Today I would like to focus on the confusing reporting of findings using mean +/- error bars. Error bars are graphical representations that can help convey information about the variability or uncertainty in data. They are used in charts, graphs, or plots to show the range of values within which the true value of a measurement is likely to lie.
“Error bars commonly appear in figures in publications, but experimental biologists are often unsure how they should be used and interpreted. In this article we illustrate some basic features of error bars and explain how they can help communicate data and assist correct interpretation. Error bars may show confidence intervals, standard errors, standard deviations, or other quantities. Different types of error bars give quite different information, and so figure legends must make clear what error bars represent. We suggest eight simple rules to assist with effective use and interpretation of error bars.” Cumming et al.
The Issues
There is a very heterogeneous use of error bars in scientific publications. It can be quite confusing.
Here are some commonly encountered problems:
- Some are unlabeled (yes this occurs quite often unfortunately even in 2025). Articles with incomplete legends represent both the biological and physical sciences, across many different disciplines, and clearly should not be considered isolated examples.
- Some are used in a descriptive manner: range shows the spread of the data, SD quantifies the variability in the data around the mean.
- Some are used for inferential purposes (classic SE, robust SE, CI, etc.)
Quantifying and Depicting Uncertainty
Several measures exist. It’s crucial to understand what they represent and when they should be used.
Descriptive Measures
- Range: Amplitude the data in a distribution – Maximum value – minimum value
- Standard Deviation (SD): Represents how spread out the data is around the mean. This is often used when you want to show the variability of a dataset.
▶️ Such descriptive measures are useful when developing a new method and interest lies in establishing its precision.
Inferential Measures
- Standard Error (SE or SEM): Represents the accuracy of the sample mean estimate. SEM is typically smaller than the SD and is used to indicate how close the sample mean is to the true population mean. This is the reason why SE is reported more often than SD or CI.
- Confidence Interval: Represents a range of values that is likely to contain the true population parameter (e.g., the mean) with a certain level of confidence (e.g., 95%) over repeated sampling.
▶️ Inferential measures are needed when the goal is comparing conditions/treatments/interventions/groups.
4 Basic Rules for Reporting Error Bars
When reporting error bars in studies, several common errors can occur. These errors can mislead readers and obscure the true meaning of the data.
Here are some basic rules to follow:
Rule 1️⃣: When showing error bars, always describe in the figure legends what they are.
Rule 2️⃣: The value of n (i.e., the sample size, or the number of independently performed experiments: true replications) must be stated in the figure legend.
Rule 3️⃣: Error bars and statistics should only be shown for independently repeated experiments (true biological replications), and never for technical replicates.
Rule 4️⃣: Because experimental investigators are usually trying to compare experimental results with controls, it is usually appropriate to show inferential error bars, such as SE or CI, rather than SD. However, if n is very small (for example n = 3), rather than showing error bars and statistics, it is better to simply plot the individual data points.
In general for inferential purposes, it is more appropriate to report CI than SE.
Conclusions
Error bars in scientific journal articles can help understand results and justify conclusions, but there are several pitfalls. Before interpreting data, consider the type of error bars, independent experiments, and the legend. Biological understanding is also crucial for understanding the numbers in the figure.
Accurate and clear reporting of error bars is essential for the proper interpretation of study results. By following best practices and avoiding common errors, researchers can effectively communicate the variability and precision of their data, enhancing the transparency and reliability of their findings.
Reference
Belia, S., F. Fidler, J. Williams, and G. Cumming.2005. Researchers misunderstand confidence intervals and standard error bars. Psychol. Methods. 10:389–396
Cumming, G., J. Williams, and F. Fidler. 2004. Replication, and researchers’ understanding of confidence intervals and standard error bars. Understanding Statistics. 3:299–311.
Cumming G, Fidler F, Vaux DL. Error bars in experimental biology. J Cell Biol. 2007 Apr 9;177(1):7-11. doi: 10.1083/jcb.200611141. PMID: 17420288; PMCID: PMC2064100.
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