Error bar

A dot on a chart is a claim about a number, and most of the numbers worth charting are estimates: a rate measured from a sample, a forecast, a model output. An error bar is the rest of that claim, drawn as whiskers running out from the mark to the ends of the range the value could plausibly take. It is the only common component whose job is to make a chart say less, and it is the cheapest correction available for the most persistent lie in data display, which is that a mark drawn to the pixel was measured to the pixel.

The bar means nothing until it says what it is. The same whiskers are used for standard deviation, standard error, and a confidence interval at some level, and those are three different lengths on the same data, differing by more than a factor of two. A chart that draws them without a caption saying which one it drew has published an ornament. Put the definition in the caption or the label, always, including the interval level: “bars are 95 per cent confidence intervals” is nine words and it is the difference between a figure and a decoration.

Now the misreading, because almost everyone has it backwards. If two intervals do not overlap at all, the difference is very likely real at roughly that level of confidence. But overlap does not prove the opposite: two 95 per cent intervals can overlap substantially while the difference between the two values is still statistically significant, so “the bars overlap, therefore nothing is happening” is simply not a valid inference. What overlap honestly supports is a weaker and more useful sentence: this chart does not settle it. Reach for that sentence rather than for a verdict, and where the comparison itself is the point, plot the difference and its interval directly instead of asking readers to eyeball two ranges.

Drawing it is mostly restraint. Keep the whisker thinner than the mark and in the mark’s own colour so it reads as part of the same statement, cap the ends or do not, but do it the same way across every panel, and prefer a shaded band to a forest of whiskers when the series is continuous, since fifty capped bars along a line are a picket fence rather than a range. Where the interval is asymmetric, draw it asymmetric. And note the family resemblance to a truncated axis: both terms are about a chart telling the truth about magnitude, one by refusing to exaggerate the differences between marks and the other by refusing to overstate the certainty of any single one. A reference line is the natural companion, since the question an interval usually answers is whether a value has really cleared the target the line marks, and the axis has to be wide enough to hold the whole interval or the bar is clipped into a claim it never made. Claus Wilke’s chapter on visualizing uncertainty is the best short treatment of the alternatives, including the case for showing the distribution itself rather than two numbers standing in for it.