Has Water Quality Improved or Been Maintained? A Quantitative Assessment Procedure

Many policies require reporting on water quality trends. This is usually addressed by testing a hypothesis positing that there was zero slope in some parameter of the sampled population over a given period. Failure to achieve "statistical significance" is often falsely interpreted as evidence that there was no trend of concern-the -value of these tests can become ever smaller as the sample size increases and so also can the detectable trend. To avoid this problem, a new trend direction assessment (TDA) procedure is proposed, based on a formulation in psychological literature that considers error risks when inferring the direction of differences between two population means. The TDA procedure abandons testing altogether and instead calculates probabilities that water quality variables have been increasing or decreasing. Nominated probability breakpoints then give rise to a graduated scale in which phrases such as "extremely likely" or "unlikely" can be used to summarize results, avoiding casting many into a "not statistically significant" box. This trend assessment procedure requires no more information than a traditional test, for which the significance level is reinterpreted as a misclassification error rate (inferring an increase when in fact there was a decrease, or vice versa). Example applications of this procedure to small and large datasets are given. This procedure also possesses a possible framework that addresses the more complex question of whether water quality has been "maintained," in which a trend magnitude of environmental significance must be defined. The TDA procedure may be applied to any environment, not just water quality.