Bio-Rad Microplate Manager Software - Manual (Page 52)

Analyzing Data Using a Standard Curve
44
Error of the interpolated concentration (conc
y
) is related to the error of the response
s
y
according to
s
conc
= ( δ conc(y)/ δ y) s
y
The estimated standard error of concentration (SEM
conc
) calculated from the mean
response of n replicates is
SEM
conc
= (δconc(y)/δy) RMS(y) / SQR n
The (δconc(y)/δy) depends on the form of the standard curve.
For a linear standard curve (for example),
Y = A + B* conc → conc(y) = (y-A)/B
(δconc(y)/δy) = 1/B
Wt avg conc = <conc> = Σ w
i
conc
i
/ Σ w
i
Weight w
i
= 1/(SEM
i
) 2
conc
i
interpolated concentration for dilution i
If there are replicate samples with dilution i, conc
i
will be the mean of these
replicates.
SEM
i
is Standard Error of the Mean for conc
i
.
Example of Weighted Mean
For two concentrations with SEM values as shown,
100 ± 10
150 ± 50
the mean concentration should NOT be taken as 125. The weighted mean of these
two concentrations is 102, since 25 times as much weight is given to the value of 100
with the 5-fold smaller standard error value. When concn is calculated using the
<conc> = Σ w
i
conc
i
/ Σ w
i
with w
i
= 1/(SEM
i
) 2