#### MEASURING INEQUALITY OF HAPPINESS IN NATIONS

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

ABSTRACT

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.

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