StatisticsInferential Statistics

How to Tell Confidence Intervals from Error Bars—and Interpret Overlap

Learn how to tell confidence intervals from error bars by checking the legend, distinguishing SD and SE, and avoiding false conclusions from overlap.

Question

What you can conclude when two error bars overlap (or don't)?

Answer

You cannot identify a confidence interval from an error bar's appearance alone. Read the figure legend or methods first. Error bars are a graphical device; SD, SE, and confidence intervals are different quantities that can all be drawn that way.

Identify what the bars represent

LabelWhat it describesCommon construction around a sample mean
SDVariation among individual observationsxˉ±s\bar{x}\pm s
SE or SEMEstimated sampling uncertainty of the meanxˉ±s/n\bar{x}\pm s/\sqrt{n} for independent observations
95% CIAn interval from a procedure with 95% long-run coverageOften xˉ±t0.975,n1s/n\bar{x}\pm t_{0.975,n-1}s/\sqrt{n} for a normally modeled mean with unknown variance

A 95% CI is not simply one SE on either side of the mean. For a mean under a large-sample normal approximation, its half-width is about 1.96 SE. Small samples often require a larger t multiplier. Other estimators and interval methods can produce asymmetric intervals.

What does overlap tell you?

  • SD bars: overlap or nonoverlap does not determine the significance of a difference between means.
  • SE bars: do not treat nonoverlap as a universal significance test; the comparison depends on the design and uncertainty of the difference.
  • 95% CI bars: overlapping intervals can still accompany a statistically significant difference. Nonoverlap often indicates evidence of a difference under familiar independent-group settings, but is not a universal decision rule for paired data, unequal-variance settings, or multiple comparisons.

For a defensible comparison, use the confidence interval for the difference or the appropriate hypothesis test, with the actual sampling design. If the legend does not define the bars, the information needed to interpret their overlap is missing.

Evidence boundary

This answers the complete GraphPad FAQ about overlap, with error-bar identification explained before any inference. No particular graph, group means, or sample sizes are supplied. The comparison table describes common mean-based constructions, not every estimator or confidence-interval method.

Sources

These references support the concepts and methods used in the explanation above.

How to Tell Confidence Intervals from Error Bars—and Interpret Overlap | Verla