It is quite common in political science for researchers to run statistical models, find that a coefficient for a variable is not statistically significant, and then claim that the variable "has no effect." This is equivalent to proposing a research hypothesis, failing to reject the null, and then claiming that the null hypothesis is true (or discussing results as though the null hypothesis is true). This is a terrible idea. Even if you believe the null, you shouldn't use p > 0.05 as evidence for your claim. In this post, I illustrate why...
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