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Much empirical social-science research, including work in economic and demographic history, has relied on the analysis of published information on administrative districts. One famous example of this type of research, the Princeton Project on the Decline of Fertility in Europe (EFP), was carried out at Princeton University’s Office of Population Research in the 1960s and 1970s. This project aimed to characterize the decline of fertility that took place in Europe during the nineteenth and early twentieth centuries. The project’s summary statements argued that social and economic forces played little role in bringing about the fertility transition. A central feature of the EFP argument is a series of statistical exercises which purport to show that changes in economic and social conditions exerted little influence on fertility. Two recent articles on Germany for this period have used similar data and methods to draw different conclusions. We show that the difference reflects problems in the Princeton project’s statistical methods. Those problems affect, potentially, virtually all quantitative research of this type. Our findings suggest cautious re-thinking of conclusions based on this type of evidence, starting with the EFP.