I am creating an ELISA curve fitting software from scratch and one thing I noticed is that when R^2 are calculated by the typical method (sum of squares of residual between expected y and real y), the curve only has to get the few points with the highest readings right to get a very high R square value. That's because curve is serial diluted so the points with lower readings are magnitudes lower in value compared to the high points. So even if the lower points' expected values miss the actual values by a lot percentage wise, the absolute impact on the overall "error" (statistically speaking) of the curve is minimal. This results in the curve only has to fit the highest few points well, and can really mess up the low concentration points and still come out looking OK.
My question is, when we fit the curves using the least squares method, when we calculate the error, should we normalize the error of each point (differences between actual Y and expected Y) by dividing the error against the expected Y? This way we are maximizing the fitness of the curve in terms of percentage of unexplained difference at each point, instead of absolute values.
Let me know what you think and if I can clarify on anything. Appreciated
Suppose there are two measurement points, A and B. If A's value is 20.3±1.8 and B's value is 5.6±1.8, then there is no need to normalize. However, if the value of A is 20.3 ± 1.8 and the value of B is 5.6 ± 0.7, then normalization is recommended. If not, then the importance of measurement point B is underestimated. No normalization in fit means that the measurement accuracy of all measurement points is the same. Or it means that the importance of all measurement points is assumed to be the same in your analysis.
Hi Kengo,
Thanks for your insights. I am on the same page with you.
The higher-reading points def have higher variances. Its more like A is 2000.3±197.8 and B is 5.6 ± 0.7.
Do you know if people (or say, ready-to-use software available on the market) routinely normalize when they fit the curve? I looked up "elisa data analysis" on Google and none of the page 1 results talk about normalization. It might be because they assume people just use some prepackaged software/stats tool to generate the fitted curve, and this detail is covered by those software/tools.
I just wonder if that is indeed the case.
This tool for example, could you tell if it has normalized data points when fitting the curve? How would I go about testing that?
https://www.elisaanalysis.com/app
Hi Sijie Xia,
For normalization, the list of errors is essential, so if the software doesn't allow you to input the list, it can't do normalization. Some software allows you to choose whether to do a "least-squares" or a "weighted least-squares". If the "weighted" option is available, the software can do normalization.
To do the test, for example, you can use the following data.
(x1,y1)=(100,100±0.1)
(x2,y2)=(200,200±0.1)
(x3,y3)=(300,300±0.1)
(x4,y4)=(400,1000±1000000)
The first three points are a straight line with little error, while the fourth point is off the line having a large error (almost no information!). Software with normalization will effectively ignore the fourth point and answers "y=1*x+0".
Don't mess with the data. Try this easy software, it uses something like the Monte Carlo method to estimate the errors on the parameters.
www.lerenisplezant.be/fitting.htm
- Badges
- Science topic
- Similar topics
- Biological Science
- Histology
- Sectioning