Error bar

Error bars are used for the graphical representation of numerical data and are used to visualize based on systematic or statistical errors possible deviations of the measured values ​​from the actual value of the considered metric.

Types of error bars

Most error bars are represented by a mean of measured values ​​and it ranges from then. The length of the interval is then.

  • Either is taken for the sample standard deviation of the sample. In this case, the position and the dispersion of the sample is to be visualized. If the data are distributed approximate normal, then about 68 % of the data or approximately 95 % of the data are included in the error bar interval.
  • Or for the standard error of the mean is taken, the results from the sample standard deviation divided by the square root of the sample size. Then, the error bar is a visualization of the estimation interval, the mean values. The goal is to find out where the true mean of the population is and how exactly you can measure it at all. Is then selected, the error bar interval / estimation interval is contained in about 68% of cases and at just 95 % of the cases the true mean of the population.

Error bar chart

The error bar chart on the right shows the mean and the associated estimation interval for the resting heart rate at different exercise (rarely / once every 14 days / week / more than once a week). One can see that the average resting heart rate decreases, the more you operated in sports. Since in this case estimation intervals are shown for the mean and not overlap the error bars for the first and last group, this is a first indication that a test of the null hypothesis of equality of the mean in all groups (ANOVA or non-parametric equivalents) will be rejected.

Arithmetic mean Error analysis
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