Label What Error Bars Actually Represent

Name the quantity before drawing the bar

Error bars can represent SDs, standard errors, confidence intervals, prediction intervals or another range. These quantities answer different questions. A figure that says mean with error bars leaves readers unable to determine whether the bars describe individual observations or uncertainty about the mean.

The Matplotlib errorbar reference accepts symmetric or asymmetric error sizes. The plotting function does not know the inferential meaning of those values; the analyst must supply correct lengths and an explicit caption.

Connect the bar to its denominator

Record the number of independent units supporting each estimate. Repeated measurements should not automatically be counted as independent participants when calculating a standard error. If group sizes differ, uncertainty bars can differ even when observed variability is similar.

For asymmetric intervals, convert endpoints to distances from the estimate if the software expects distances. Passing the raw lower and upper endpoints as error lengths can draw the wrong interval without raising an obvious error.

Compare a hypothetical mean

Suppose a sample has mean 10, sample SD 4 and 16 independent observations. The standard error of the mean is 4/√16 = 1. An SD bar extends from 6 to 14, while a one-standard-error bar extends from 9 to 11. A confidence interval requires an appropriate critical value and assumptions; it is not automatically either of those bars.

For an estimate of 2 with interval [1.2, 3.5], the lower and upper error distances are 0.8 and 1.5. Check that the rendered endpoints are 1.2 and 3.5 rather than 0.8 and 5.5 after an accidental endpoint-as-length substitution.

Avoid visual hypothesis tests by eye

Overlap or non-overlap of separate group intervals is not a universal test of the group contrast. Dependence and the chosen interval type matter. If the scientific question concerns a difference, report that contrast and its uncertainty directly rather than asking readers to infer it from two bars.

State the estimate, bar type, interval level, sample size and relevant dependence handling in the caption or adjoining text. Where raw observations are useful and safe to display, show their distribution separately. The final figure should make variation and estimation uncertainty visible without encouraging readers to confuse one with the other.

Source verification: 6 November 2026. Examples are hypothetical.