error bar

An error bar is a type of indicator on a graph showing a degree of uncertainty regarding the graphed amount. The error bar consists of a line segment crossing a plotted point, or crossing through the top of a bar graph's bar, the line segment's length indicating a range of values around the graphed value. Plots of points can have one or a pair of error bars, in the latter case, each parallel to one of the graph's axes. The error bar indicates the plotted value is only the mean or the most probable value, and the error bar's length indicates some statistic regarding distribution of the measured values, or the sample size, or sources of error. Various statistics are commonly indicated by such error bars:

• standard deviation - to indicate distribution of observed data, basically showing where 2/3 of the data lies.
• confidence interval (often 95% percent confidence interval but other percentages may be specified) - shows a range encompassing this percentage chance of including the mean.
• standard error of the mean - indicates how well the sample represents an entire population.

A fourth usage of error bars, probably best not described as "error bars", simply indicates the full range of data, i.e., marking the highest and lowest value.

As a general rule, the shorter the error bar, the "better" or "more significant", but each of the three types has its own formula and shows as a different length based on the same data, suggesting an indication of the type of error bar helps the viewer. The appropriate choice of type/calculation depends upon the nature of the data and what is being demonstrated.

For a written number, any of these same concepts may be indicated by the symbol ±, e.g., 81.24±.03, with the implication that the interval covers the same span both above and below the number. (As above, it can help to indicate which of the possible statistical meanings.) Another notation common in science, but with the potential to confuse, is to use parenthesis instead of ±. In this case, the parenthesized value has an implied decimal point: to interpret it, assume a decimal point in the parenthesized number as many places from the right as within the unparenthesized number, so 23.45(7) means 23.45±.07, ".45" showing where the decimal point is assumed. Examples of equivalent specifications: