This document discusses error bars, which show the variability or confidence intervals of experimental data. It provides 8 rules for the effective use and interpretation of error bars. The rules state that figure legends should always describe the type of error bars shown. The sample size (n) must also be stated. Error bars and statistics should only be used for independent experiments, not replicates. Inferential error bars like standard error or confidence intervals are generally most appropriate for comparing experimental results to controls.

1. Error bars in experimental
biology
Presented by,
Sahana V
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Authors: Geoff Cumming, Fiona Fidler, and David L. Vaux -- Journal : The Journal of Cell Biology -- Impact Factor: 9.786

2. Background
• Error bars- common in publications
• Experimental biologists - unsure
• To use
• To interpret
• Error bars – shows confidence intervals, standard errors, standard deviations,
or other quantities.
• Different types of error bars - different information
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3. Overall Objective
• To illustrate some basic features of error bars and explain how they can help
communicate data and assist correct interpretation.
• Eight simple rules to assist with effective use and interpretation of error
bars.
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4. What are error bars for?
• Journals that publish science—knowledge gained through repeated
observation or experiment—evidences to verify that the authors’ reasoning
• Error bars can, if used properly (1–6):
• Descriptive statistics
• Inferential statistics
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depicted in exactly the same way - fundamentally different

5. What do error bars tell you?
Descriptive Error Bars
• To show how the data are spread
• Increase the size of your sample
• Range and standard deviation
(SD)
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6. What do error bars tell you?
Inferential Error Bars
• Comparing samples from two
groups
• To make a judgment
• Standard error (SE) bars and
confidence intervals (CIs).
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7. 3/11/2015 7

8. RULE-1
• When showing error bars, always describe in the figure legends what they are.
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9. Statistical significance tests
• Statistical significance test  P value
• P < 0.05 - statistically significant
• P < 0.01 - Highly significant - More
confident
• It may fail- inferential bars hence
used.
• Wide- Large error
• Short- High precision
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10. What is n?
• Wide variation that occurs in nature by measuring
• a number (n) of independently sampled individuals,
• independently conducted experiments
• independent observations
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11. RULE-2
• The value of n (i.e., the sample size, or the number of independently
performed experiments) must be stated in the figure legend
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12. Replicates or Independent samples
• n (the number of independent results) - multiple measurements of the same
or identical samples.
• The number of replicates- repetition of measurement on one individual in a
single condition.
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13. RULE-3
• Error bars and statistics should only be
shown for independently repeated
experiments, and never for replicates.
• If a “representative” experiment is shown,
it should not have error bars or P values,
because in such an experiment, n = 1
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14. RULE-4
• Because experimental biologists are usually trying to compare experimental
results with controls, it is usually appropriate to show inferential error
bars, such as SE or CI, rather than SD. However, if n is very small (for
example n = 3), rather than showing error bars and statistics, it is better to
simply plot the individual data points
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15. Inferential Error bars
• SE:
• SD/√n
• More n- Smaller SE - More accurate
• CI:
• M ± 2xSE  95% CI
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16. RULE-5
• 95% CIs capture μ on 95% of occasions, so you can be 95% confIdent your
interval includes μ.
• SE bars can be doubled in width to get the approximate 95% CI, provided n
is 10 or more.
• If n = 3, SE bars must be multiplied by 4 to get the approximate 95% CI
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17. RULE-6
• When n = 3, and double the SE
bars don’t overlap, P < 0.05, and if
double the SE bars just touch, P is
close to 0.05.
• If n is 10 or more, a gap of SE
indicates P ≈ 0.05 and a gap of 2
SE indicates P ≈ 0.01
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18. RULE-7
• With 95% CIs and n = 3,
• Overlap of one full arm indicates
P ≈ 0.05
• Overlap of half an arm indicates P
≈ 0.01
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19. RULE-8
• In the case of repeated measurements on
the same group (e.g., of animals,
individuals, cultures, or reactions), CIs or
SE bars are irrelevant to comparisons
within the same group.
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20. Thank you!
1. Belia, et al. 2005. Psychol. Methods. 10:389–396.
2. Cumming et al. 2004. Understanding Statistics. 3:299–311.
3. Vaux, D.L. 2004. Error message. Nature. 428:799.
4. Cumming et al. 2007Psychol. Sci. In press.
5. Schenker, N., and J.F. Gentleman. 2001.Am. Stat. 55:182–
186.
6. Cumming, G., and S. Finch. 2005. Am. Psychol. 60:170–180.
7. International Committee of Medical Journal Editors. 1997.
Ann. Intern. Med. 126:36–47.
8. Carroll, L. 1876. Macmillan, London. 83 pp
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