A Robust Confidence Interval for Location for Symmetric, Long-Tailed Distributions

A procedure called the wave-interval is presented for obtaining a 95% confidence interval for the center (mean, median) of a symmetric distribution that is not only highly efficient when the data have a Normal distribution but also performs well when some or all of the data come from a long-tailed distribution such as the Cauchy. Use of the wave-interval greatly reduces the risk of asserting much less than one's data will support. The only table required is the usual t-table. The wave-interval procedure is definitely recommended for samples of ten or more, and appears satisfactory for samples of nine or eight.