https://www.journals.uchicago.edu/doi/abs/10.1086/701679

Happiness is reported in ordered intervals (e.g., very, pretty, not too happy). We review and apply standard statistical results to determine when such data permit identification of two groups’ relative average happiness. The necessary conditions for nonparametric identification are strong and unlikely to ever be satisfied. Standard parametric approaches cannot identify this ranking unless the variances are exactly equal. If not, ordered probit findings can be reversed by lognormal transformations. For nine prominent happiness research areas, conditions for nonparametric identification are rejected and standard parametric results are reversed using plausible transformations. Tests for a common reporting function consistently reject.