One-sided simultaneous prediction limits for at least p of m correlated observations in-bounds from each of r correlated population

In groundwater monitoring, a statistical procedure for multiple correlated comparisons is necessary to detect possible contamination from a facility. The procedure needs to control the facility-wide false positive rate (FWFPR) in the presence of spatial and temporal variabilities while maintaining a high power to real contamination.;Common practices of interwell and intrawell comparisons can not account for all inherent variability. The sequential p of m testing procedure of McNichols and Davis can be used in controlling the Type I and II errors. Since multiple parameters are monitored at multiple wells, application of the p of m procedure leads to multiple correlated sample vectors from correlated populations. For such a correlation structure, existing statistical methods cannot be used, since the independence assumption of observations is violated.;In this dissertation, the p of m procedure has been extended to the case where spatial and temporal variabilities are present. The method accounts for all inherent variability for both known and unknown groundwater flow direction and controls Type I and II errors. To test the hypothesis of no contamination, the critical value for the test statistic is determined by simulation and approximated analytically.;The c.d.f. of the order statistics for correlated observations is developed by modifying the DMT method of McNichols and Davis. By spreading the contaminate-wise false positive rate (CWFPR) over the number of monitoring wells. the critical values are approximated by the modified DMT method.;Comparisons of simulation and DMT results show that the percent difference between their critical values varies from 0.0% to 1.75% and from $-$0.8% to 0.8% for CWFPR $>$ 0.005 and CWFPR $le$ 0.005, respectively.;The true FWFPR for the DMT critical values varies from 0.046 to 0.054 as opposed to the desired risk of 0.05. Power comparisons for the DMT critical values and the "standard" t-test show that the DMT method controls the FWFPR while maintaining good power. From comparisons it is concluded that the DMT critical values can be used in confidence for CWFPR $le$ 0.005 and 30 or more monitoring wells. Apart from this region, the simulation critical values are preferred.