The phrase “absolute accuracy” as applied to any measurement might seem to imply that measurements can be taken that are the “real or true value,” unquestioned and indubitable. Unfortunately, there is no such thing as an absolutely accurate measurement even with the finest instruments that man can make. The accuracy of any measurement must always be qualified by a measure of error, either absolute or relative.
To understand why an absolute measurement cannot be obtained, it is helpful to understand the basic math related to accuracy and error.
Environmental Effects on Measurement
Any measurement is subject to error from various causes, not the least of which is the accuracy of both the measuring instrument and the instruments used in its manufacture. There are also environmental factors such as the ambient temperature at the time of measurement.
If a steel tape is hot or freezing cold, it will expand or contract, respectively. The amount of tension applied to the tape affects its accuracy also. In the end, all you can say is that your measured value is such-and-such within some error value. The trick is to reduce the error enough to make it relatively insignificant in the big picture, if possible.
The best water tape manufacturers, such as Heron Instruments, produce water tapes with graduations of 1 mm. Thus, they would specify the tape’s accuracy to be within 1 mm.
Another way to state this is that the error is a maximum of plus or minus a half millimeter, since the error could be in either direction. In other words, the 1 mm of possible error is centered on each mm mark of the tape.
For example, if you used this tape and it showed the level of water in a well to be 10.555 meters below the surface, then the most accurate way to state that is as 10.555 +/- .0005 meters or between 10.5545 and 10.5555 meters high. Absolute error dispenses with the plus or minus to state that the water level is at 10.555 meters with an absolute error of 0.5 mm or 0.0005 meters. That the error can lie in either direction is understood.
While absolute error imparts a discrete value to measurements, relative error provides an intuitive scale to measurements that help compare the accuracy of measurements and measuring instruments. It is derived by dividing the absolute error by the total value of the measurement. Thus, for the previous water level measurement, this would be 0.5 millimeter, or 0.0005 meter, divided by 10.555 meters, which equals 0.00047. Often, relative error is expressed as Percentage Error, which would represent 0.00047 as 0.047 percent accuracy. That sounds pretty accurate, but it is only one measurement.
Why Accuracy and Error Are So Important
Especially since we are precluded by physical laws from obtaining an actual “true” measurement and must instead use a measured value, the error value becomes critical as we compare measurements at subsequent times or by other people. Furthermore, the amount of error multiplies rapidly when combined with the error values of other measurements or instruments.
For instance, if we were computing the area of a body of water, then absolute, relative and percentage error is squared, since the calculations involve two or probably more measurements. The volume of an aquifer involves three dimensions, so the total error is proportionally cubed when calculating this volume.
High Accuracy Goes a Long Way
That is why it certainly pays to rely on durable, rugged measuring instruments from whose error values you can draw confidence that your results most accurately express the monitoring situation you are working on.
Heron Instruments Groundwater Monitoring, Inc. has decades of commitment to providing you with the most accurate and highest quality measuring instruments in their industry. If you have a need for groundwater monitoring instruments, contact us now.