If you're using a 5% significance level, you'd expect 5 datasets of 100 to come up with a statistically significant result even though there's no there there (i

If you're using a 5% significance level, you'd expect 5 datasets of 100 to come up with a statistically significant result even though there's no there there (ie even though the null hypothesis is true for all the datasets). That's by definition. This is even before p-hacking. Having said that, the study reported on here has significance levels better than 1%: > The farther away a municipality (in dots) is from a historical mission, the lower its literacy level today. This unconditional relationship is negative and highly significant with a t-statistic of -4.36. So, notwithstanding the experts here eyeballing the graph and dismissing it as embarrassing, I'd say there is something going on here. Paper: Caicedo, F. V. (2018). The Mission: Human Capital Transmission, Economic Persistence, and Culture in South America*. The Quarterly Journal of Economics. doi:10.1093/qje/qjy024