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Simpson’s Paradox: Examples
  1. Bokai Wang1,
  2. Pan Wu2,
  3. Brian Kwan3,
  4. Xin M. Tu3 and
  5. Changyong Feng1,4
  1. 1Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY, USA
  2. 2Value Institute, Christiana Care Health System, John H Ammon Medical Education Center, Newark, DE, USA
  3. 3Division of Biostatistics and Bioinformatics, University of California San Diego, La Jolla, CA, USA
  4. 4Department of Anesthesiology, University of Rochester, Rochester, NY, USA
  1. correspondence: Dr. Changyong Feng. Mailing address: Department of Biostatistics and Computational Biology, University of Rochester, 601 Elmwood Ave., Box 630, Rochester, NY, USA. Postcode: NY 14642. E-Mail: changyong_feng{at}


Simpson’s paradox is very prevalent in many areas. It characterizes the inconsistency between the conditional and marginal interpretations of the data. In this paper, we illustrate through some examples how the Simpson’s paradox can happen in continuous, categorical, and time-to-event data.

  • conditional expectation
  • odd ratio
  • time-to-event analysis

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