In search for proper statistics

Wim Kalmijn and Ruut Veenhoven
Journal of Happiness Studies, special issue on 'Inequality of Happiness in Nations', 2005 vol. 6, pp. 357-396

Comparative research on happiness typically focuses on the level of happiness in nations, which is measured using the mean. There have also been attempts to compare inequality of happiness in nations and this is measured using the standard deviation. There is doubt about the appropriateness of that latter statistic and some prefer to use the statistics currently used to compare income inequality in nations, in particular the Gini coefficient.
In this paper, we review the descriptive statistics that can be used to quantify inequality of happiness in nations. This review involves five steps: (1) we consider how happiness nations is assessed, (2) next we list the statistics of dispersion and considered their underlying assumptions; (3) we construct hypothetical distributions that cover our notion of inequality; (4) we define criteria of performance and (5) we check how well the step-2 statistics meet the step-4 demands when applied to the step-3 hypothetical distributions We then applied the best performing statistics to real distributions of happiness in nations.
Of the nine statistics considered, five failed this empirical test. One of the failed statistics is the Gini coefficient. Its malfunction was foreseen on theoretical grounds: the Gini coefficient assumes a ratio level of measurement, while happiness measures can at best be treated at the interval level. The Gini coefficient has been designed for application to 'capacity' variables such as income rather than to 'intensity' variables such as happiness.
Four statistics proved to be satisfactory; these were (1) the standard deviation, (2) the mean absolute difference, (3) the mean pair difference and (4) the interquartile range. Since all four statistics performed about equally well, there is no reason to discontinue the use of the standard deviation when quantifying inequality of happiness in nations.

Full text