This work deals with nonparametric test procedures for comparing effects of two treatments in two period parallel group design, where each subject receives the same treatment over the two periods. The procedures are based on consistent estimators of relative treatment effects in each period and that of covariate adjusted effects with responses in period 1 as covariates. Related asymptotic results are obtained followed by necessary simulation studies to evaluate the performance of the tests.
MannHBWhitneyDR. On a test of whether one of two random variables is stochastically larger than the other. Ann Math Stat.1947; 18: 50–60.
2.
ArkitasMGArnoldSFBrunnerE. Nonparametric hypotheses and rank statistics for unbalanced factorial designs. J Am Stat Assoc.1997; 92(437): 258–265.
3.
BrossIDJ. How to use ridit analysis. Biometrics.1958; 14(1): 18–38.
4.
BrunnerEMunzelU. The nonparametric Behrens–Fisher problem: Asymptotic theory and a small-sample approximation. Biometrical Jt.2000; 42(1): 17–25.
5.
BrunnerEKonietschkeFPaulyMPuriML. Rank-based procedures in factorial designs: Hypotheses about non-parametric treatment effects. J R Stat Soc Ser Bt.2017; 79(5): 1463–1485.
6.
ChatterjeeDBandyopadhyayU. Testing in nonparametric ANCOVA model based on ridit reliability functional. Ann I Stat Matht.2018; 71: 327–364.
7.
BathkeABrunnerE. A nonparametric alternative to analysis of covariance. In: Akritas MG, Politis DN, editors. Recent advances and trends in nonparametric statistics (pp. 109–120). Amsterdam: Elsevier; 2003.
8.
LeeAJ. U-statistics: Theory and Practice. New York, NY: Marcel Dekker; 1990.
9.
RoyJ. Step-down procedure in multivariate analysis. Ann Math Stat.1958; 29(4): 1177–1187.
