A New Method for Ranking n Statistical Units.

In many research problems it is useful to summarize some indices or indicators to express a synthetic, indirect measure of a concept which is revealed by p variables observed in each statistical unit. This is because the p variables are considered to be indirect measures of a complex (perhaps indefinable) concept. Within this context and for ranking the n statistical units the author suggests the index: $$ R_i = (\operatorname{sgn} {\mathbf{ }}c_i 1)(\sum\limits_r {c_{ir}^2 } )^{1/2} $$ where the cir (i = 1, 2,...,n; r = 1, 2,..., p) represent the values of the p principal components connected with the i-th statistical unit. This index is applied for ranking the 20 Italian Regions for quality of life for the years 2000-2002. The results are compared with those that are furnished by the single source method. [ABSTRACT FROM AUTHOR]