Continuous measures of confidence in direction of environmental trends at site and other spatial scales

Abstract

Managers and decision makers need to know if variables measured by environmental monitoring programs are increasing or decreasing, both at individual sites and at larger spatial scales, and the degree of statistical support for these assessments. Traditionally, null hypothesis significance testing (NHST) has been used to evaluate whether an assessed trend is a reliable estimate of the true (i.e., population) trend but has two shortcomings. First, failure to achieve “statistical significance” is often falsely interpreted as evidence that there was no trend. Second, the acceptable Type 1 error risk tends to be chosen arbitrarily and without consideration of the risk of failing to identify important trends. As an alternative to NHST, we propose a continuous measure of confidence in the direction of an individual site trend based on the posterior probability distribution. Confidence that the trend direction is correctly inferred (i.e., that the assessed trend direction has the same sign as the population value) is expressed as a probability. The approach is extended to assessing confidence in the direction of aggregate trends (i.e., trends observed over multiple sites representing a spatial domain such as a geographic region). The aggregate trend assessment accounts for the confidence in the individual site trends and spatial correlation in the observations, which reduces the effective size of the dataset. The approach is demonstrated for site and aggregate river water quality trends for 352 sites in New Zealand. Compact graphical reporting of the results indicated appreciable variation in trend direction between sites for all variables, as well as patterns in trend direction at larger spatial scales. The new method provides decision makers with a more complete description of the statistical support for the assessment of trend direction than an arbitrary “significant/not significant” designation associated with NHST.