The implementation of the Stockholm Convention (SC) in 2004 should become evident in decreases in environmental concentrations of various pollutants even in countries that not have ratified the SC. However, in some cases, there may be no decreases at all. This paper develops a statistical strategy for investigating time-series measurements such that the rate of change of a pollutant's concentrations at any time can be compared to those at an earlier or later time and thus determine the effectiveness of the SC at any location. The general approach is to modify a first-order regression to include a second order time term: ln(Ct)= a0 + a1 t + a2 t2, where Ct is the concentration at time t. Thus, the rate constant at any time is k(t) = a1 + 2 a2 t. Given that the errors associated with a1 and a2 can be calculated, one can compare the rate constants at different times with statistical rigor to determine if the rates at which the concentrations are changing are significantly different. As examples of this approach, this paper uses vapor and particle phase atmospheric concentrations of several organic pollutants measured at six sites around the North American Great Lakes every 12 days since about 1992. After correcting for the population near the sampling sites, for seasonality, and for the different numbers of samples collected on the same date, up to 830 data were used in this second-order regression. In general, the loss rates of vapor phase chlorinated pesticides have slowed by about a factor of 2 between 1995 and 2015, which is not SC-like behavior. The exceptions are the endosulfans, the vapor and particle phase concentrations of which were both doubling in 1995 but were both decreasing in 2015, probably because of the greatly diminished use of this insecticide in the United States over the last 20-25 years. The loss rates of vapor phase polychlorinated biphenyls became more rapid between 1995 and 2015, which is SC-like behavior.