Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
It seems very difficult to derive the detectable effect size, because our design includes
144 decision constellations, applied in a country were previous experimental results are
very rare and non-existant for an experiment comparable to ours. When we determined
the sample size per city/region and role (100 observations per role, 200 observations per city/region), we followed the conventions of comparable studies (see for example Herrmann, B., Thöni, C., & Gächter, S. (2008). Antisocial punishment across societies. Science, 319(5868), 1362-1367). Moreover, in a comparable interregional study in China, Chmura at al. (2016), e.g., had only less than half of the observations (956 in total) we will have (Chmura, T., Goerg, S. J., & Weiss, P. (2016). Natural groups and economic characteristics as driving forces of wage discrimination. European Economic Review, 90,
178-200). The aspired number of observations also exceeds the typical convention of observations per treatment in the experimental economics society.