A New Method for Ranking n Statistical Units

Abstract

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 c _ir (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.