Nonparametric tests for equality of two treatments for continuous responses under the standard two-period crossover design

Nonparametric tests are developed to analyse the effects of two treatments in the standard two-period crossover design for continuous responses. Instead of comparing responses for each period separately, simultaneous comparisons of treatment responses, available over both the periods, are used to devise new nonparametric effects measuring the difference between the effectiveness of two treatments. Large sample test procedures are developed through inter-subject evaluation and intra-subject evaluation as per the requirement to test whether the two treatments are interchangeable. Similar tests under the parallel group design set-up are added. Performances of all these tests are studied analytically through asymptotic local power under an appropriate sequence of local alternatives and also empirically through Monte-Carlo simulation. Real-life data are also used to illustrate the proposed procedures.