the arithmetic mean of individually calculated replicates
in such case, the higher replicates would be weighted more than the lower
replicates. An outlier with high reading would influence the result much
more than an outlier with low reading. For eliminating this effect we would
have to take the geometric mean (multiply n replicate values and draw the
n-th root of the product).
At least for mathematical reasons this would be the only correct solution
in my opinion, but I have heard that nobody takes care on this matter.
I was told that it is a convention or at least general practice, to use the
arithmetic mean of replicate concentrations without respect to the axis
format!