Causal inference for multiple treatments using fractional factorial designs

Nicole E. Pashley, Marie Abèle C. Bind

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We consider the design and analysis of multi-factor experiments using fractional factorial and incomplete designs within the potential outcome framework. These designs are particularly useful when limited resources make running a full factorial design infeasible. We connect our design-based methods to standard regression methods. We further motivate the usefulness of these designs in multi-factor observational studies, where certain treatment combinations may be so rare that there are no measured outcomes in the observed data corresponding to them. Therefore, conceptualizing a hypothetical fractional factorial experiment instead of a full factorial experiment allows for appropriate analysis in those settings. We illustrate our approach using biomedical data from the 2003–2004 cycle of the National Health and Nutrition Examination Survey to examine the effects of four common pesticides on body mass index.

Original languageEnglish (US)
Pages (from-to)444-468
Number of pages25
JournalCanadian Journal of Statistics
Issue number2
StatePublished - Jun 2023

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Interactions
  • Neymanian inference
  • joint effects
  • multiple treatments
  • observational studies
  • potential outcomes


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