# correct mean of replicates

Gys de Jongh GysdeJongh at csi.com
Fri May 7 19:00:15 EST 1999

```Gottfried,
Your observations are correct in my opinion. We do elisa's by plotting the
log concentration over the OD and then use the middel aprox. lineair portion
of that curve. This means , imo, that we can only access the log of the
concentration by this method. From repeating experiments we see that the log
of the concentration is aprox. normally distributed. We just made a
histogram of the log of the concentration for twenty equal samples . This
means that we can do normal statistics with the log of the concentration. So
if the log concentration = 2  + or - 0.3010  (from1.699 till 2.301 for 95%
interval) , our best estimate of the concentration in this imperfect world
is 100 * or / a factor 2 ( from 50 to 200). What you could do is compare the
acc of a pH meter (log) with a old fashioned titration (lineair) Some people
complaint than about the acc , however it is a method with a very high
specificity : micrograms of one protein in a mixture with grams of other
proteins and a very high sens. some times down to picograms. Life is
beautifull be you can't have it al.
Gys de Jongh

Gottfried Griesmayr wrote in message <372e0158.0 at 195.70.96.56>...
>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
>reported in addition.>Others calculate concentrations only for the
individual replicates and
>report the mean of replicate concentrations to be  the sample
>concentration.

For each OD the linair portion of the OD-> log[C] calibration curve gives a
log[C]  The log[C] is normally distributed so do all you stats ( means ,
stdev , 95% interval) on this log[C] and transform only the results back .

>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).

This becomes difficult......as you point out yourself  'Outliers' , 'weigted
more' ....the problem is that at this stage in science the normal curve is
best known and investigated so simply use the log[C] instead and all nice
inferences will be math. well founded. Nothing misterious left :)

>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!
>Is this really true? Your comments are appreciated.
>
>
>Gottfried Griesmayr
>
>E-mail: gottfried.griesmayr at anthos-labtec.com
>Homepage:   http://www.anthos-labtec.com
>
>
>

```