Hi all. I got table in excel that involved the two following items:
X-axis: concentration ranges.
y-axis: values the obtained with respect to X-axis values.
Now i need to calculate the linear range based on Stern-Volmer equation and consequently calculate LOD.
what is the easiest procedure in excel to know the linearity of different wide range concentration values?
you can proceed as follows :
1. Take 'n' replicate Y measurements of your blank solution, calculate the mean YBAR and the std deviation s, compute YBAR + 3*(s/sqrt(n)), sqrt stands for square root of the argument.
2. From your regression line Y= m*X+c, calculate the X value corresponding to Y=YBAR + 3*(s/sqrt(n)), the corresponding X value is an estimate of the Limit of detection (LOD).
The response Y is not, in general, a linear function of concentration over the entire range, it is because the sensitivity (dY/dX) is a function of X, however, for a concentration range, small enough, you can approximate the actual response function Y by a low order polynomial, e.g a linear or quadratic functional forms, therefore, over a wide range of concentrations, it is advisable that the interval be subdivided into smaller intervals, and you can attempt to fit linear regression functions to data over the individual sub-intervals, the form of regression problem here can be handled much better, in a single framework, using the concept of " Dummy Regression ", you can look into this concept for more details.
a Standard text that covers this concept well is " Applied Regression Analysis " by Draper and Smith, you can also find details of Dummy regression method in the following online courses portal:
https://nptel.ac.in/courses/111104074/
Dear dr Gosh, can you please provide me with any article that support your comment? So that i can easily follow the exact procesure. Thanks in advance!
Title of book: Measurement, Statistics and Computation, ACOL series, Authors: David McCormick and Alan Roach, pages 508-513.
LOD (limit of detection ) = 3.3(Standard deviation of intercept/slope)
LOQ (limit of quantification) = 10(Standard deviation of intercept/slope)
Standard deviation of intercept = Standard error of intercept *√n
n= Number of concentrations
Standard error of intercept = Calculate from regression ( Excel -> data analysis -> regression)
Detection limits LOD, LOQ can be calculated using following equation (as per ICH Q2 guide lines) DL = 3.3 * Sigma/ Slope. , and LOQ = 10* Sigma/ slope, Where Sigma is Residual of standard deviation of regression or STD deviation of y intercept.
Sigma can be calculated by following Microsoft office Excel functions 1.Regression 2.Formula “”STYEX”” - 3.Array Function “” LINEST”” -
For tutorial of the use of above functions are watch the youtube video..
https://youtu.be/Ii2Z3hqwRGM/
dear Jayan Thermadom Rappai do you have an advice for calculation the LOQ and LOD without the slope? For my bradford assay I am using a x²-function instead of a linear calibration curve, so unfortunately I have no slope. Do you have any suggestion to calibrate those parameter for example with my Blank Value?
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