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## Very confusing; Calculation from calibration curve

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### Very confusing; Calculation from calibration curve

Hi, all,

Is anybody tell me about calculation of concentration from calibration curve?

If I get calibration curve(external calibration) at zero concentration and 100ppb concentration(2point calibration).

Unfortunately zero concentration has some y-intercept value like 80.

Finally, y = 500x + 80(calibration curve).

For example, if I get y-intercept value like 50 after sample analysis, the concentration value should be - value(x=(50-80)/(500)=-0.06) by calibration curve.
Is this value available? I don't think this is not real cocnetration.

How do I understand negative concentration? Is there any reliable understanding?

Best regards.
Li

### Re: Very confusing; Calculation from calibration curve

Negative concentration has no meaning. When you get a calculated y-intercept at zero concentration, it really means that there's some nonlinearity in your other data. Data that is slightly concaved up, will give you a negative intercept. Data that's concaved down, will give you a positive intercept.

A common convention for a detection limit is a signal-to-noise ratio of 3 for the analyte using your analysis. You should try to determine the detection limit for your analyte (concentration required to give S/N = 3) and see how that signal compares to your calculated intercept. If the signal for S/N = 3 is much different from your calculated intercept, you should find the source of the nonlinearity in your other calibration data.

### Re: Very confusing; Calculation from calibration curve

You need to check the calculation of the calibration equation - where do you get +80 from when the intercept is 8 ?

Two additional parts of your problem are that a you have only two points on the calibration, so no way of knowing if it is linear, and your lower point is actually just background + noise rather than a known concentration of analyte.

Peter
Peter Apps

### Re: Very confusing; Calculation from calibration curve

I found that there is some mistaken expression(not 8 but 80 at the y intercept).

Actually, my samples are liquid chemicals to detect trace amount of metallic impurities.

Calibration curve(y=500x +80) are actually example.
But this calibration could be made by metal impurities from liquid chemicals.

Before anayzing samples, I have to diulute liquid chemicals about 10~100 fold.
And then, I wanna make calibration curve using external standard or internal standard method.
Are these approch right?

Regards.
Li

Best regards.

### Re: Very confusing; Calculation from calibration curve

A couple of comments:

(1) You can't really have a real calibration point at zero concentration. You can force a one-point calibration curve through the origin, if you wish, but that's different (and that should give you a calibration curve that is really y = 500x + 0).

(2) If you have a curve like y = 500x+80 then the 80 must be the actual measured value in your zero-concentration sample. This means that you integrated a peak that wasn't there. It's possible the integrator parameters were set to such a sensitive level that they were integrating noise.

(3) This brings up the concepts of limit-of-detection and limit-of-quantification. Your results will not be reliable if the peak is not reliably bigger than noise. This is the limit of detection. They will also have large errors unless your peak is big enough that statistical random variations don't affect its area greatly. This is the limit of quantification. There are lots of defined ways to measure them, but that's not really the issue here. The issue is that the bottom end of your calibration curve, if it is from a zero-concentration standard, must, definitely, be below the limit of quantification, so you cannot trust measured values around this point. The problem is, how much higher does the concentration have to be, before you can trust it? Currently, you don't know, but you need to know.

(4) What you need to do is create a calibration curve with a series of points spread across the range of concentrations you intend to measure (for example, a dilution series from a high concentration).

(5) Another question is whether an error of 80 at zero concentration is relevant. If your calibration curve spans the region 100-1000 units on the x axis, and the curve is y = 500x + 80, then the actual measurements are 50,000 to 500,000, and 80 is merely an insignificant statistical error. If your calibration curve spans the region 1-2 units and you have this y-axis intercept, then the actual measurements presumably span the region 500-1000, and 80 is 16% of the low-end of the calibration range. That's not good.

(6) If you have a problem and 80 is significant, it may (as others have said) mean that your calibration is non-linear. This isn't necessarily tragic. Some detectors are linear, others do tend to non-linear curves, and every bit of software I've ever used can fit curves. If you need to fit a curve, you need enough points to be sure the curve is a good fit.

(7) But the bottom line is that whatever you do, your data are really only valid if they are somewhere between the lowest concentration standard and the highest. Anything outside this region is extrapolation, and will be increasingly inaccurate the further it strays from the standards. You are right to highlight the problem of negative concentrations for samples that don't reach the low end of the calibration curve, if the curve isn't forced through the origin. All this really means is that they are indistinguishable from zero. You can force a method to fail more elegantly by forcing the curve through the origin, but it doesn't make the data more reliable! Theoretically these low results should merely be reported as < LOD, but I do understand that in some fields, people expect numbers.

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