Error bars
Error bars are used in the graphic representation of numerical data and serve to visualize the possible deviations of the measured values from the actual value of the measured variable under consideration, based on systematic or statistical errors .
Types of error bars
Usually error bars are shown around an average of measured values and then it is enough . The length of the interval is then .
![{\ displaystyle [{\ bar {x}} - c \ cdot s; {\ bar {x}} + c \ cdot s]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/163340973416000003b574b251be8031fb58e8eb)
- Either the sample standard deviation of the sample is taken. In this case, the location and the spread of the sample should be visualized. If the data are approximately normally distributed, then approx. 68% of the data or approx. 95% of the data are contained in the error bar interval.
- Or the standard error of the mean is taken for, which 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 of the mean values. The aim here is to find out where the true mean of the population lies or how precisely it can be measured at all. If you then choose, the error bar interval / estimation interval will contain the true mean of the population in approx. 68% of the cases or in approx. 95% of the cases.
Error bar graph
The error bar diagram on the right shows the mean value and the associated estimation interval for the resting heart rate for various types of exercise (rarely / once every 14 days / weekly / more than once a week). You can see that the average resting heart rate decreases the more you exercise. Since estimation intervals for the mean value are shown here and the error bars for the first and last group do not overlap, this is a first indication that the null hypothesis that the mean values are equal in all groups ( analysis of variance or nonparametric equivalents) is rejected in a test .