Comprehensive Guide to Error in Science Experiments

All science experiments contain error, so it's important to know the types of error and how to calculate it. (Image: NASA/GSFC/Chris Gunn)

All science experiments contain error, so it’s important to know the types of error and how to calculate it. (Image: NASA/GSFC/Chris Gunn)

Science labs usually ask you to compare your results against theoretical or known values. This helps you evaluate your results and compare them against other people’s values. The difference between your results and the expected or theoretical results is called error. 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, you’ll be asked to go over your procedure and identify any mistakes you may have made or places where error might have been introduced. So, you need to know the different types and sources of error and how to calculate them.

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. You could report the error with a sign, so the absolute error in this example could be -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 to be a measure of how accurate your measuring instrument is. If you are using a ruler that reports length to the nearest millimeter, you might say 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 is based on 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%

Sources and Types of Error

Every experimental measurement, no matter how carefully you take it, 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. All of these errors will be 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 Errors

  • 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 may 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, so 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. 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 are due to fluctuations in the experimental or measurement conditions. Usually these errors are small. Taking more data tends to reduce the effect of random errors.
Examples of Random Errors

  • 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 can be a systematic or random error, depending on the circumstances. What incomplete definition means is that it can be hard for two people to define the point at which the measurement is complete. For example, if you’re measuring length with an elastic string, you’ll need to decide with your peers when the string is tight enough without stretching it. During a titration, if you’re looking for a color change, it can be hard to tell when it actually occurs.

Personal Errors

When writing a lab report, you shouldn’t cite “human error” as a source of error. Rather, you should attempt to identify a specific mistake or problem. One common personal error is going into an experiment with a bias about whether a hypothesis will be supported or rejects. Another common personal error is lack of experience with a piece of equipment, where your measurements may become more accurate and reliable after you know what you’re doing. Another type of personal error is a simple mistake, where you might have used an incorrect quantity of a chemical, timed an experiment inconsistently, or skipped a step in a protocol.

Comprehensive Guide to Error in Science Experiments
Last modified: November 3rd, 2016 by Anne Helmenstine

2 thoughts on “Comprehensive Guide to Error in Science Experiments

  1. Max Power

    I haven’t done any chemistry in awhile as most of my work has been in testing electrical circuits, but boy if you could have seen some of my early lab reports tou might find them a tad humorous.

  2. ken osborn

    As the former QA Officer for an environmental laboratory I appreciate this overview of measurement error. The issue of random error and the meaning of an analytical measurement at the low end has been a troublesome one for laboratories, regulatory agencies, environmental community, and industry. The answer to the question ‘what is real’ depends on a theoretical boundary termed the Method Detection Limit (MDL) in the US and Limit of Detection (Ld) everywhere else. Subtle differences in these terms make for interesting discussions that bear remarkable similarity to political debates but with the distinction of the phrase ‘scientifically justifiable’ tossed in at random moments. The final word is still somewhere in the collection of random variations that constitute what shall be reported to the appropriate regulatory agency.

    In the meantime here is what I wrote some years back about random error and the MDL in “Why You Don’t Need Detection Limit Studies.” [NB there appears to be no way to attach a PDF file so I’m leaving the abstract. If there is interest in seeing the full paper, let me know at kozborn@sbcglobal.net and I’ll provide it.]

    Abstract: The determination of analytical detection limits, such as the EPA MDL or the IUPAC Ld, can be a time consuming and resource intensive process. Furthermore, once a detection limit is determined, most laboratories have no mechanism to verify that detection is actually occurring on a day-to-day basis at the established detection value. This paper proposes an alternative that, once the initial determination of detection has been performed, no additional detection limit studies are required. This is accomplished by the inclusion of a quality control check sample for false negatives in the analytical batch. The False Negative Quality Sample (FNQS) is a QC check sample set at a concentration two to three times of the detection limit and is included in each analytical batch, analogous to the method blank to check for false positives. Tracking the performance of the FNQS eliminates the need to re-evaluate the detection limit and provides a measure of method performance in the region of detection.

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