Weighting for calibration, 1/x^1/30 ?

[carls]

Now I get good linearity and accuracy nearly over the whole concentration range.

Is the %error highest at the low or high end of the conentration range?

What is the concentration range of your calibration?

[Peter Apps]

If the linear fit is closer for means of replicates than for raw data it indicates that the source of the deviations from linearity was random errror, because only random error gets smaller as the number of replicates gets bigger.

Do you have enough replicates at each level to calculate a standard deviation and relative standard deviation (CV) of peak area ? If you do, is there any trend in either of these ?, and how do those trends compare with the residuals of the linear fit ?

Peter

[dresdentl]

I have 9 calibration points. For each calibration point I have 9 -15 replicates. R^2 is the same for weighted and unweighted regression. But the lower calibration points get much more close to the the theoretic value with weighting. The range is from 1 to 250 (Cmax/Cmin = 250).
Here is an excerpt of the results of the complete statistical analyses:

Results for weighted fitting (w = 1/s^2)
Model = Least squares best fit line

(R-squared = 0.9996, R = 0.9998, p = 0.0000)



Analysis of residuals: WSSQ = 1.362E+00
P(chi-sq. >= WSSQ) = 0.987
R-squared, cc(theory,data)^2 = 1.000
Largest Abs.rel.res. = 10.56 %
Smallest Abs.rel.res. = 1.11 %
Average Abs.rel.res. = 4.20 %
Abs.rel.res. in range 10-20 % = 11.11 %
Abs.rel.res. in range 20-40 % = 0.00 %
Abs.rel.res. in range 40-80 % = 0.00 %
Abs.rel.res. > 80 % = 0.00 %
No. res. < 0 (m) = 4
No. res. > 0 (n) = 5
No. runs observed (r) = 5
P(runs =< r : given m and n) = 0.500
5% lower tail point = 2
1% lower tail point = 1
P(runs =< r : given m plus n) = 0.637
P(signs =<least no. observed) = 1.000
Durbin-Watson test statistic = 0.714 <1.5, +ve serial correlation?
Shapiro-Wilks W (wtd. res.) = 0.874
Significance level of W = 0.135
Akaike AIC (Schwarz SC) stats =-1.299E+01 (-1.260E+01)
Verdict on goodness of fit: incredible

[H.Thomas]

I'm not sure what all these data mean. The only thing you need are the variances of the lowest and of the highest standard. You calculate the ratio of the two. Then you look up the F-value F(n-1, n-1, 99%) in a table and compare it to your calculated ratio. If it is less than the F-value, you have homogenity of variances and can calibrate without weighting. If it is higher (which i strongly assume, given your calibration range) you have to use weighting. Otherwise you have the problems that you already noticed (bad accuracy in the low range).
The r^2 is no good measure of fit, if you do not have evenly spaced calibration points.

[Peter Apps]

But the lower calibration points get much more close to the the theoretic value with weighting.

How do you calculate (or measure ?) the theoretical value ?

Peter

[dresdentl]

I posted some results of the F-Test under the new topic F-Test.

It is also possible to plot the concentration versus standard deviation. If the slope of the strait line (p) exceeds 0,01 (1%) weighting is necessary.

I think I know the difference between error and residual. Error refers to the theoretical value, whereas residuals refer to the estimated function value. You never know the exact curve (theorectical value). Only the estimated function value is observable. Therefore you should only talk about residuals. For the same reason statisticians avoid the terminus accuracy.