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I have recently been studying development of experiments and how to statistically plan/optimize an experiment for x number of variables based on y number of responses.

To begin with, I am just going to use a 2D central composite full factorial design (CCD) to make sure I don't screw up bigger designs later. My two factors are 'load pH' and 'load conductivity'. My min/max values will be 6.5 - 7.5 and 5.5 - 6.5 respectively. My alpha value = sqrt(2) and I have scaled my model so far to (from min to max):

$$ -\sqrt{2}, -1, 0, +1, \sqrt{2} $$

In a 2D CCD where 9 experiments are needed (depending on number of centre points), what relevance are the -1 and +1 values? To clarify, if my 2D array is effectively a 3x3 grid then the x and y axis will respectively read $-\sqrt{2}, 0, +\sqrt{2}$. What is the purpose of -1/+1?

enter image description here

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closed as off-topic by Curt F., getafix, Wildcat, ron, Jan Dec 27 '16 at 15:36

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  • $\begingroup$ The best source of experimental design pedagogy for beginners (and beyond) is Kevin Dunn's course, learnche.org/pid ... the more appropriate question is do you really need the root two values? That is, do you need the two purple squares on your diagram above x1 above at this stage? Have a look at learnche.org/pid/design-analysis-experiments/… from Kevin Dunn. $\endgroup$ – user1945827 Oct 24 '16 at 7:59
  • $\begingroup$ I appreciate the swift response and thank you for linking me some reading material. $\endgroup$ – Oliver Barker Oct 24 '16 at 10:53
  • $\begingroup$ I have just realized what's happened. My design was for a face centred composite (FCC) design. In this situation only 3 levels are needed, -1, 0 and 1. I've confused myself by constructing five levels for a central composite design (CCD) in which the root 2 values are used to extend outside the characterised square space and detect curvature better. Thus, I either need to switch to CCD or ignore the root 2 values and continue with an FCC design. I hope that makes sense. $\endgroup$ – Oliver Barker Oct 24 '16 at 13:05
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    $\begingroup$ I'm voting to close this question as off-topic because it is a better fit for Cross Validated, the Stack Exchange site for statistical questions. $\endgroup$ – Curt F. Dec 27 '16 at 6:26
  • $\begingroup$ The question is too old to migrate, so the preferable course of action is to re-ask it at Cross Validated and delete it here. $\endgroup$ – Martin - マーチン Dec 27 '16 at 7:53
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FCC is a variant of a CCD design. It's usual to run your 2 factorial design first and establish which factors are relevant. In your case, it won't matter so much but if you have 5 or more factors, it does. The 2 factorial establishes your range with an upper and lower limit (+1 and -1). When you move to CCD, you now have options. Using alpha of root 2 gives your "response surface design" orthogonality and rotatability, meaning, loosely, it is easier to analyse for variance in your model. The reason for varying alpha usually comes down to operational reasons e.g if a negative time or negative mass would result. This is when a FCC might be used instead. If you ignored your coded +1 and -1, in effect your root 2 values would become your new +1 and - 1. The rationale for this is when a formula is generated to model each response, the one using coded factors (set at +1 or -1) will indicate the relative influence of each factor, which the actual factor values will not do. The formula using coded values will not base it on your alpha value.

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