Physics Practical Skills Part 3: Systematic VS Random Errors (2024)

Introduction to Systematic vs Random Errors

In Part 2 of the Physics Practical Skills Guide, we looked at reliability, accuracy and validity and how they are affected by different types of errors.In this part of the Physics Practical Skills Guide, we look at experimental errors (systematic and random errors) in more detail.

In this article we discuss:

Experimental errors
Systematic vs random errors
How to reduce systematic errors
How to reduce randomerrors

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Experimental errors

What are experimental errors?

There are two types of experimental error:

Random error
Systematic error

Systematic errors affect accuracy whereas random errors affect the reliability of experimental results.

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Systematic vs Random errors

What are systematic errors?

Systematic errors will shift measurements from their true value by the same amount or fraction and in the same direction all the time. These do not affect the reliability (since they’re always the same) but affect accuracy. These usually arise from problematic or incorrectly used equipment, e.g. poor calibration.

What are random errors?

Random errors will shift each measurement from its true value by a random amount and in a random direction. These will affect reliability (since they’re random) but may not affect the overall accuracy of a result.

What are the sources of systematic or random errors?

Different types of errors and their origin are listed below. Each one can be described as a random or a systematic error.

Error	Description	Systematic or Random error
Scale error	If a piece of equipment is not calibrated correctly (e.g. a wooden ruler has shrunk), all measurements will be offset by the same fraction.	Systematic error
Zero error	If a piece of equipment has an offset (e.g. a mass balance shows a reading that is not zero when there is nothing on it), all measurements will be offset by the same amount.	Systematic error
Parallax error	If you make a measurement by comparing an indicator against a scale (e.g. reading a dial on a voltmeter, or using a mercury thermometer), the angle at which you view it will affect the reading.	Systematic error if you always view the dial from the same angle. Random error if you view the dial from a random angle each time.
Errors arising from the environment	Ideally, the control variables are kept constant, but some may be beyond your control, e.g. air pressure, temperature, humidity, vibrations.	Changes to the control variablescan result in both systematic and random errors. One consistent change will give a systematic error. Random changes will give random errors.
Reaction time	If a measurement relies on your reaction time, then you may react too early or too late by different amounts of time.	Random error.
Measurement errors from insufficient precision	If you’re measuring something that falls between two markings on a scale (e.g. you’re using a ruler to measure something that’s 10.25 mm long), you cannot measure its precise value and will need to round it up or down (does it look like 10 mm or 10.5 mm?).	Random error.

What about “human error”?

“Human error” is not a source of experimental error. You must classify specific errors as random or systematic and identify the source of the error.

Human error cannot be stated as experimental error.

Percentage errors

Percentage errors express an uncertainty or discrepancy in a value as a percentage of the value.

An uncertainty describes the range of values a result or measurement can take, and is related to reliability or precision. If a value is given as x ± 5%, then the value may be larger or smaller by 5%.

A discrepancy is related to the difference between the final result of the experiment and the accepted value, and hence is related to accuracy.

How to reduce systematic errors

Systematic error arises from equipment, so the most direct way to eliminate it is to use calibrated equipment, and eliminate any zero or parallax errors.

Even if your measurements are affected, some systematic errors can be eliminated in the data analysis.In the analysis we typically draw a graph that gives a straight line, we draw the line of best fit and measure its gradient. By measuring the gradient we are looking at changes only, not absolute values. Zero errors would result in shifting the line up and down (i.e. to the y-intercept of the graph) butwill not affect the gradient. Hence, we eliminate zero errors, which increases accuracy.

How to reduce random errors

Since random errors are random and can shift values both higher and lower, they can be eliminated through repetition and averaging. A true random error will average out to zero if enough measurements are taken and averaged (through a line of best fit). This is why repetition of measurements can improve the reliability of the final result of an experiment.

In the analysis, drawing a graph and the line of best fit serves to reduce the random error in the final experimental result. Firstly, outliers can be eliminated. Secondly, the line of best fit is drawn to accommodate as much of the data as possible by cutting in between the set of data points. In this way, the data is averaged, with most weighting given to the most similar values. This reduces the effects of random error and increases reliability.