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Assume a survey plot that shows a histogram of percentages of respondent's answers, like the following which shows "Percentages of respondents' answers for five tornado warning behaviors across six lead time and daylight scenarios":

enter image description here

Do error bars make any sense for a plot like that? As far as I know, error bars are useful only when showing averages or median values.

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  • $\begingroup$ How can I add CIs to stacked bar charts? Please help $\endgroup$
    – Atsu Seake-Kwawu
    Jul 27, 2018 at 7:55

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This is not a histogram, but a barchart meant for visualising absolute and relative frequencies between different groups and subgroups. A histogram is a visualisation of a univariate numeric variable which is created by splitting the variable's range into intervals and plotting the absolute or relative frequencies in the style of a barchart. It is meant to approximate the density function. It makes absolute sense to add error bars to a barchart, such as your graph. However, adding error bars to a histogram is unreasonable, as these 'pointwise' error bars do not improve the 'overall' density approximation which the histogram should illustrate.

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  • $\begingroup$ Thanks I edited the title. I understand the error bar when it indicates deviation from the average. But what do error bars indicate when plotting absolute frequencies? $\endgroup$
    – Vasilis
    Jun 2, 2018 at 16:52
  • $\begingroup$ Error bars are derived for the estimation of the (binomial) sample proportion, which correspond to the relative frequencies. Multiplying them with the number of obersvations rescales them to absolute frequencies. $\endgroup$
    – Alex2006
    Jun 2, 2018 at 18:43
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    $\begingroup$ Think of error bars as confidence intervals. If you have obtained data on a random sample of the population of interest, then error bars will show results that would likely occur if you sampled again, many times. $\endgroup$
    – rolando2
    Jul 27, 2018 at 14:55
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Error bars make sense on values that go into a bar chart, but despite how common they are, there’s a fair literature on why they should not be there. In essence, people make visual judgements based on the highest point (the top of the upper error bar) instead of the bar itself. If error bars are large and different, that leads to a very confusing plot. Conversely, if the error bars are small and similar, you probably don’t need them at all.

To complicate matters, different charts will use error bars for different things (+- 1 standard error; +-2; 90% conidence; 95% confidence)so there is no safe intuition about their meaning. And there is no simple interpretation of error bar overlap; overlap does not mean lack of difference (although lack of overlap of 95% intervals does).

Further, in a barplot with error information, readers show ‘containment bias’; they tend to respond as if values inside the bar are more likely than values outside (above) it.

So yes; error bars ‘make sense’ in a bar plot in the sense that they encode meaningful information. But in a big-picture sense, a barplot with error bars is not the ideal way of displaying information combined with confidence limits.

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