Delhey and Kohler assume that the happiness distribution at the population level is essentially normal, but that this is distorted by the fact that happiness is measured in samples using scales that are discrete and two-sided bounded. This assumption is tested using the probit method and rejected.

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Kalmijn, W.M.. (2012). Happiness is not normally distributed: A comment to Delhey and Kohler. Social Science Research, 41(1), 199–202. doi:10.1016/j.ssresearch.2011.11.008