Non-parametric confidence intervals for shift effects based on paired ranks

Abstract

Non-parametric approaches to derive confidence intervals for the shift effect in paired samples are discussed. These approaches are based on the sign statistic, Wilcoxon’s signed ranks (WSR) and paired ranks. While the intra-individual differences of the observations are ranked for the WSR approach, the observations are first ranked and the differences are considered afterwards for the paired rank approach. Confidence intervals by using paired ranks are derived by iterating the possible shift effects. In this context, an asymptotic as well as an exact approach is proposed. In simulation studies, the performance of all approaches are compared. Finally, an example from a clinical study is analysed.

For all approaches the results are almost equal under hypothesis and under alternative. The differences between the asymptotic and the exact version of the paired rank test are negligible. In the case of normal distributions, the approaches based on paired ranks and signed ranks lose only little efficiency while a huge gain in efficiency can be expected in other situations. This is especially true for the paired rank approach, which is more efficient than the approach based on the sign statistic in all investigated situations and more efficient than the signed rank approach in very most situations.

Keywords:

• Paired samples
• Sign test
• Wilcoxon’s signed rank test
• Paired rank test
• Exact test

Additional information

Notes on contributors

Ullrich Munzel

Email: [email protected]