# Significance of interactions

It was suggested to me recently that the significance of an interaction term in a glm has to be higher than a main effect. For example, p<0.05 is commonly thought of as significant for a main effect but a two-way interaction has to be higher (p<0.025 or something) and a three-way even higher. However, I can't find any literature on this so I am unsure. Are they getting confused with multiple comparisons I wonder? Or am I confused and the two things are linked?

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I can conceive that someone might choose to apply a more stringent significance level on interactions. Since the number of interactions and higher order interactions grow at a rapid rate (if there are enough factors), I can see some argument for it, such as if one were trying to make a similar number of type I errors at each order. I don't see how that somewhat plausible argument leads to an 'ought', though. –  Glen_b Feb 15 at 23:08