Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The MDE was derived by simulation from the retailer's transaction database. A 15,000-customer sample was randomly drawn from March–June 2025, customers were randomly assigned to the four arms (~3,750 per arm), and a placebo regression equivalent to the primary consumer-level count specification was run for each of 100 simulated assignments. The standard error was taken as the average across simulations. At α = 0.05 and power = 0.80, MDE = 2.80 × SE = 0.065, corresponding to a minimum-detectable treatment effect of approximately 6.7% in purchase counts. This is in the range of effects documented in comparable settings: Dubois et al. (2021) ≈14% for in-store nutrition labels, Cawley et al. (2015) ≈8.3% for supermarket nutrition ratings, and Katare & Zhao (2024) ≈25% for online behavioral interventions.
Cawley, J., Sweeney, M. J., Sobal, J., Just, D. R., Kaiser, H. M., Schulze, W. D., Wansink, B. (2015). The impact of a supermarket nutrition rating system on purchases of nutritious and less nutritious foods. Public Health Nutrition, 18(1), 8–14.
Dubois, P., Albuquerque, P., Allais, O., Bonnet, C., Bertail, P., Combris, P., Lahlou, S., Rigal, N., Ruffieux, B., Chandon, P. (2021). Effects of front-of-pack labels on the nutritional quality of supermarket food purchases: evidence from a large-scale randomized controlled trial. Journal of the Academy of Marketing Science, 49(1), 119–138.
Katare, B., Zhao, S. (2024). Behavioral interventions to motivate plant-based food selection in an online shopping environment. Proceedings of the National Academy of Sciences, 121(50), e2319018121.