The data
The data cover sixteen socioeconmic indicators for 26 different provinces of Iran. The selected
indicators measure various socieconomic aspects of life in provinces of Iran. A number of
points should be made regarding the data. The selected indicators should have the property of
being operational. By that we mean that it should be possible to have an effect on aspects
measured by these indicators through the implementation of projects and policies. While the
need for further discussion of the theoretical issues regarding the selection of indicators is
acknowledged we do not address such issues in this article.9 However, we have attempted to
select a set of indicators which are within the spirit of the components of the HDI.
Sixteen indicators for which regional data is available are selected. They include five indicators
of longevity, health and poverty, six indicators of education (and gender) and five economic
indicators.10 The list of the selected indicators is presented in Appendix A. Table B1 in
Appendix B presents the data for these indicators.
Methodology
We start with the matrix of data, X, containing data on m socio-economic indicators for n
provinces. To remove the scale effect and to have the indicators spread around the same
mean with the same variance, we first standardise the data. The standardised indicators
would then constitute m vectors in a multi-dimensional vector space. Conceptually this
makes sense as any composite socio-economic index for human development should be
defined within the context of all provinces. As the length of a standardised indicator is equal to
the square root of the number of provinces which remains the same for all indicators, the length
of the standardised indicator vectors are equal.11
With this property, in turn these vectors of equal length can constitute the axes of a space
within which each province is presented by a vector. In effect in the standardised data matrix,
where rows and columns are the provinces and indicators respectively, the vector space consists
of the row vectors and the matrix columns are a co-ordinate system for this space. In other
words each province can be mapped as an m-dimensional vector in the space of the selected
indicators. The distance between any two such vectors may then be measured by the length
of the so-called distance vector.