Need Help with Factorial Design LSSBB Practice Question

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    I am studying for the LSSBB exam and I am reviewing prior exam questions as part of my study. Unfortunately the practice exam questions do not give explanations. I need help with the question below (see attached excel file). My question for each correct answer (per the exam) are below:

    B- I am not clear from from graph how they arrive this answer. I am having difficulty seeing the relationship between metal hardness and cutting speed.

    C- To me this is not a 32 factorial design. I see this design as having 3 factors, 2 levels and -0- replicates which indicates a 8 factorial design (2 to the 3rd power)

    E- This OK. I understand.

    More questions coming…

    Thank you!!

    1. LSSBB-A-40.xlsx
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    Robert Butler

    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 years, 11 months ago by Robert Butler.
    • This reply was modified 2 years, 11 months ago by Robert Butler.


    Hi Robert…
    Thank you for your reply. The testing company insists that their answers are correct. (I sincerely doubt that they checked). I copied the question word for word .. and I doubt that this is a typo on their side.
    I will ask further from them.


    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 years, 11 months ago by Robert Butler. Reason: typo

    Chuck White

    I would say only D and E are correct.

    I agree with @rbutler about B — the only way low cutting speed results in a higher tool age is if there is an interaction, but since they didn’t provide an interaction plot, it would be impossible to conclude that.

    My guess on C is that the 2 is supposed to be a superscript (3 to the 2nd power), but that would still be incorrect. As you correctly stated (and is confirmed by answer E), the main effects plot shows 3 factors at 2 levels each, which would be 2^3, not 3^2. This design has 8 runs, so interpreting 32 as the number of runs would be incorrect as well

    The testing company may insist all they want — it is clear that at least for this question, their answers are not correct.

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