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If I create a barplot using Seaborn and specify the geometric mean or the median as the estimator, does Seaborn know to use the appropriate standard error formula to create error bars?

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This information is in the documentation of Seaborn.

They show a bootstrap confidence interval, computed by resampling units (rows in the 2d array input form). By default, in seaborn version 0.8.1 it uses 95% of confidence interval, which is equivalent to a standard error. This value is a parameter that can be changed.

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