# Analysis 2^3 with 3 center points

Discussion in 'DOE - Design of Experiments' started by A.dubia, Jul 12, 2020.

1. ### A.dubiaNew Member

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Dear community,

I conducted a full factorial experiment with three factors à 2 levels each. I did not conduct replicates of those but added 3 center points.

Factors:
o Incubation time (0h, 2h, 4h)
o Process temperature (30°C, 40°C, 50°C)
o Process duration (Time) (4h, 7h, 10h).

Ouput variables: texture coefficient, yield.

Here’s my data:
Nr. Text. Yield Incub Temp Time
1 h1 2.63 54 0 30 4
2 h2 1.71 51 4 30 4
3 h3 2.37 56 0 50 4
4 h4 4.00 51 4 50 4
5 h5 1.63 55 0 30 10
6 h6 1.47 55 4 30 10
7 h7 3.11 43 0 50 10
8 h8 2.42 60 4 50 10
9 c1 2.07 51 2 40 7
10 c2 2.37 46 2 40 7
11 c3 2.48 39 2 40 7

I already created plots and interaction plots and tried to calculate ANOVA for main effects and interactions but still lack full understanding of what I am doing. I would be super thankful for any hint and answers to my questions.

a) I used the actual factor levels when plotting and calculating ANOVA. I find it easier to read that way, is that fine or is it required to code them as -1, 1 or +, - prior analyzing?

b) I plotted the variables, and it looks like for the output „yield“, there was nonlinearity. Is there a test, that indicates that curvature, besides visually checking?

c) If there is a curvature, I cannot analyze it with regression (nor by ANOVA?), right? I would have to add axial points to be able to model the relationship via response surface modelling, right?

d) Generally, in the context of DoE, I did not get, when to conduct regression and when ANOVA and how to check the preconditions as homogenity of variance and normal distrubution. In the examples I have seen so far, nobody conducted Levene test or Shapiro wilk.. I am also not sure, if when having 2 output variables I should look at them one by one or via MANOVA.

e) And, my last point, if I look at the center points, they look as if they had a large variance.. If the variance is that large, my methods are probably a bit unprecise, can I still estimate anything from the results?

Plots for Yield (which I suppose as nonlinear) and plots for Texture (which I suppose as roughly linear but also somewhat unprecise) are attached.

Kind regards
A.dubia

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