A non-parametric cause-effect testing for environmental variables — method and application

Traditional similarity or resemblance indexes are insufficient to directly reveal the cause-effect relations between environmental variables. Even the typical regression methods are not persuasive enough, since they rely on the assumptions about the data distribution and thus they are not really suitable for small amount of data. In this research, we devise a method to measure the strength of cause and effect (SCE), which is then turned into a non-parametric statistic. By analysing the empirical environmental data from the European Union, we calculate the SCE of these related variables. In addition, by constructing the ranking space and calculating the statistic distribution, we further specify the critical levels and values to conduct the cause-effect testing of these variables. The results show some sectoral activities do, to some degree, directly affect the quality of water and air. Moreover, there is a very clear-cut cause-effect relation between water quality and biodiversity. These results shall provide the policy makers with some ideas regarding the relations between environmental variables. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11356-022-21423-3.