Error Bars in Experimental Biology

Error bars are a crucial feature of all experimental research. This is because there is always uncertainty associated with any given measurement. Without mentioning the margin of error, a measurement is meaningless. Understanding error bars and their role in the interpretation of research results is also vital for critically evaluating scientific studies.

The accuracy and precision of a measurement can differ greatly depending on many factors. The more fine-grained the ticks on a ruler is, the more accurate it will be able to measure. If a scale produces the same results for repeated measurements of the same thing, the more precise it will be.

There are many different forms of variation. Technical variation is the variation in measurements introduced by imperfections in the measurement equipment and measuring procedure. There is another type of variation called biological variation. This does not depend on the act of measuring but on the variation in the population. For instance, the variation in height among people of the same age is a form of biological variation.

It is important to handle technical variation to ensure that biases and errors are not introduced during the measurement. It is also important to handle biological variation. Otherwise we cannot generalize the research findings from a sample to a population. Different members of the same group are usually not all alike.

One way to measure variation is by using something called error bars. There are many different kinds of errors bars. They tell you slightly different things about the dataset. Error bars should only be used for estimating the biological variation between independent (biological) replicates. Trying to use error bars for technical replicates will only tell you about the consistency of pipetting. It is not information about the differences between treatments.

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Different kinds of error bars

Standard errors are descriptive error. Standard errors and confidence intervals are inferential error bars. The latter allow you, if used correctly, to make claims about the underlying population. However, this requires that the error bars are selected, calculated and understood correctly. If not, this can lead to a number of harmful consequences. This includes mathematical errors and errors in interpretation. These errors can mislead individual scientists and the scientific community as a whole.

Error bars in Experimental Biology is a paper about how to calculate, use and interpret different kinds of error bars for the clear display of experimental data. It was written by Geoff Cumming, Fiona Fidler and David L. Vaux and was published in the Journal of Cell Biology in 2007. If you only have time to read a single paper about error bars, this is it.

Why care about error bars?

So why should we care about error bars? Because it provides much more details than merely relying on p values. It also helps the reader understand the magnitude of the observed effect and the margin of error. In other words, getting an idea of the size of the effect and the biological context.

The paper is part of the initiative called the New Statistics to focus on effect size, precision and what research results mean in the scientific context instead of having a tunnel vision on p values. This paper describes the basic mathematics of different kinds of error parts and lists eight guidelines for using and interpreting error bars.

When error bars are used in a graph, it is crucial to describe what they are. Are they standard error, range, confidence intervals or standard deviation? The figure legend should also state the number of independent replicates. Very small error bars are hardly impressive if the sample size is very low. This is because the experiment has probably not sampled the variation in the population sufficiently. Error bars should only be shown for independent replicates to give an idea of the biological variation.

Technical variation is important. However it is not informative about the biological differences between different groups or treatments. Most experiments in biology attempts to make inferential claims about the differences between groups. In this case it is more appropriate to use standard error or confidence intervals. For small sample sizes, it is more informative to just plot the individual points. The paper also goes into some details about some simple rules for translating between standard error and confidence intervals depending on sample size.

Guidelines for using and interpreting error bars

For repeated measurements of different groups over time, error bars can only be used to compare different groups at the same time, but not the same sample over time. This is because those two measurements are deeply correlated and those error bars do not take that correlation into account. The proper way to do it would be to calculate the difference between the two times for each sample and then graph the mean for those differences. If that 95% confidence interval does not include 0, the difference is statistically significant.

Every time you see a graph with error bars, you should ask yourself four questions. First, how large is the sample size? Second, are they independent replicates? Third, what type of error bars are used? Fourth and finally, what does the observed difference and the error bars mean in the biological context.

The paper is available in full text online and as a PDF file. A cache of the online version can be found here and a cache of the PDF file can be found here.