Error, Accuracy, and Precision

November 12, 2018
Figure 1
Figure 1: An example of noise in an infrared spectrum, seen as the random wiggles or “fuzz” in the baseline.
Abstract / Synopsis: 

In the science of analytical chemistry, we quantitate things such as weights and concentrations. All of these measurements generate a number, but to truly understand the quality of data we have to know the size of the error in the measurement. Well known measures of data quality include accuracy and precision. Do you know the difference between these two metrics? Do you know how to quantitate them? And how does all of this apply to cannabis analysis? Please read on to find out more.

Any time a quantity is measured, be it your weight on a bathroom scale, the speed of light, or potency of a cannabis bud, there will be error involved in the measurement. Sources of error include environmental changes, power fluctuations, electronics, and good old fashioned human error. Error exists because human beings are not gods and thus cannot control all the variables all the time for any given measurement (1). Two of the most important types of noise are random noise and systematic noise. Let’s discuss random noise first.

Random Noise

Random error is caused by variables we cannot control as mentioned above. The sign of random error is random, that is, it is equally probable to be positive or negative. This is why measurements are often times expressed as X±y, where X represents the value of the measurement and y represents the amount of error in the measurement. Error is sometimes called noise, and the quality of data can be expressed as a signal-to-noise ratio (SNR) defined in equation 1.

SNR = (Signal)/(Noise)               [1]

The SNR concept is perhaps best illustrated using a cell phone call. In this case, the volume of the caller’s voice is the signal and the static in the connection is the noise. If the volume of the caller’s voice is large compared to the static, the connection has a good SNR and you can clearly hear what the other person is saying. Alternatively, if the static in the connection is high, and the caller’s voice can barely be heard above it, the SNR of the call is low and you will have trouble understanding what your caller is saying. Note that a high SNR phone call, or any high SNR data, will carry a lot of information. Whereas a low SNR phone call or low SNR data will carry very little information. This is why SNR is a measure of data quality.

In analytical chemistry error is often seen as “fuzz” in the baseline of chromatographic and spectroscopic measurements. An example of this is seen in Figure 1. (See upper right for Figure 1, click to enlarge. Figure 1: An example of noise in an infrared spectrum, seen as the random wiggles or “fuzz” in the baseline.)

Figure 1 shows noise measured by a Fourier transform-infrared (FT-IR) spectrometer. Since the sign of random noise is random, the baseline fluctuates up and down randomly. The size of these wiggles is a measure of the noise (2). Note in Figure 1 that the size of the noise varies with wavenumber, which is typical of any spectrum measured using light (electromagnetic radiation).

The big peak at 2350 cm-1 in Figure 1 is an artifact, which is a peak or signal in your data that is not from the sample. This peak is from the presence of unwanted atmospheric carbon dioxide inside the instrument. If you see a CO2 peak in an FT-IR spectrum that you measure, it is an artifact.

  1. B.C. Smith, Quantitative Spectroscopy: Theory and Practice, (Elsevier, Boston, Massachusetts, 2002).
  2. B.C. Smith, Fundamentals of Fourier Transform Infrared Spectroscopy, (CRC Press, Boca Raton, Florida, 2011).
  5. M.O. Bonn-Miller, M.J.E. Loflin, B.F. Thomas, J.P. Marcu, T. Hyke, and R. Vandrey, JAMA, J. Am. Med. Assoc. 318, 1708 (2017).
  6. B. Smith, P. Lessard, and R. Pearson, manuscript in preparation.

Brian C. Smith, PhD, is Founder, CEO, and Chief Technical Officer of Big Sur Scientific in Capitola, California. Dr. Smith has more than 40 years of experience as an industrial analytical chemist having worked for such companies as Xerox, IBM, Waters Associates, and Princeton Instruments. For 20 years he ran Spectros Associates, an analytical chemistry training and consulting firm where he taught thousands of people around the world how to improve their chemical analyses. Dr. Smith has written three books on infrared spectroscopy, and earned his PhD in physical chemistry from Dartmouth College.

How to Cite This Article

B.C. Smith, Cannabis Science and Technology 1(4), 12-16 (2018).