A simulation study of two-sample inference based on one-sample nonparametric confidence iintervals

Abstract

Hettmansperger (1984) developed two-sample inference on population medians based on disjointness of one-sample confidence intervals. Due to the discrete nature in the confidence coefficient of non-parametric sign confidence intervals, the desired test size may not be available. Consequently, confidence intervals based on interpolated adjacent order statistics or various approximations of the asymptotic distribution of the sample median can be used to achieve the desired test size. An evaluation, via simulation, of five methods for constructing confidence intervals (normal approximation to binomial, direct linear, Hettmansperger-Sheather nonlinear, McKean-Schrader, and Hall-Sheather) are made for a variety of underlying distributions. Some recommendations for choice of interpolation method are given in an assortment of experimental settings. Sample size is discussed. Based on these recommendations, further simulation discusses level and power.

Keywords:

• Nonparametric sign interval
• order statistic
• linear and nonlinear interpolation
• normal approximation to binomial