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The error bars in the figures and tables of most papers may often be symmetrical and of the same length, either vertically or horizontally, with the representative value at the center. However, there are figures in which the error bars are not necessarily symmetrical up and down (left and right) or asymmetrical, that is, they are not the same in length as the representative value at the center.
In this article, we explain cases in which the error bars are vertically asymmetrical (left to right).
When showing averages, error bars also show indicators of variation
The results of a given test do not always yield the same results. Therefore, when graphing data, error bars should be displayed as indicators of variability. Error bars indicate the degree of error (error) in the data and are divided into ± standard deviation (SD), ± standard error (SE), percentile, and 95% confidence interval (CI).
In this study, we used the standard deviation(SD), which is used purely to show the variation in data or to compare them.
Normal and non-normal distribution cases
Some clinical trial data does not follow a standard normal distribution. The distribution of income amounts for each household in Japan is not a standard normal distribution, but a one-log normal distribution, as shown in Figure 1.
If the results of a clinical trial follow a one-log normal distribution, as shown in Figure 2, rather than a standard normal distribution, the error bars will be asymmetric rather than symmetric (left and right). In other words, their length may differ.
As a concrete example, let us consider the asymmetric error bars in fictitious data for training. Figure 3 shows the data representing the drug pharmacokinetics. The blood concentration of the drug was examined after administration.
The length (interval width) of the error bars, calculated using the mean value ± standard deviation, was asymmetric on a semi logarithmic axis. In addition, the 24-hour value in this graph may not display a lower error bar because the mean value – standard deviation is a negative value. Therefore, only the upper error bar is displayed often, as in the mean + standard deviation; however, the lengths (interval widths) of the upper and lower error bars may be different when viewing the charts in papers.
If a standard normal distribution can be estimated from the obtained data, when plotting a graph of symmetrical length (interval width), only the upper or lower error bars may be displayed to prevent the graph from becoming difficult to read because of overlapping graphs.
In all cases, when an error bar is seen in the figures, it is important to read the description carefully to determine the definition of the error bar.
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