  Researchers across the health and social sciences generally assume that
observations are independent, even while relying on convenience samples that
draw subjects from one or a small number of communities, schools, hospitals,
etc. A paradigmatic example of this is the Framingham Heart Study (FHS). Many
of the limitations of such samples are well-known, but the issue of statistical
dependence due to social network ties has not previously been addressed. We
show that, along with anticonservative variance estimation, this can result in
spurious associations due to network dependence. Using a statistical test that
we adapted from one developed for spatial autocorrelation, we test for network
dependence in several of the thousands of influential papers that have been
published using FHS data. Results suggest that some of the many decades of
research on coronary heart disease, other health outcomes, and peer influence
using FHS data may suffer from spurious associations, error-prone point
estimates, and anticonservative inference due to unacknowledged network
dependence. These issues are not unique to the FHS; as researchers in
psychology, medicine, and beyond grapple with replication failures, this
unacknowledged source of invalid statistical inference should be part of the
conversation.
