Using asymptotic results to obtain a confidence interval for the population median

Almost all introductory and intermediate level statistics textbooks include the topic of confidence interval for the population mean. Almost all these texts introduce the median as a robust measure of central tendency. Only a few of these books, however, cover inference on the population median and in particular confidence interval for the median. This may be due to the somewhat complex nature of the problem. This paper attempts to popularize a method that is conceptually and computationally simpler than the currently used methods in textbooks and has the promise of being more accessible to elementary/intermediate level statistics students. The method is conceptually simpler, because its development parallels that of obtaining a confidence interval for the mean and it involves concepts that are well-covered in elementary courses. It is computationally simple, because its major computational component is a smoothing method that is widely available in statistical software. For the latter reason, the proposed method is referred to as the Smoothing method. A simple R program is given that produces confidence intervals using the Smoothing method. Utilization of Minitab, SAS, and SPSS for this purpose is also discussed. A simulation study is performed to compare statistical properties of the proposed method to those of the two currently popular methods of Bootstrap and Binomial. Based on this limited simulation studies, it is observed that the Smoothing method is at least as good as, and in some respects is superior to, the Binomial and Bootstrap methods in samples of size as large or larger than 30.