# Cannabis Potency Testing & Calibration Curves

17 Feb 2021Calibration curves are an essential part to potency testing. A question often brought up by customers is “how many calibration points are needed for a calibration curve?” The answer to this question isn’t the same for everyone, as it depends on your laboratory’s objectives and accreditation body guidelines. Since the answer could potentially be different between labs, let’s do some statistics with different numbers of calibration points to gain insight on the effects of choosing more or less points.

Confidence intervals can be calculated for calibration curves and can give us an indication of how close to the “true value” we are when we quantitate samples. This is different from standard deviation, which provides an indication of the precision of a sample. Using statistics we can calculate a range within which the “true value” of a sample will lie by determining the upper and lower confidence limit. This can be performed in excel by using the “regression” function in Data Analysis. Below I have calculated confidence intervals for a hypothetical calibration curve containing either 3, 5, or 7 points using N-1 degrees of freedom and 95% confidence.

Figure 1. Upper and lower confidence intervals calculated for calibration curves containing 3, 5, and 7 points.

The confidence limits were calculated using the same data, just using either 3, 5, or 7 points. If we zoom in on the calibration curve we can start to see the significance the number of calibration points has on the upper and lower confidence intervals.

Figure 2. Zoomed in portion of Figure 1.

When we look at Figure 2 we can see that for more points on a calibration curve the narrower the band is for upper and lower confidence intervals. We can say with 95% confidence that the true value lies within this region. The more points that you have in a calibration curve, the narrower the range that your “true value” will likely occur, so you’re getting a more accurate quantitation for your unknown. As less points are used in the calibration curve the larger the range in which the “true value” could lie and the greater error you can expect when calculating concentration of an unknown.

Now that we understand the effect the number of points has on quantitation, the question next comes up, “how often do I need to run a calibration curve?” The best place to look to answer this question is to your laboratory’s guidelines or SOPs. If your guidelines do not require daily runs of calibrations you can ensure that the instrument is working properly by running daily quality control (QC) points to verify that calibration is still valid. When performing this test, the QC accuracy values should fall between 95-105% to be considered acceptable.

Plotting the points on a calibration curve should result in a linear response. A trend line can be fit to the data to give an equation of the line and R^{2} value. R^{2 }shows the proportionality of instrument response to quantity being analyzed. In most cases the closer to 1 the R^{2 }value the more linear the line is. There can be instances where you have a value of 0.99 and not have a linear relationship. In these cases lack-of-fit can be more reliable to confirm linear relationship between concentration and instrument response.

The way calibration standards are made can affect linearity. Each standard should be made individually from a concentrated stock solution and not by serial dilution. Serial dilution is when the most concentrated standard is made, and then used to make the next concentration of standard and so on. Serial dilution of standards introduces propagation of error and can adversely affect the linearity of the calibration curve. The concentration of standards should ideally range over 3 orders of magnitude, be within the concentration range of the samples being quantitated, and should fall within the linear dynamic range of the instrument. For instance, if your calibration curve is “flattening out” near the high concentration points then you are reaching the upper limit of your detector and are no longer in the ideal linear range.

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