Error bars in experimental biology

Error bars in experimental biology

April 9, 2007 | Geoff Cumming, Fiona Fidler, and David L. Vaux
Error bars are commonly used in experimental biology to show the variability or uncertainty in data. They can represent descriptive statistics like range or standard deviation (SD), or inferential statistics like standard error (SE) or confidence intervals (CIs). It is crucial to clearly state in the figure legend what type of error bars are used, as different types convey different information. The article outlines eight rules for the proper use and interpretation of error bars. Descriptive error bars, such as SD, show how data are spread. SD is calculated using the formula SD = sqrt(Σ(X-M)^2 / (n-1)), where X is each data point, M is the mean, and n is the number of data points. About two-thirds of data points fall within ±1 SD, and 95% within ±2 SD. Larger sample sizes lead to narrower inferential error bars and more precise estimates of true population values. Inferential error bars, such as SE and CIs, are used to estimate the range within which the true population mean (μ) lies. SE is calculated as SD / sqrt(n), while CIs are calculated using a t-value that depends on the sample size. Larger samples result in narrower CIs and more accurate estimates of μ. CIs are generally preferred over SE bars because they provide a more accurate estimate of the true mean regardless of sample size. The article emphasizes the importance of distinguishing between independent experiments and replicates. Error bars and statistics should only be shown for independently repeated experiments, not for replicates. When n is small (e.g., n = 3), error bars may not be reliable, and individual data points should be shown instead. Rules for interpreting error bars include: (1) always describe error bars in the figure legend; (2) n should be stated in the figure legend; (3) error bars and statistics should only be shown for independent experiments; (4) inferential error bars (SE or CI) are usually appropriate for comparing experimental results with controls; (5) 95% CIs capture μ on 95% of occasions, and SE bars can be doubled to approximate 95% CIs when n ≥ 10; (6) when n = 3, double the SE bars touching indicates P ≈ 0.05; (7) with 95% CIs and n = 3, full arm overlap indicates P ≈ 0.05, and half an arm overlap indicates P ≈ 0.01; (8) CIs or SE bars are irrelevant for within-group comparisons when the same group is measured multiple times. The article concludes that error bars can be valuable for understanding results in a journal article, but they must be interpreted correctly. It is important to consider the biological context and not rely solely on statistical measures. The research was supported by the Australian Research Council.Error bars are commonly used in experimental biology to show the variability or uncertainty in data. They can represent descriptive statistics like range or standard deviation (SD), or inferential statistics like standard error (SE) or confidence intervals (CIs). It is crucial to clearly state in the figure legend what type of error bars are used, as different types convey different information. The article outlines eight rules for the proper use and interpretation of error bars. Descriptive error bars, such as SD, show how data are spread. SD is calculated using the formula SD = sqrt(Σ(X-M)^2 / (n-1)), where X is each data point, M is the mean, and n is the number of data points. About two-thirds of data points fall within ±1 SD, and 95% within ±2 SD. Larger sample sizes lead to narrower inferential error bars and more precise estimates of true population values. Inferential error bars, such as SE and CIs, are used to estimate the range within which the true population mean (μ) lies. SE is calculated as SD / sqrt(n), while CIs are calculated using a t-value that depends on the sample size. Larger samples result in narrower CIs and more accurate estimates of μ. CIs are generally preferred over SE bars because they provide a more accurate estimate of the true mean regardless of sample size. The article emphasizes the importance of distinguishing between independent experiments and replicates. Error bars and statistics should only be shown for independently repeated experiments, not for replicates. When n is small (e.g., n = 3), error bars may not be reliable, and individual data points should be shown instead. Rules for interpreting error bars include: (1) always describe error bars in the figure legend; (2) n should be stated in the figure legend; (3) error bars and statistics should only be shown for independent experiments; (4) inferential error bars (SE or CI) are usually appropriate for comparing experimental results with controls; (5) 95% CIs capture μ on 95% of occasions, and SE bars can be doubled to approximate 95% CIs when n ≥ 10; (6) when n = 3, double the SE bars touching indicates P ≈ 0.05; (7) with 95% CIs and n = 3, full arm overlap indicates P ≈ 0.05, and half an arm overlap indicates P ≈ 0.01; (8) CIs or SE bars are irrelevant for within-group comparisons when the same group is measured multiple times. The article concludes that error bars can be valuable for understanding results in a journal article, but they must be interpreted correctly. It is important to consider the biological context and not rely solely on statistical measures. The research was supported by the Australian Research Council.
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[slides and audio] Error bars in experimental biology