I was interested in finding the theory behind the formula used to calculate where notches are to be placed in a boxplot to signify 95% confidence interval, which is median +/- 1.57*IQR/sqrt(n). An earlier answer related to the '1.57' multiplier goes into explaining that 1.57 was chosen empirically. I have also read elsewhere that this is valid only for normally-distributed data. So I was wondering how might the formula change if I have sets of non-parametric data? Thanks!
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