Graphical representations of the variability of data
Error bars are graphical representations of the variability of data and used on graphs to indicate the error or uncertainty in a reported measurement. They give a general idea of how precise a measurement is, or conversely, how far from the reported value the true (error free) value might be. Error bars often represent one standard deviation of uncertainty, one standard error, or a particular confidence interval (e.g., a 95% interval). These quantities are not the same and so the measure selected should be stated explicitly in the graph or supporting text.
Error bars can be used to compare visually two quantities if various other conditions hold. This can determine whether differences are statistically significant. Error bars can also suggest goodness of fit of a given function, i.e., how well the function describes the data. Scientific papers in the experimental sciences are expected to include error bars on all graphs, though the practice differs somewhat between sciences, and each journal will have its own house style. It has also been shown that error bars can be used as a direct manipulation interface for controlling probabilistic algorithms for approximate computation.[1] Error bars can also be expressed in a plus–minus sign (±), plus the upper limit of the error and minus the lower limit of the error.[2]
A notorious misconception in elementary statistics is that error bars show whether a statistically significant difference exists, by checking simply for whether the error bars overlap; this is not the case.[3][4][5][6]
^Sarkar, Advait; Blackwell, Alan F.; Jamnik, Mateja; Spott, Martin (2015). "Interaction with Uncertainty in Visualisations" (PDF). Eurographics Conference on Visualization (Eurovis) - Short Papers. doi:10.2312/eurovisshort.20151138.
^Brown, George W. (1982). "Standard Deviation, Standard Error: Which 'Standard' Should We Use?". American Journal of Diseases of Children. 136 (10): 937–941. doi:10.1001/archpedi.1982.03970460067015. PMID 7124681..
^Cumming, Geoff; Fidler, Fiona; Vaux, David L. (9 April 2007). "Error bars in experimental biology". The Journal of Cell Biology. 177 (1): 7–11. doi:10.1083/jcb.200611141. PMC 2064100. PMID 17420288.
^Knol, Mirjam J.; Pestman, Wiebe R.; Grobbee, Diederick E. (19 March 2011). "The (mis)use of overlap of confidence intervals to assess effect modification". European Journal of Epidemiology. 26 (4): 253–254. doi:10.1007/s10654-011-9563-8. PMC 3088813. PMID 21424218.
^Munger, Dave. "Most researchers don't understand error bars". Cognitive Daily. Archived from the original on 2018-11-01. Retrieved 17 March 2018.
Errorbars are graphical representations of the variability of data and used on graphs to indicate the error or uncertainty in a reported measurement....
sample, x ¯ {\displaystyle {\bar {x}}} , will have an associated standard error on the mean, σ x ¯ {\displaystyle {\sigma }_{\bar {x}}} , given by: σ x ¯ =...
In statistical hypothesis testing, a type I error, or a false positive, is the rejection of the null hypothesis when it is actually true. For example...
communications, the HTTP 404, 404 not found, 404, 404 error, page not found, or file not found error message is a hypertext transfer protocol (HTTP) standard...
Cumulative distribution function-based nonparametric confidence interval Errorbar – Graphical representations of the variability of data Estimation statistics –...
={\frac {\mathrm {RMSD} }{\bar {y}}}} . This value is commonly referred to as the normalized root mean square deviation or error (NRMSD or NRMSE), and often...
An error message is the information displayed when an unforeseen problem occurs, usually on a computer or other device. Modern operating systems with...
processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure...
In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a function defined as: erf z = 2 π ∫ 0 z e − t 2...
deviation Errorbar Geometric standard deviation Mahalanobis distance generalizing number of standard deviations to the mean Mean absolute error Pooled variance...
appropriate. Bar charts of continuous data with errorbars are sometimes referred to as dynamite plots. Limited use for small sample sizes: Bar charts may...
approximates v with absolute error ε>0 if | v − v approx | ≤ ε {\displaystyle |v-v_{\text{approx}}|\leq \varepsilon } where the vertical bars denote the absolute...
after "The Runaway" but actually broadcast before, creating a continuity error), bar a couple of stock footage shots of the Jeep parked outside of the Duke...
of the correct value with respective errorbars, and the correct value is likely to be within those errorbars. The problem Monte Carlo integration addresses...
14m40s, with an errorbar of 14s. That is right in the middle of the values measured by the two types of experiments, with an errorbar that is big, and...
A medical error is a preventable adverse effect of care ("iatrogenesis"), whether or not it is evident or harmful to the patient. This might include an...
point cannot be counteracted through the use of Flinders bar, Kelvin's balls, Heeling error magnets and Horizontal magnets, a deviation card, or graph...
In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element...
digits to the ten for error detection and correction. Then they decided to add odd/even parity to the number of units filled with bars in each side. Odd/even...
{\displaystyle \sigma ^{2}} , the standard error of the weighted mean, σ x ¯ {\displaystyle \sigma _{\bar {x}}} , can be shown via uncertainty propagation...
In social psychology, fundamental attribution error, also known as correspondence bias or attribution effect, is a cognitive attribution bias in which...
bar purchased in Germany. The error was traced back to a Mars, Inc. factory in Veghel, The Netherlands. In May 2007, Mars UK announced that Mars bars...