The Difference Between Systematic & Random Errors

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No matter how careful you are when conducting experiments, there will likely be an experimental error. Whether through the challenges inherent taking the measurements accurately or problems with your equipment, avoiding error altogether is next to impossible. To counteract this issue, scientists do their best to categorize errors and quantify any uncertainty in measurements they make. Finding out the difference between systematic and random errors is a key part of learning to design better experiments and to minimize any errors that do creep through.

TL;DR (Too Long; Didn't Read)

Systematic errors usually result from equipment that isn’t correctly calibrated. Every measurement you take will be wrong by the same amount because there is a problem with your measuring device. Random errors are unavoidable and result from difficulties taking measurements or attempting to measure quantities that vary with time. These errors will fluctuate but generally cluster around the true value.

What Is Random Error?

Random error describes errors that fluctuate due to the unpredictability or uncertainty inherent in your measuring process, or the variation in the quantity you’re trying to measure.

A scientist measuring an insect, for example, would try to position the insect at the zero point of a ruler or measuring stick, and read the value at the other end. The ruler itself will probably only measure down to the nearest millimeter, and reading this with precision can be difficult. You may underestimate the true size of the insect or overestimate it, based on how well you read the scale and your judgment as to where the head of the insect stops. The insect might also move ever so slightly from the zero position without you realizing. Repeating the measurement multiple times yields many different results because of this, but they would likely cluster around the true value.

Similarly, taking measurements of a quantity that changes from moment to moment leads to random error. Wind speed, for example, may pick up and fall off at different points in time. If you take a measurement one minute, it probably won’t be exactly the same a minute later. Again, repeated measurements will lead to results that fluctuate but cluster around the true value.

What Is Systematic Error?

A systematic error is one that results from a persistent issue and leads to a consistent error in your measurements. For example, if your measuring tape has been stretched out, your results will always be lower than the true value. Similarly, if you’re using scales that haven’t been set to zero beforehand, there will be a systematic error resulting from the mistake in the calibration (e.g., if a true weight of 0 reads as 5 grams, 10 grams will read as 15 and 15 grams will read as 20).

Other Differences Between Systematic and Random Errors

The main difference between systematic and random errors is that random errors lead to fluctuations around the true value as a result of difficulty taking measurements, whereas systematic errors lead to predictable and consistent departures from the true value due to problems with the calibration of your equipment. This leads to two extra differences that are worth noting.

Random errors are essentially unavoidable, while systematic errors are not. Scientists can’t take perfect measurements, no matter how skilled they are. If the quantity you’re measuring varies from moment to moment, you can’t make it stop changing while you take the measurement, and no matter how detailed your scale, reading it accurately still poses a challenge. The good news is that repeating your measurement multiple times and taking the average effectively minimizes this issue.

Systematic errors may be difficult to spot. This is because everything you measure will be wrong by the same (or a similar) amount and you may not realize there is an issue at all. However, unlike random errors they can often be avoided altogether. Calibrate your equipment properly prior to using it, and systematic errors will be much less likely.

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