I have a question regarding designing experiments that i can't quite wrap my head around. The question will be posted as an image below!

Image of the question

So the question gives us three factors with a specified amount of levels corresponding to each of these factors. One of the levels is a default level.

So I would write:

Request rate : 9 = 8 + 1 (default) Job size : 8 = 7 + 1 (default) Processor speed : 7 = 6 + 1 (default)

But when doing the calculations for b) I get a bit confused. What does "default scenario as a baseline" mean in that context?

For a) - I would interpret this as: We have the default scenario which is 1 combination. Then if we "lock" the job size at a specific value and the processor speed at a specific value we get 8 possible combinations for request rate. If we do the same procedure with the other factors we would get:

8 + 7 + 6 = 21 combinations. But we have to add the default scenario. So we would get 22 combinations. This seems to be the correct answer for a)

But for b), the default scenario is not 1 according to numerous sources. I understand that we take two factors at a time and fix the third. So this would give us (excluding default levels):

8 * 7 * 1 + 8 * 6 * 1 + 6 * 7 * 1 = 146 combinations. But somehow (according to some answers), we have to add the result in a) to this. Why?

I believe that I am missing something here. What does "default scenario as baseline" mean when doing experiments?



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