# Systematic vs Random Error – Differences and Examples

Systematic and random error are an inevitable part of measurement. Error is not an accident or mistake. It naturally results from the instruments we use, the way we use them, and factors outside our control. Take a look at what systematic and random error are, get examples, and learn how to minimize their effects on measurements.

• Systematic error has the same value or proportion for every measurement, while random error fluctuates unpredictably.
• Systematic error primarily reduces measurement accuracy, while random error reduces measurement precision.
• It’s possible to reduce systematic error, but random error cannot be eliminated.

### Systematic vs Random Error

Systematic error is consistent, reproducible error that is not determined by chance. Systematic error introduces inaccuracy into measurements, even though they may be precise. Averaging repeated measurements does not reduce systematic error, but calibrating instruments helps. Systematic error always occurs and has the same value when repeating measurements the same way.

As its name suggests, random error is inconsistent error caused by chance differences that occur when taking repeated measurements. Random error reduces measurement precision, but measurements cluster around the true value. Averaging measurements containing only random error gives an accurate, imprecise value. Random errors cannot be controlled and are not the same from one measurement to the next.

### Systematic Error Examples and Causes

Systematic error is consistent or proportional to the measurement, so it primarily affects accuracy. Causes of systematic error include poor instrument calibration, environmental influence, and imperfect measurement technique.

Here are examples of systematic error:

• Reading a meniscus above or below eye level always gives an inaccurate reading. The reading is consistently high or low, depending on the viewing angle.
• A scale gives a mass measurement that is always “off” by a set amount. This is called an offset error. Taring or zeroing a scale counteracts this error.
• Metal rulers consistently give different measurements when they are cold compared to when they are hot due to thermal expansion. Reducing this error means using a ruler at the temperature at which it was calibrated.
• An improperly calibrated thermometer gives accurate readings within a normal temperature range. But, readings become less accurate at higher or lower temperatures.
• An old, stretched cloth measuring tape gives consistent, but different measurements than a new tape. Proportional errors of this type are called scale factor errors.
• Drift occurs when successive measurements become consistently higher or lower as time progresses. Electronic equipment is susceptible to drift. Devices that warm up tend to experience positive drift. In some cases, the solution is to wait until an instrument warms up before using it. In other cases, it’s important to calibrate equipment to account for drift.

### How to Reduce Systematic Error

Once you recognize systematic error, it’s possible to reduce it. This involves calibrating equipment, warming up instruments because taking readings, comparing values against standards, and using experimental controls. You’ll get less systematic error if you have experience with a measuring instrument and know its limitations. Randomizing sampling methods also helps, particularly when drift is a concern.

### Random Error Examples and Causes

Random error causes measurements to cluster around the true value, so it primarily affects precision. Causes of random error include instrument limitations, minor variations in measuring techniques, and environmental factors.

Here are examples of random error:

• Posture changes affect height measurements.
• Reaction speed affects timing measurements.
• Slight variations in viewing angle affect volume measurements.
• Wind velocity and direction measurements naturally vary according to the time at which they are taken. Averaging several measurements gives a more accurate value.
• Readings that fall between the marks on a device must be estimated. To some extent, its possible to minimize this error by choosing an appropriate instrument. For example, volume measurements are more precise using a graduated cylinder instead of a beaker.
• Mass measurements on an analytical balance vary with air currents and tiny mass changes in the sample.
• Weight measurements on a scale vary because it’s impossible to stand on the scale exactly the same way each time. Averaging multiple measurements minimizes the error.

### How to Reduce Random Error

It’s not possible to eliminate random error, but there are ways to minimize its effect. Repeat measurements or increase sample size. Be sure to average data to offset the influence of chance.

### Which Types of Error Is Worse?

Systematic errors are a bigger problem than random errors. This is because random errors affect precision, but it’s possible to average multiple measurements to get an accurate value. In contrast, systematic errors affect precision. Unless the error is recognized, measurements with systematic errors may be far from true values.

### References

• Bland, J. Martin, and Douglas G. Altman (1996). “Statistics Notes: Measurement Error.” BMJ 313.7059: 744.
• Cochran, W. G. (1968). “Errors of Measurement in Statistics”. Technometrics. Taylor & Francis, Ltd. on behalf of American Statistical Association and American Society for Quality. 10: 637–666. doi:10.2307/1267450
• Dodge, Y. (2003). The Oxford Dictionary of Statistical Terms. OUP. ISBN 0-19-920613-9.
• Taylor, J. R. (1999). An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. University Science Books. ISBN 0-935702-75-X.