the Confidence Ellipses in Multiple Non Symmetrical Correspondance Analysis for the Evaluation of the Innovative Performance of the manufacturing enterprises in Campania

Non-Symmetric Correspondence Analysis-NSCA (D’Ambra and Lauro, 1989) is a useful technique for analyzing a two-way contingency table. There are many real-life applications where it is not ap- propriate to perform classical correspondence analysis because of the obvious asymmetry of the as- sociation between the variables. The key difference between the symmetrical and non-symmetrical versions of correspondence analysis rests on the measure of the association used to quantify the re- lationship between the variables. For a two-way, or multi-way, contingency table, the Pearson chi- squared statistic is commonly used when it can be assumed that the categorical variables are sym- metrically related. However, for a two-way table, it may be that one variable can be treated as a predictor variable and the second variable can be considered as a response variable. Yet, for such a variable structure, the Pearson chi-squared statistic is not an appropriate measure of the associa- tion. Instead, one may consider the Goodman-Kruskal tau index. In the case that there are more than two cross-classified variables, multivariate versions of the Goodman-Kruskal tau index can be considered. These include Marcotorchino’s index (Marcotorchino, 1985) and Gray-Williams’ index (Gray and Williams, 1975). In the present paper, the Multiple non- Symmetric Correspondence Ana- lysis- MNSCA (Gray and Williams, J. S,1975), is used for the evaluation of the innovative perfor- mance of the manufacturing enterprises in Campania. Innovation represents a very important ele- ment for the competition of the enterprises and economic growth. Only the enterprises which are able to innovate regularly can have at their disposal a range of more and more appealing products for the customers. Moreover, only a constant innovation provides the constant efficiency of the pro- cesses and the optimization of the production costs. Finally, the use of the ellipse confidence has allowed to identify a category which is statistically significant