More Than You Ever Wanted to Know About Calibrations, Part 3 – Dealing with Zero Points

In previous blog posts I’ve talked about calibration types and curve fits. In this installment I’ll cover issues around the calibration zero point. This is a topic that many methods give little guidance on, and various methods can handle it very differently; so it’s easy to be confused over what best practices are, and hopefully I can clear up some confusion.

When I talk about zero points in calibrations, there are two different things to consider. First, whether a zero point or blank needs to be included in the calibration, and second, whether a calibration curve should be forced through zero. I’ll go over how these might affect your calibration before discussing some examples of how various EPA methods handle them.

In the first case, I’d argue that you should always run a blank or zero point with your calibration so you know what background or interferences may be present in your calibration. The real question is whether it should be included as part of the calibration curve itself. If you’re using an average response factor (RF) curve the answer is easy. Since RF is defined as area/concentration, having a concentration of 0 would give an undefined value, so zero points can’t be used with average RF calibrations. For linear and quadratic calibrations, pretend you’re chemistry Marie Kondo and ask yourself “Does it spark joy?” Or rather, “Does it add value?” If you’re calibrating and analyzing samples at high concentrations, then adding a zero point likely won’t improve your calibration. If you have no background, then your calibration likely passes very close to zero anyway, so adding a zero point again is unlikely to improve the calibration.

Where a zero point becomes potentially helpful is if you have an elevated background and are analyzing low level samples. In this case a zero point may help better define that background in the calibration, though it may be unnecessary if you have several calibration points at the lower end of the calibration. To show this, some mock calibration data is given in Table 1, which shows how recoveries compare when adding a 0 point to a calibration. The top calibration changes a great deal at the lowest level, having a 21% difference in recovery of the 0.1 standard level. However, the bottom calibration adds two calibration points to the low end, and you can see that the effect of adding the 0 point decreases as the low end of the calibration becomes better defined.

Standard level	Response	Without 0	With 0
0	100	% Recovery		Difference
0.1	220	59%	80%	21%
0.5	630	105%	109%	4%
1	1067	102%	104%	2%
10	8989	100%	100%	0%
Standard level	Response	Without 0	With 0
0	100	% Recovery		Difference
0.1	220	74%	85%	11%
0.2	345	108%	113%	5%
0.3	368	81%	84%	4%
0.5	630	108%	110%	2%
1	1067	103%	104%	1%
10	8989	100%	100%	0%

Table 1 – Comparison of inclusion of 0 values in calibrations

For this to be true your background must be consistent however, because including a zero point when you have inconsistent background would just add noise and introduce error to your calibration. This is also true of any low calibration points having a response that is significantly affected by the background contributions.

Whether you include the zero point or not; when allowing a y-intercept, the entire calibration takes into account the elevated background, acting almost as a blank subtraction built into the calibration. It’s important to note that this only works if the background is consistent between both your standards and samples. If the background comes from the blank matrix used to make standards it likely won’t be present in real samples, which will lead to under-reporting results on those samples. If the background comes from something shared between samples and standards, such as your instrument or internal standards, then the background should be consistent between standards and samples.

Forcing the calibration through zero is much different than including a zero point. It’s basically removing the y-intercept from the regression equation, assuming that a concentration of zero gives zero response. This is true in an ideal situation, and compounds that show no background will have y-intercepts very close to zero. For compounds that do have some background, forcing through zero can help to show the concentration of your background. Often though, forcing the calibration through zero can give very poor results for the lower end of the calibration curve, which becomes more pronounced as the background increases.

To see how forcing through 0 can give bad recoveries, let’s look at an example calibration from my lab. We have some carbon disulfide background in the lab due to the solvent being used in other parts of the lab, which affects our TO-15 analysis. Table 2 shows a recent calibration for carbon disulfide, and you can see that the blank or zero point has a significant response.

Standard level (ppbv)	Response
0	30000
0.2	42765
0.4	49972
1	75671
2	108822
5	260352
10	464684

Table 2 – Carbon Disulfide calibration data

If we do a linear calibration both with and without the zero point we can see in Table 3 that the inclusion of the zero point doesn’t greatly affect the calculated concentrations, which indicates that the background response is consistent through all the calibration points. Despite this, the calculated recoveries of the calibration are still within ±30%, which is due to the blank subtraction effect I mentioned earlier. The higher recovery at the lowest calibration point is due to a non-weighted calibration being used for simplicity.

