A Simple Confidence Interval for the Median

Large sample confidence intervals often have the form Dn ± z1−α/2 SE(Dn) whereDn is an estimator of the parameter and P (Z ≤ zα) = α when Z has a normal N(0,1) distribution. Replacing z1−α/2 by tp,1−α/2 can be viewed as multiplying z1−α/2 SE(Dn) by a finite sample correction factor tp,1−α/2/z1−α/2 in order to improve the performance of the interval for small sample sizes. This technique is used to modify a large sample confidence interval for the population median. This interval is compared to the intervals based on the sample mean and 25% trimmed mean.