# Negative values in calibration curve

• frankmp40
In summary, the conversation discusses how to report negative values caused by a non-zero intersection in a calibration curve. The speaker notes that it is a common error and suggests possible reasons for it, such as interference from other substances or incorrectly calibrated equipment. They also mention the importance of using measurements within the calibrated range and not extrapolating. The topic of confidence intervals and background readings is also brought up. The mathematical formulation of the problem is briefly discussed, with the maximum likelihood principle being used to find the value of c that maximizes the probability of the measured value.
frankmp40
Hi

I just wondering how to report negative values cuased by non-zero intersection.
For example, when the absorbance<0.037 in the figure, the concentration would be negative.

Thank you!

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What do you mean by "how to report"?

I mean how to explain

It is a rather common error. You may have some interference from other substances, you may have some substance present in the reagents used, you may have incorrectly calibrated spectrometer and so on. As long as the calibration curve is nicely linear and all measurements fall within the range covered, there is typically no problem with using it.

Can I see the concentration is zero when it becomes slightly negative

No, that would mean something went wrong. Note that you will be outside of the calibrated range, and I told you it is OK to use measurements that fall within the range tested.

Even if you have a plot that looks perfectly linear and looks like it crosses 0,0 point, but you did the calibration for 10..100 range (of whatever unit), extrapolating the calibration outside of the 10..100 and saying "my concentration was measured to be 1" would be generally speaking a bad practice. In some cases it can be acceptable, but it depends on the application.

1 person
That's rather a question for the statistics forum than for the chemistry forum. Obviously a reading < 0.037 won't correspond to a negative concentration, simply because there can be no negative concentrations.
You should also never report an estimator without some confidence interval.

1 person
Did you subtract out a background reading? Calibration curves almost never behave in a perfect manner where they intersect through 0,0. No instrument is perfect.

gravenewworld said:
Did you subtract out a background reading? Calibration curves almost never behave in a perfect manner where they intersect through 0,0. No instrument is perfect.

Of course he did. If not, there wouldn't be the parameter a for the curve.
One of the easiest ways to formulate the problem mathematically is the following.
The absorbance A is distributed (e.g. normally) around ##a+bc##, i.e.
##A\sim N(a+bc,\sigma)##. From the maximum likelihood principle we find c as that value which maximizes the probability to find the value of A actually measured under the constraint ##c\ge 0##.
That is ## \hat{c}=\mathrm{max}(0, (A-a)/b)##, where ##\hat{c} ## is the maximum likelihood estimator for c. If the standard deviation ## \sigma## depends on c, too, or if the distribution is not normal the result may be more complicated but the principle remains the same.

## What are negative values in a calibration curve?

Negative values in a calibration curve represent a negative relationship between the independent and dependent variables. This means that as the independent variable increases, the dependent variable decreases, and vice versa.

## Why do we sometimes see negative values in a calibration curve?

Negative values can occur in a calibration curve due to a variety of reasons, such as experimental error, instrumental limitations, or the nature of the relationship between the variables being studied.

## How do negative values affect the accuracy of a calibration curve?

Negative values can significantly impact the accuracy of a calibration curve, as they can introduce errors and uncertainties in the measurements. It is important to carefully consider and address any negative values in order to obtain accurate results.

## Can negative values be ignored in a calibration curve?

No, negative values should not be ignored in a calibration curve. They may provide valuable information about the relationship between the variables being studied and can also impact the overall accuracy and reliability of the results.

## How can we minimize or eliminate negative values in a calibration curve?

To minimize or eliminate negative values in a calibration curve, it is important to carefully design and conduct the experiment, ensure accurate and precise measurements, and address any sources of error. Additionally, choosing appropriate mathematical models and data analysis techniques can also help to minimize negative values.

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