Advances on multisample permutation tests for "V-shaped" and "U-shaped" alternatives with application to circular economy

Sample surveys and related inferential statistical methods are suitable tools to support decision-making practices for policymakers. For instance, to achieve the environmental sustainability goals connected to Circular Economy and product and process innovation, Governments and Parliaments should evaluate and stimulate the propensity of companies towards such virtuous behaviors. This practice becomes fundamental in a country like Italy with an economic system mainly based on small and medium enterprises. The paper deals with complex tests of hypotheses for investigating the effects of important factors such as company's size on the reluctance of enterprises towards Circular Economy. Frequently, the complexity is given by the "V-shaped" or "U-shaped" effects of the ordinal factors on the response. In other words, in the tested hypothesis, the reluctance towards Circular Economy is decreasing up to a pick point and then increasing with respect to the ordinal factor under study. The proposed solution is based on a nonparametric method which consists in a combined permutation test. The good performance of the method and its usefulness in real data problems are proved through a Monte Carlo simulation study considering the application to data concerning a survey on Circular Economy respectively.