Standard level (ppbv)	Without 0 (ppbv)	% recovery	With 0 (ppbv)	% recovery
0	-0.04		-0.03
0.2	0.25	125%	0.26	130%
0.4	0.42	104%	0.42	106%
1	1.00	100%	1.01	101%
2	1.76	88%	1.77	89%
5	5.24	105%	5.24	105%
10	9.93	99%	9.92	99%
	%RSE	14.2%	%RSE	16.4%

Table 3 – Results for carbon disulfide calibration with and without zero point.

If we force the calibration through zero however, the recovery and %RSE gets much worse, because the assumption of no response at our zero point does not hold true. Table 4 shows the results of the aforementioned scenario.

Standard level (ppbv)	force 0 (ppbv)	% recovery
0	0.62
0.2	0.89	444%
0.4	1.04	259%
1	1.57	157%
2	2.26	113%
5	5.41	108%
10	9.65	96%
	%RSE	191.9%

Table 4 – Results for carbon disulfide calibration when forced through 0.

To me, this shows the practical limitations of using calibrations that are forced through zero. If you have no background, then forcing through zero will likely not change your results much, since the calibration will run through zero or nearly so on its own. But with a larger background it can give terrible results on the lower end. There’s a sweet spot where the background is low enough that it still gives a decent calibration, but high enough where it’s useful to calculate the background concentration. It basically turns you into the Goldilocks of calibrations.

However, even with the poor calibration recoveries, the information gained from forcing through zero can still be useful, in that the calculated value of the 0 point can be used as an estimation of the blank concentration. If you correct the blank and all calibration points for this we see that it gives a very accurate calibration, as shown in Table 5. Both the % recovery and the %RSE is under 10%. While reporting data off an adjusted calibration like this would likely be unacceptable to most quality systems it still shows that it provides a good estimate of the background concentration.

adjusted standard (ppbv)	adjusted recovery (ppbv)	% recovery
0.62	0.59	95%
0.82	0.88	107%
1.02	1.05	102%
1.62	1.64	101%
2.62	2.40	91%
5.62	5.86	104%
10.62	10.54	99%
	%RSE	6.0%

Table 5 – Carbon disulfide calibration adjusted for background.

Unfortunately, there doesn’t seem to be consistency between EPA methods on how to handle zero points. Looking into some of the methods I’ve been working on lately gives very different guidance on whether forcing the curve through zero is appropriate, and very little guidance on whether including a zero point in the regression itself is appropriate. Below is just a quick sampling of a handful of EPA methods.

• Method 533 – Requires the calibration to be forced through zero. No guidance given on using a zero point in the regression.
• Method 1633 – No guidance on whether the calibration can be forced through zero or if a zero point should be used in the regression.
• Method OTM-45 – States that forcing through zero may improve the estimate of background levels, but does not require it. No guidance on using a zero point in the regression.
• Method TO-15A – States that a calculated y-intercept may be appropriate if the background is a consistent behavior of the measurement system (i.e., is present in both standards and samples) rather than an artifact of the calibration process. States that a zero point should be considered to be used in the calibration regression, but that one should be analyzed even if it’s not included.
• SW-846 – States that forcing an unweighted curve through zero may be appropriate, but it should not be done for weighed curves. Forbids the use of zero points in the calibration regression.

How to handle the zero point of a calibration is a surprisingly complicated thing, and it wasn’t until I sat down and started writing this post that I realized how complicated it could be. The lack of consistency between methods doesn’t help and makes it very important to closely read the methods to make sure you’re following the requirements as written, or documenting deviations from it if allowed. With inconsistent or unclear guidance from methods, hopefully this information helps gives some clarity on best zero point calibration practices for your lab.

The next blog post in the series will cover calibration acceptance criteria, so stay tuned for that.

View all of the posts in the "More Than You Ever Wanted to Know About Calibrations" series.