Points of Significance: Error bars

Journal name:
Nature Methods
Volume:
10,
Pages:
921–922
Year published:
DOI:
doi:10.1038/nmeth.2659
Published online

The meaning of error bars is often misinterpreted, as is the statistical significance of their overlap.

At a glance

Figures

  1. Error bar width and interpretation of spacing depends on the error bar type.
    Figure 1: Error bar width and interpretation of spacing depends on the error bar type.

    (a,b) Example graphs are based on sample means of 0 and 1 (n = 10). (a) When bars are scaled to the same size and abut, P values span a wide range. When s.e.m. bars touch, P is large (P = 0.17). (b) Bar size and relative position vary greatly at the conventional P value significance cutoff of 0.05, at which bars may overlap or have a gap.

  2. The size and position of confidence intervals depend on the sample.
    Figure 2: The size and position of confidence intervals depend on the sample.

    On average, CI% of intervals are expected to span the mean—about 19 in 20 times for 95% CI. (a) Means and 95% CIs of 20 samples (n = 10) drawn from a normal population with mean m and s.d. σ. By chance, two of the intervals (red) do not capture the mean. (b) Relationship between s.e.m. and 95% CI error bars with increasing n.

  3. Size and position of s.e.m. and 95% CI error bars for common P values.
    Figure 3: Size and position of s.e.m. and 95% CI error bars for common P values.

    Examples are based on sample means of 0 and 1 (n = 10).

References

  1. Belia, S.F., Fidler, F., Williams, J. & Cumming, G. Psychol. Methods 10, 389396 (2005).
  2. Frøkjær-Jensen, C., Davis, M.W., Ailion, M. & Jorgensen, E.M. Nat. Methods 9, 117118 (2012).
  3. Cumming, G., Fidler, F. & Vaux, D.L. J. Cell. Biol. 177, 711 (2007).

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Author information

Affiliations

  1. Martin Krzywinski is a staff scientist at Canada's Michael Smith Genome Sciences Centre.

  2. Naomi Altman is a Professor of Statistics at The Pennsylvania State University.

Competing financial interests

The authors declare no competing financial interests.

Author details

Supplementary information

Other

  1. Supplementary Table 1 (156 KB)

    Examples and sample calculations spreadsheet. Please note that the workbook requires that macros be enabled.

Additional data