Use of poset theory with big datasets: a new proposal applied to the analysis of life satisfaction in Italy

The aim of this work is to propose a tool for measuring a complex concept, and to apply it to big sets of data measured on ordinal and/or dichotomous scales. An important field of application are subjective data, that are often based on opinions or personal evaluations. Many national and international surveys employ this kind of data, measured among thousands of individuals. Thanks to the use of the average rank (AR) as a synthetic measure of a complex concept, we believe that poset theory could be a very useful approach for dealing with ordinal data avoiding the use of scaling procedures. Because classic poset approaches are at their best when applied to few data at a time, our idea is based on a procedure for sampling units from a big population using a simple criterion to summarize the resulting values appropriately. Applying the central limit theorem enables a comparison of the results obtained from different groups using statistical tests on the means. We used our Height Of Groups by Sampling (HOGS) method to compare the average rank among groups that are defined by one or more socio-demographic variables influencing the level of the complex concept we wish to measure. The application of the HOGS procedure to life satisfaction in Italy generated convincing results, revealing significant differences between regions, genders and levels of formal education. We compared the results given by HOGS with the non linear principal component analysis and obtained an easy readable output with convincing precision and accuracy; we are confident that the HOGS procedure can be applied to many other concepts investigated in the social sciences