A clear understanding of statistics can help evaluating measurement accuracy. But do you still remember what the proper definition of precision is or how to calculate the coefficient of variation?
To refresh your memory, we present the following article regarding accuracy in relation to cell counting in automated devices.
What parameter are important for accuracy?
To begin, let us look at some definitions that should be used. The ISO definition of accuracy is described as the “closeness of the agreement between the result of a measurement and a true value of the measurand”. Accuracy is the sum of two subcomponents called trueness and precision.
Trueness or bias, is defined as the “closeness of agreement between the expectation of a test result or a measurement result and a true value”. This means that trueness describes the systemic error of quantitative measurements. In figure 1, a representation of trueness is shown. The average value is near the bullseye, but the individual points are not due to lack of precision.
Precision, is defined as the “closeness of agreement between independent test/measurement results obtained under stipulated conditions”. Hence, it is a measure of repeatability and relates to the robustness of a quantitative device. It is depicted as repeating values being close to each other but not near the bullseye, see figure 1. The variance or standard deviation is often used to describe the precision of a device.
Only a device that measures with both high a degree of trueness and a high degree of precision will produce accurate results.
Fig. 1: Various kinds of accuracy presented with increasing trueness and precision.
A. With only high precision, a system will underscore or overscore the actual sample.
B. Only with high trueness and precision a system is accurate.
C. With low trueness and low precision, very low accuracy is achieved.
D. With only high trueness, the average value is correct but many samples are needed.
How to measure the trueness of a cell counter
The trueness of a cell counter is described as, how close the calculated average value of the measurements of the device are to the actual concentration. To determine this, you need to analyze a sample with a known concentration using the device.
You also must be aware that cell counters can perform differently at the extremes of their operating concentration range. Knowing this, a simple test for trueness assessment is performed by diluting a sample with a known concentration several times. This will create a so-called calibration curve. This curve will reveal the trueness of the cell counter within the whole operating range, and not only at one specific concentration.
If you produce such a calibration curve, a cell counter with a high trueness will show two things:
- A linear relationship between measured concentration and theoretical concentration
- An incline close to one
How to measure the precision of a cell counter
Now that you know how to determine the trueness, we will describe the precision of a cell counter. As stated previously, the precision of a cell counter defines how robust the system is. Therefore, if you count the same sample multiple times you should get similar results.
Statistically this is represented by the coefficient of variation (CV value) and can be calculated by using equation 1. With σ being the standard deviation and being the mean of your dataset.
This calculated CV value should always be compared to its theoretical CV value, which can be calculated using equation 2. The theoretical CV value is a reference value for the measured CV value to determine the precision.
The measured CV value should be close to the theoretical value but should not be lower than the theoretical CV value. The measured CV value will be higher because an increased standard deviation due to error caused by the system and the operator on top of theoretical CV value.
We showed that accuracy is made up of two components, trueness and precision. It is shown how these two are related to the performance of a cell counting system. With this information, you can evaluate information provided by manufactures and put a system to the test.
To investigate the trueness of a device, you should perform a calibration curve. A cell counter with a high trueness will show a linear relationship between measured concentrations and the theoretical concentrations.
For precision, you should look for the CV value given by manufacturers of a system and compare it to the theoretical value. The CV value should always be lower than the theoretical value.