[dan_mctree]

Is it just me or does this require background knowledge that isn't widely available? I couldn't get through it as it never seemed to really explain what Aliases or Alias structures are, how determining those aliasing structures works (why multiply by C?), how this primary effect thing works and how any of this actually relates to the experiments in any way. As in, like, ok I do tests 1-4, now how do I turn that into insight with this algebra?

If someone could elaborate how this all fits together that would be great, because it does seem like there's some nuggets of insight to be found here

[stdbrouw]

Let's say you're testing different formulations for cake but because you don't have time to do the full cartesian product of all possible variations over sugar content x fat content x type of flour, you just pick a handful, and it turns out that every time you're testing a high-sugar variation you are also testing spelt flour -- that's an alias because if you really like these particular cakes there's no way to know whether it was the spelt or the sugar that did it.

What experimental design brings to the table is a disciplined way to figure out what variables will be aliased and to make sure that these aliases are mostly harmless, either with the help of subject matter knowledge (you can taste sugar so it's fine if it's aliased with other things) or mathematically (let's try to avoid aliasing sugar content with fat content, but instead alias sugar content with the interaction effect of sugar, fat and flour type because that higher-order interaction is unlikely to matter over and above the first-order effects.)

Fractional designs in particular are typically used in agriculture and industrial settings, places where you want to try to optimize over very many factors at once but cannot afford to test every variation. It is not common in web analytics because (1) we usually assume that one particular change to a site or app will be independent of another change elsewhere, so there is no need to test them concurrently to see if a particular combo stands out and (2) if we did want to test combinations of variables concurrently, there's usually enough users or visitors to just test the entire grid and not worry about picking a selection of variations.