A NOTE ON THE APPLICATION OF SIMPLE LINEAR-REGRESSION METHODS FOR TREND DETECTION AT MULTIPLE SITES AND VISITS

In comparing running median, tolerance, cusum, and regression methods for trend detection over a small number of visits, Yang et al. found t hat application of multiple Z-tests on the basis of a simple linear re gression for each site separately was the most efficient for detection of trends at several sites simultaneously. Because the use of multipl e Z-tests completely ignores the covariance among measurements taken f rom different sites, to improve the power we propose a global chi2-tes t. Assuming the covariance matrix known, we have found that the propos ed chi2-test procedure is more powerful than multiple Z-tests for two- sided alternatives when both the correlation among measurements and th e number of sites are small. We also have found that the former proced ure can have power uniformly larger than the latter when ratios of slo pes to standard deviations of measurements at different sites vary and the number of sites is large. In fact, in the latter situation, the p roposed global chi2-test procedure, usually used only for two-sided al ternatives, can even have power larger than that of multiple Z-tests f or one-sided alternatives. In the situation where the ratios of slopes to standard deviations of measurements are all equal, however, the pr oposed multivariate approach based on the chi2-test distribution is th e least efficient, especially when the number of sites and the correla tion are moderate or large. Finally, to account for the effect of mult iple tests over a series of visits on the overall alpha-level, on the basis of Monte Carlo simulations, we compute critical values for seque ntial use of the proposed multivariate test procedure.