In a project on software measurement, we plan to use aggregating statistics (e.g., Gini) to describe the concentration of certain observed program attributes (size) among program units (e.g., modules, functions). This is a purely exploratory, descriptive effort (e.g., no hypothesis testing involved).

We are aware of the limitations of e.g. Gini (sample bias, symmetry, different distribution/same Gini etc.) and the various sample/population estimation approaches to inequality measures such as Gini (jackknifing estimates & bootstrap estimates such as here).

For a given program, we compute several Gini coefficients, each representing a different "perspective" on the program structure:

                   P1        P2               ...        P_n
Program            0.5578098 0.7981829        ...        0.7981829
  1. As a purely descriptive statistic, is it acceptable to compare the observed Gini coefficients directly, to state Gini(P1) <|>|... Gini(P2) etc.? Should we take corrective actions (e.g., small-sample bias correction?!)
  2. Is it necessary to report estimate of variance and/or standard error in this case? In our view, we compute the statistic on the actual population data rather than some sample. Besides, we do not run hypothesis tests on some confidence interval(s). If so, how can this be achieved best (var, se, quantile error bounds, ...)?

Thank you for your critical comments/suggestions!


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