Types of Measurement Error

We always want to avoid error, but it is a fact of life. At the foundation of analysis and modelling, we rely on measurements. Because errors in measurements are inescapable, the important question is how much does the error affect the result? I start the conversation by explaining what measurement error is, including its component parts, and what we can do to minimize its effect.

It is practically impossible to consistently measure anything with perfect accuracy. There are always factors complicating the measurement, clouding the actual value. Similarly, because of those complicating factors, it is difficult to measure anything exactly the same every time (repeatability; see post contrasting accuracy and precision). The conditions of these complicating factors change, resulting in different answers, even when we think we are using the same method to measure the same thing. This is why statistics considers the ‘true’ value to be unobservable. However, statistics embraces this inherent variability and uses our knowledge of it to better interpret observations.

The description of ‘complicating factors’ in the previous paragraph sounds vague, but that is the point. If we fully understood them, we could account for them and reduce the measurement error. So in this sense, measurement errors are the differences produced by any of the things that make it impossible to directly observe the true value of what we want to measure. However, we can minimize this error to the point that it doesn’t have a consequence on what we want to know. For example, if I want to know what city I am in, reducing the measurement error of my location to within a few centimeters will almost always be sufficient to correctly answer the question.

I should also mention that the error being described here may not be noticeable if the measuring instrument is not sufficiently sensitive. In other words, this measurement error always exists, but the differences can be smaller than the device can detect. In which case, the sensitivity of the measuring instrument becomes the dominant factor in deciding if the quality of the measurement is sufficient.

An illustration of using the observed systematic error to make a correction to all of the observed values. The two outside points dominate the estimation of the systematic error. For the middle point, making a correction for the observed systematic error appears to move the value too far. The difference is the error we cannot account for and we assume the remaining error is random. For the observed values without a corresponding “known” value, we can only make the assumption that applying the systematic correction will improve accuracy (this is usually the case).

Because measurement error can have predictable and not so predictable components, we like to divide measurement error into systematic and random error. Systematic error (sometimes called bias) is a measurement error with an observed pattern. Of course, observing a pattern in the error requires some kind of knowledge about what the true value should be for comparison. Random error is essentially the part of the error that we cannot explain, which often means we must rely on statistical assumptions to interpret how this remaining component might affect our results. You may have noticed that the boundaries for these categories of error are largely dependent on what we know. With advancements in technology, we are regularly decreasing measurement error and detecting patterns that help minimize random error, even if we don’t fully understand the processes behind the systematic error.

To decrease the proportion of measurement error relegated to random error, we need some basis of comparison for identifying the systematic error. If we have a way to compare our measurement of something with its measurement by a more reliable source, we could look for a pattern in those differences and adjust the rest of our measurements accordingly. For example, a network of reference stations exists for recording measurement errors in the global positioning system (GPS). These stations have had their locations determined by very accurate methods. At these stations, the difference between the location measured instantaneously by GPS and the established location are recorded. These differences can then be used to improve the accuracy of GPS measurements taken elsewhere by shifting the measurements by the error observed for the same time at the nearest reference station. GPS devices with DGPS capability can now make these differential corrections in real-time by receiving a radio signal from such reference stations.

Although measurement error is inevitable, there are some things we can do to prevent it from being an obstacle for what we want to know. We can use measurement instruments that are sensitive enough to detect the level of detail we need. However, there are sometimes measurement errors that our available technology cannot directly overcome. In those cases, we can sometimes further reduce the measurement error if we have some reference points that we can use to at least detect patterns in the error. That little bit of knowledge can improve the accuracy of measurements, even if the reasons behind that systematic error are not well understood. For what is left, we have to call random error.

For more, see:
Measurement Error (Research Methods Knowledge Base)

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