Need Help with Factorial Design LSSBB Practice Question

I would say C,D,E and I think C is a typo – my guess is that they meant to have 3*2 = 6 experiments.

Actually, there is another possibility – but if it is the case then the problem is poorly presented and C still remains a typo. Since they do claim it is a factorial design one could take a saturated 3 variable in 4 experiments design and augment it with two additional runs. This would still be a factorial design in 6 experiments but not if we are abiding by the standard definition (which I’m assuming they are) of a factorial design. So, if they mean a factorial design in the usual sense, then it would be a 2**3 design which still means C is a typo.

Neither A or B are correct.

• This reply was modified 2 months, 2 weeks ago by  Robert Butler.
• This reply was modified 2 months, 2 weeks ago by  Robert Butler.

I’m sure they do. Here’s the issue

1. What exactly is a 32 factorial design? I’m not aware of any reference that expresses design nomenclature in this manner.

The usual practice is to say say things such as the following:

1. I have a two level design with 3 factors
2. I have a full 2 level factorial design for 5 variables for a total run of 32 experiments.
3. I have a saturated design of 32 runs to investigate 31 variables in 32 experiments.

As for the claim concerning the correctness of B – just look at the graph – the greatest tool age occurs with all 3 variables at their highest settings. The only way you could justify the claim would be if you had an interaction plot showing the effects of cutting speed and metal hardness and on THAT graph you had a situation where the combination of low cutting speed and high metal hardness resulted in greater tool aging. You cannot deduce answer B from an examination of those main effects plots.

You are welcome to ask them but, given my experience with such entities it will be nothing more than contrivindum non pissandum.

• This reply was modified 2 months, 2 weeks ago by  Robert Butler. Reason: typo