Error in science experiments is the difference between your results and the true, expected, or theoretical results. The amount of error that is acceptable depends on the experiment, but a margin of error of 10% is generally considered acceptable. If there is a large margin of error, go over your procedure and identify any mistakes you made or likely sources of error. So, you need to know the different types and sources of error and how to calculate them.
Key Points: Error in Science Experiments
- The two key types of error in science experiments are systematic error and random error. Sometimes blunders/mistakes are also considered a type of error.
- Systematic error affects all measurements, typically in the same direction. For example, not calibrating a thermometer affects all readings.
- Random error results from uncontrollable fluctuations in the environment or observations. Typically these errors are small and minimized by taking enough data. For example, the density of gravel depends on the sample.
- Absolute error, relative error, and percent error are ways of reporting error.
Sources and Types of Error
Every experimental measurement, no matter how careful you are, contains some amount of uncertainty or error. You are measuring against a standard, using an instrument that can never perfectly duplicate the standard, plus you’re human, so you might introduce errors based on your technique. The three main categories of errors are systematic errors, random errors, and personal errors. Here’s what these types of errors are and common examples.
Systematic Errors
Systematic error affects all the measurements you take. Typically, all of these errors are in the same direction (greater than or less than the true value) and you can’t compensate for them by taking additional data.
Examples of Systematic Error
- If you forget to calibrate a balance or you’re off a bit in the calibration, all mass measurements will be high/low by the same amount. Some instruments require periodic calibration throughout the course of an experiment, so it’s good to make a note in your lab notebook to see whether the calibrations appears to have affected the data.
- Another example is measuring volume by reading a meniscus (parallax). You likely read a meniscus exactly the same way each time, but it’s never perfectly correct. Another person taking the reading may take the same reading, but view the meniscus from a different angle, thus getting a different result. Parallax can occur in other types of optical measurements, such as those taken with a microscope or telescope.
- Instrument drift is a common source of error when using electronic instruments. As the instruments warm up, the measurements change. Other common systematic errors include hysteresis or lag time, either relating to instrument response to a change in conditions or relating to fluctuations in an instrument that hasn’t reached equilibrium. Note some of these systematic errors are progressive, so data becomes better (or worse) over time, so it’s hard to compare data points taken at the beginning of an experiment with those taken at the end. This is why it’s a good idea to record data sequentially. You can spot gradual trends if they occur. This is also why it’s good to take data starting with different specimens each time (if applicable), rather than always following the same sequence.
- Not accounting for a variable that turns out to be important is usually a systematic error, although it could be a random error or a confounding variable. If you find an influencing factor, it’s worth noting in a report and may lead to further experimentation after isolating and controlling this variable.
Random Errors
Random errors results from fluctuations in the experimental or measurement conditions. Usually these errors are small. Taking more data often reduces the effect of random errors.
Examples of Random Error
- If your experiment requires stable conditions, but a large group of people stomp through the room during one data set, random error will be introduced. Drafts, temperature changes, light/dark differences, and electrical or magnetic noise are all examples of environmental factors that can introduce random errors.
- Physical errors may also occur, since a sample is never completely homogeneous. For this reason, it’s best to test using different locations of a sample or take multiple measurements to reduce the amount of error.
- Instrument resolution is also considered a type of random error because the measurement is equally likely higher or lower than the true value. An example of a resolution error is taking volume measurements with a beaker as opposed to a graduated cylinder. The beaker will have a greater amount of error than the cylinder.
- Incomplete definition is either a systematic or random error, depending on the circumstances. What incomplete definition means is that two people define a measurement point differently. For example, if you’re measuring length with an elastic string, you decide when the string is tight enough without stretching it. During a titration, you look for a color change.
Personal Errors (Blunders and Mistakes)
Accidents and mistakes happen!
When writing a lab report, don’t cite “human error” as a source of error. When possible, do identify a specific mistake or problem. One common personal error is going into an experiment with a bias about whether a hypothesis is correct. Another common personal error is lack of experience with a piece of equipment, where your measurements become more accurate and reliable after you know what you’re doing. Another type of personal error is a simple mistake, where use an incorrect quantity of a chemical, time an experiment inconsistently, or skip a step in a protocol.
There are different methods of reporting error: absolute error, relative error, percent error, and percent difference:
How to Calculate Absolute Error
One method of measuring error is by calculating absolute error, which is also called absolute uncertainty. This measure of accuracy is reported using the units of measurement. Absolute error is simply the difference between the measured value and either the true value or the average value of the data.
absolute error = measured value – true value
For example, if you measure gravity to be 9.6 m/s2 and the true value is 9.8 m/s2, then the absolute error of the measurement is 0.2 m/s2. If you report the error with a sign, the absolute error in this example is -0.2 m/s2.
If you measure the length of a sample three times and get 1.1 cm, 1.5 cm, and 1.3 cm, then the absolute error is +/- 0.2 cm or you would say the length of the sample is 1.3 cm (the average) +/- 0.2 cm.
Some people consider absolute error as a measure of how accurate your measuring instrument is. If you are using a ruler that reports length to the nearest millimeter, the absolute error of any measurement taken with that ruler is to the nearest 1 mm or (if you feel confident you can see between one mark and the next) to the nearest 0.5 mm.
How to Calculate Relative Error
Relative error starts with the absolute error value. It compares how large the error is to the magnitude of the measurement. So, an error of 0.1 kg might be insignificant when weighing a person, but pretty terrible when weighing a apple. Relative error is a fraction, decimal value, or percent.
Relative Error = Absolute Error / Total Value
For example, if your speedometer says you are going 55 mph when you’re really going 58 mph, the absolute error is 3 mph / 58 mph or 0.05, which you could multiple by 100% to give 5%. Relative error may be reported with a sign. In this case, the speedometer is off by -5% because the recorded value is lower than the true value.
Because the absolute error definition is ambiguous, most lab reports ask for percent error or percent difference.
How to Calculate Percent Error
The most common error calculation is percent error, which is used when comparing your results against a known, theoretical, or accepted value. As you probably guess from the name, percent error is expressed as a percentage. It is the absolute (no negative sign) difference between your value and the accepted value, divided by the accepted value, multiplied by 100% to give the percent:
% error = [accepted – experimental ] / accepted x 100%
How to Calculate Percent Difference
Another common error calculation is called percent difference. It is used when you are comparing one experimental result to another. In this case, no result is necessarily better than another, so the percent difference is the absolute value (no negative sign) of the difference between the values, divided by the average of the two numbers, multiplied by 100% to give a percentage:
% difference = [experimental value – other value] / average x 100%
References
- land, 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
- Taylor, J. R. (1999). An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. University Science Books. ISBN 0-935702-75-X.