Graph "Error Bars"

What is an Error Bar?

Error bars are graphical representations of the variability of a data set. In other words, they represent an impression of our confidence in any central tendency values. Range bars simply show the maximum and minimum values of a data set. Error bars commonly represent ± 1SD or ± 2SDs from the mean, though they can also be used to show other measures of confidence such as the standard error of
the mean (SEM) or 95% confidence interval (95% CI). In all circumstances, clear labelling is important with respect to identifying the type of bars used, and the reasons for this choice should be made clear as appropriate. Error and range bars are best displayed using vertical bars extended above and below a data point plotted on a graph. 

Example graphs with error bars:

Why Include Error Bars on a Graph?

Error bars can communicate the following information about your data:

• How spread the data are around the mean value (small SD bar = low spread, data are clumped around the mean; larger SD bar = larger spread, data are more variable from the mean).

• The reliability of the mean value as a representative number for the data set.  In other words, how accurately the mean value represents the data (small SD bar = more reliable, larger SD bar = less reliable).  It's important to note that just because you have a larger SD, it does not indicate your data is not valid.  Biological measurements are notoriously variable.

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• The likelihood of there being a significant difference between between data sets.  More on this below...

Types of Error Bars:
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• Ranges (Min/Max): the error bar represents the full range of data points from the minimum to the maximum. This type of error bar is useful for showing the total spread of a dataset, but it can be highly sensitive to outliers, which might give a misleading impression of the data's central tendency.  Typically only used if the sample size is less than three trials.

 

• Standard Deviation (σ): A standard deviation error bar shows how much data points in a data set deviate from the mean. A small standard deviation indicates that the data points are clustered closely around the mean, suggesting low variability. A large standard deviation indicates that the data points are spread out over a wider range, suggesting high variability. This type of error bar is best used when your goal is to describe the distribution of the data within a sample of at least five trials.

 

• ​Standard Error (SE): The standard error of the mean indicates how well the sample mean represents the true population mean. As the sample size increases, the standard error decreases, reflecting a more precise estimate of the population mean. Standard error error bars are often used when the goal is to make inferences about a population based on a larger sample.

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• When creating graphs with error bars, it's crucial to state clearly in the figure legend which measure of uncertainty is being used. ​

What do Error Bars Indicate about Statistical Significance?

A "significant result" means that the results that are seen are most likely not due to chance.  In any experiment or observation that involves sampling from a population, there is always the possibility that an observed effect would have occurred due to chance alone.  But if result is "significant,"  then the investigator may conclude that the observed effect actually reflects the characteristics of the population rather than just sampling error or chance.  

As arithmetic range and standard deviation quantify variability but do not account for sample size, they should not be used to assess statistical significance with regard to the overlap of error bars. 

When standard deviation error bars do not overlap, it's a clue that the difference may be significant, but you cannot be sure.  You must actually perform a statistical test to draw a conclusion.

When standard deviation errors bars overlap quite a bit, it's a clue that the difference is not statistically significant.  You must actually perform a statistical test to draw a conclusion. 

When standard deviation errors bars overlap even less, it's a clue that the difference is probably not statistically significant.  ​You must actually perform a statistical test to draw a conclusion.

Analyzing error bars is NOT an inferential statistical test.  To assess statistical significance, the sample size must also be taken into account. Therefore, while error bars can give you a clue about statistical significance, you must actually perform a statistical test to draw a valid conclusion. 

For more, you can read the article "Error bars in experimental biology."