Tom Rees has a blog post, Religion and marital infidelity, which shows that religious attendance, but not belief, correlate with a tendency to not have affairs. I think the critical point here is that religion is a complex phenomenon, and we condense many separate dimensions or parameters into one term. For example, there seems to be a tendency with higher socioeconomic status to be positively associated with religious attendance and affiliation, but negatively associated with religious beliefs.
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