Ranking ski courses using permutation methods for multivariate populations.

Monitoring perceived performance of sport trainers is usually a difficult task. The Board of Professional Ski Instructors of the Province of Bolzano and the Ski Schools in ‘Alto Adige’ were interested in investigating the satisfaction of people attending Ski courses in this area. A specific survey has been planned to investigate different aspects of satisfaction, such as on course organization, on teaching, on fun etc. The aim of the statistical analysis was multifold (1) to obtain a ranking of the ski courses from the ‘best’ to the ‘worst’, (2) to identify relevant drivers to differentiate ski instructors/schools and (3) to set up a suitable multivariate methodology able to test for multiple outcomes with stratified data. Usually such analysis is performed for each domain of satisfaction and they are kept separate. In the present work we provide a procedure to compare the performance of ski courses considering simultaneously all domains of satisfaction/quality and stratifying by covariates e.g. the nationality or the age of the attendees. This procedure is based on an extension of the Nonparametric Combination (NPC) of dependent permutation tests (Pesarin and Salmaso, 2010) and it allows us to take into account several aspects affecting the ski performances.