Exact Confidence Intervals for Nonconstant Effects by Inverting the Signed Rank Test

Wilcoxon's signed rank test is often inverted, using Walsh averages, to yield exact, distribution free, randomization based confidence intervals for a constant treatment effect or center of symmetry; however, many treatment effects are not constant, so that this interval is not applicable. This article proposes a new way to invert the signed rank test, again using Walsh averages, to produce an exact, distribution free, randomization based confidence interval describing treatment effects that are not constant. The procedure is simple to apply, comparable to the signed rank test itself. Also, the procedure permits a sensitivity analysis in observational studies that estimate treatment effects in the absence of randomization. The method is illustrated using an observational study of the frequency of micronuclei in the cells of alcoholics and matched controls.