Barras De Errores En Biologia

JCB: FEATURE

Error bars in experimental biology
Geoff Cumming,1 Fiona Fidler,1 and David L. Vaux2
1

School of Psychological Science and 2Department of Biochemistry, La Trobe University, Melbourne, Victoria, Australia 3086

THE JOURNAL OF CELL BIOLOGY

Error bars commonly appear in figures in publications, but experimental biologists are often unsure how they should be used andinterpreted. 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 eightsimple rules to assist with effective use and interpretation of error bars.
What are error bars for?

error bars encompass the lowest and highest values. SD is calculated by the formula

SD =

∑ ( X − M )2
n −1

where X refers to the individual data points, M is the mean, and Σ (sigma) means add to find the sum, for all the n data points. SD is, roughly, the average or typical differencebetween the data points and their mean, M. About two thirds of the data points will lie within the region of mean ± 1 SD, and 95% of the data points will be within 2 SD of the mean.

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Journals that publish science—knowledge gained through repeated observation or experiment—don’t just present new conclusions, they also present evidence so readers canverify that the authors’ reasoning is correct. Figures with error bars can, if used properly (1–6), give information describing the data (descriptive statistics), or information about what conclusions, or inferences, are justified (inferential statistics). These two basic categories of error bars are depicted in exactly the same way, but are actually fundamentally different. Our aim is to illustratebasic properties of figures with any of the common error bars, as summarized in Table I, and to explain how they should be used.
What do error bars tell you?
Descriptive error bars. Range and standard deviation (SD) are used for descriptive error bars because they show how the data are spread (Fig. 1). Range
David L. Vaux: d.vaux@latrobe.edu.au

It is highly desirable to use larger n, toachieve narrower inferential error bars and more precise estimates of true population values.
Descriptive error bars can also be used to see whether a single result fits within the normal range. For example, if you wished to see if a red blood cell count was normal, you could see whether it was within 2 SD of the mean of the population as a whole. Less than 5% of all red blood cell counts are morethan 2 SD from the mean, so if the count in question is more than 2 SD from the mean, you might consider it to be abnormal. As you increase the size of your sample, or repeat the experiment more times, the mean of your results (M) will tend to get closer and closer to the true mean, or the mean of the whole population, μ. We can use M as our best estimate of the unknown μ. Similarly, as you repeat anexperiment more and more times, the

Figure 1. Descriptive error bars. Means with error bars for three cases: n = 3, n = 10, and n = 30. The small black dots are data points, and the column denotes the data mean M. The bars on the left of each column show range, and the bars on the right show standard deviation (SD). M and SD are the same for every case, but notice how much the range increaseswith n. Note also that although the range error bars encompass all of the experimental results, they do not necessarily cover all the results that could possibly occur. SD error bars include about two thirds of the sample, and 2 x SD error bars would encompass roughly 95% of the sample.

SD of your results will tend to more and more closely approximate the true standard deviation (σ) that you...