Normally indicators which used to calculate social exclusion index capture every dimension of deprivation, to calculate social exclusion between groups and within groups can be done after calculation of social exclusion index, you can present your result accordingly

Provided you have a continuous social exclusion variable, you could also try to use the various decomposable measures that have been developed for assessing income

Income inequality (e.g. The Theil index, which allows you to split the dispersion between and within groups)

agreed with j.vrooman, but i think Thiel index is for inequality measurement, social exclusion is a different thing, not necessarily associated with income inequality at later stage, social exclusion index itself helps to calculate extent of deprivation among and within groups. HDR report (2011) "beyond transition" helps you as you can found a new concept of "social exclusion head count" and that measure can help you to make analysis within group and among groups

Of course Theil has been developed within the context of inequality measurement, but that does not imply you cannot use it for decomposing social exclusion (or any other continuous variable). We should seperate methodology and content here, I would think.

Since 2001, EU member states have produced national action plans for social exclusion. The European Union considered that the treatment of social exclusion is the most important part in the context of social protection.

International attention to the question of social exclusion has been extended beyond Europe, but so far it has not been given the same importance in the United States. International agencies working in the least developed countries have found that the study of social exclusion is important to study the challenges of integration and integration into ethnocentric societies , The restoration of religious cleavages, the rights of indigenous peoples and expatriates. United Nations agencies and international development banks have funded programs to promote inclusion and social integration, particularly in the countries of the global South.

For example, Giddens (2001) discussed the issue of social exclusion in The Third Way, as Tony Blair adopted the idea. Esping-Andersen cited the challenges of social exclusion in his book Why We Need a New Welfare State. The France National Observatory for the Study of Social Exclusion produced annual reports and research submitted to the Government.

There are those who discuss the idea of social exclusion, and provide argument after argument without paying close attention to social inequality and class struggle. Reducing social exclusion, as a political goal, is a commendable goal. But the definition of social exclusion, and the normative justification of its reduction policies, is unclear.

It seems that the idea of social exclusion is strained by policy makers and academics. It is difficult to find one trait that unites potential categories of social exclusion. If attempts to define the concept of "justice" or "rationality" have taken centuries of debate, social exclusion is no exception.