Nonparametric partially random sequential test under Phase II sampling: An illustration to monitor water samples for arsenic contamination

We introduce a class of nonparametric two-sample tests based on a new partially sequential sampling scheme. Existing partially sequential procedures based on inverse sampling schemes, pioneered by Wolfe (1977 Wolfe, D. A. (1977). On a Class of Partially Sequential Two Sample Test Procedure, Journal of American Statistical Association 72: 202–205.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and Orban and Wolfe (1980 Orban, J. and Wolfe, D. A. (1980). Distribution Free Partially Sequential Placement Procedure, Communications in Statistics - Theory &; Methods 9: 883–902.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), are updated in the light of random sequential sampling techniques, proposed by Mukhopadhyay and de Silva (2008 Mukhopadhyay, N. and de Silva, B. M. (2008). Theory and Applications of a New Methodology for the Random Sequential Probability Ratio Test, Statistical Methodology 5: 424–453.[Crossref] , [Google Scholar]). In a quality control setup, the present procedure can be looked upon as a Phase II on-line monitoring with rational subgroups of variable sizes where standards are unknown. We consider a training sample of prefixed size m as Phase I observations and adopt a random sequential sampling in Phase II. We discuss statistical methodologies in detail and provide some asymptotic results. Numerical results based on Monte Carlo are presented to justify asymptotic theory. We computationally investigate the power performances of the proposed test against some fixed alternative. We illustrate our procedure with real data related to water samples for monitoring arsenic contamination. Some concluding remarks along with possible future research problems are offered