The Importance of Representative Sampling in Cannabis Analysis

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Developing a precise and accurate analytical method is important, but it is not enough. The
sample itself plays a role in determining the quality of your results. Your sample needs to be stable,
homogeneous, and representative of the batch from which it is taken. We discuss all this in more
detail below and what it means for the quality of the results obtained in cannabis analysis.

The term sample is defi ned as a part of anything presented. . . as evidence of the quality of the whole (1). Samples are something we encounter in our everyday lives. We may nibble on a sample of food presented to us at a grocery store. Your doctor may collect a sample of your blood. Come election
time we are bombarded with opinion polls that talk about something called “sample size” and that pesky “margin of error.” Ideally, all these samples represent a greater whole from which
they are drawn. Hopefully, the product you buy because of a food sample will be as tasty as the nibble that originally enticed you. Your blood sample needs to be representative of your
health or your doctor might make a wrong diagnosis. If a political poll is biased it can be misleading. A sample taken improperly, one that does not represent the quality of the whole, is called an unrepresentative sample.

Unrepresentative sampling leads to what is called sampling error. What’s all this got to do with cannabis analysis? In many other industries we must collect representative samples to perform chemical analyses, the cannabis industry is no different. In fact, in California the cannabis analysis laboratories themselves are tasked with collecting representative samples for compliance .

Imagine the results for the fi ve aliquots using grinding method 2 are as such 16%, 18%, 20%, 22%, and 24%. The  average here is still 20%. Since these two sets of measurements gave the same average, are the grinding methodsof equivalent quality? The answer is no. Since we sampled the same material here, and assuming the potency method was performed the same on all samples, the spread in the two sets of readings can tell us how homogeneous the samples are, which is another way of saying the sampling error. The fi rst method is superior to the second because the tighter spread of readings produced a more homogeneous sample than the second method. How do we go about then quantitating the spread in a set of data, and get a handle on the size of sampling error?

We can quantitate the amount of scatter in a data set, and thus obtain a numerical measure of dataset quality, by calculating its standard deviation, which is calculated as such (15):
σ = (Σ(x – x’)2/n-1)1/2 [2]
where σ is the standard deviation, x is a measured value, x’ is the average of a set of values, and n is the number of observations in the dataset.

To calculate the standard deviation for a set of values calculate the average, subtract each measured value from the average, square each of those differences, add them together, divide by the number of observations averaged minus 1, and then take the square root of that number. The standard deviation comes out in the same units as x. Thus, if x is in units of weight percent (wt.%) THC, so is the standard deviation. Simply put, the standard deviation is the average deviation between a set of individual readings and their average. A dataset with large amounts of scatter will have a larger standard
deviation than a dataset with a smaller amount of scatter.

The dataset from grinding method 1 above has a standard deviation of 1.58 wt.% THC, while the second grinding method dataset has a standard deviation of 3.16 wt.% THC. Even though both datasets have an average of 20 wt.%, the fi rst grinding method is superior to the second because its standard deviation is smaller by a factor of 2.

Simply put, grinding method 1 produces a more homogeneous sample and thus has less sampling error than grinding method 2.

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