Use of the Wilk-Shapiro test in Two-Stage Adaptive Tests for Paired Data JOSEPH L. GASTWIRTH George Washington University  Abstract: Motivated by a matched study of emissions submitted as evidence in  an important legal case, several robust methods for the analysis of such data  are examined. We propose a new method, using the Wilk-Shapiro test to select the second stage non-parametric test and show that when the differences may not be normally distriubuted it usually has superior power properties than the t or Wilcoxon tests as well as a procedure developed by the Environmental Protection Agency.