The most interesting thing about this is not that wellness programs don't work (this is the null hypothesis for all interventions, behavioral interventions part

The most interesting thing about this is not that wellness programs don't work (this is the null hypothesis for all interventions, behavioral interventions particularly, and diet/exercise interventions especially) but that it offers a direct examination of 'correlation!=causation': they did the cluster randomized trial, but they also did the naive correlational analysis ignoring the randomization to see how misleading the estimates would be. They compare the estimates side by side in the supplement https://www.gwern.net/docs/statistics/causality/2019-song-supplement2.pdf#page=45 https://www.gwern.net/docs/statistics/causality/2019-song-su... You can see that the estimates are... different. Frequently, the point estimates aren't even the same sign. Self-selection and 'healthy user bias' are very much things. --- This parallels an earlier workplace wellness randomized experiment: https://www.gwern.net/docs/statistics/causality/2018-jones.pdf https://www.gwern.net/docs/statistics/causality/2018-jones.p... which comes with nice graphs/tables comparing & contrasting the correlational vs actual causal effects: https://www.gwern.net/images/causality/2018-jones-table5-nyt-randomizedvscorrelation.png https://www.gwern.net/images/causality/2018-jones-table5-nyt... https://www.gwern.net/images/causality/2018-jones-figure8-randomizedvscorrelationliterature.png https://www.gwern.net/images/causality/2018-jones-figure8-ra... https://www.gwern.net/images/causality/2018-jones-supplement-randomizedvscorrelation-tablea3-ac.png https://www.gwern.net/images/causality/2018-jones-supplement... https://www.gwern.net/images/causality/2018-jones-supplement-randomizedvscorrelation-tablea3-de.png https://www.gwern.net/images/causality/2018-jones-supplement... https://www.gwern.net/images/causality/2018-jones-supplement-randomizedvscorrelation-tablea3-fg.png https://www.gwern.net/images/causality/2018-jones-supplement... https://www.gwern.net/images/causality/2018-jones-table5-correlationvsrandomized.png https://www.gwern.net/images/causality/2018-jones-table5-cor... (I collate a bunch more of these kinds of correlation!=causation results in https://www.gwern.net/Correlation https://www.gwern.net/Correlation as a way of making the point that, empirically and especially when it comes to humans, correlation frequently is not causation, and this is not merely some carping pedantic statistician's complaint, but normal.)