In a full factorial design you’re able to calculate the main effects and all the interactions between everything and everything else: not just pairwise but all

In a full factorial design you’re able to calculate the main effects and all the interactions between everything and everything else: not just pairwise but all combinations of variables. You may not care for that because you don’t think there are such interactions or perhaps you just don’t have the experimental budget. In fractional designs you can chose to confound some of the interactions so that you can’t tell what’s happening beyond a certain level. Eg just main and pairwise effects, with the rest confounding those effects. You would do this because it requires fewer runs. You can also use it as a sort of screener when you have many variables by confounding things together in such a way that you can at least tell which variables are having the effects even if you can’t calculate the individual effects.