The medicine is worse than the disease: Comment on Delhey and Kohler's proposal to measure inequality in happiness using 'instrument-effect-corrected' standard deviations.

Inequality of happiness in nations can be measured using the standard deviation of responses to surveys questions. The standard-deviation is not quite independent of the mean, being zero when everybody is maximally happy or unhappy while the possible value of the standard deviation is highest when the mean is in the middle of the response scale. Delhey and Kohler see this intrinsic dependency as a problem and propose two ways to compute 'corrected' standard deviations. I advise against this medicine. One reason is that there is no real disease, since the presumed problem does not occur with commonly used numerical rating scales of 10 or more steps. The second reason is that one of Delhey and Kohler's medicines have side effects, their first correction affects the mean and their second correction is based on implausible assumptions. A third reason is that there are better ways to estimate the effect happiness-inequality net happiness-level. Partialling out mean happiness did not affect the non-correlation between inequality of income and inequality of happiness in an analysis of 116 nations.