Yule (1903) and Simpson (1951) described a statistical paradox that occurs when data is aggregated. In such situations, aggregated data may reveal a trend that directly contrasts those of sub-groups trends. In fact, the aggregate data trends may even be opposite in direction of sub-group trends. To reveal Yule-Simpson’s paradox (YSP)-type occurrences, researchers must simultaneously consider the effect of an intervention at specific levels and on the overall model to ensure datasets are accurately analyzed and research findings are appropriately interpreted. The primary objectives of this manuscript are to: (1) examine the history of YSP; (2) describe necessary and sufficient causes for YSP occurrences; (3) provide examples of YSP in research and explain YSP’s relationship to multi-level modeling including Hierarchical Linear Modeling (HLM); and (4) discuss YSP’s implications for researchers. Accessed 11,204 times on https://pareonline.net from October 18, 2010 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.