So I did a blocking(X1), two levels(-1,+1) three factors(A,B,C). 5 runs in one block, and 5 runs in the next block. One control in each block. The Alias was interaction A*B*C. I couldn't control one of my parameters for two of the runs. For C, two of the run was actually control at +0.70 instead of +1. So, I input that into the software.
1 analysis) Using the Fit model platform, A and B was not significant. C was significant. The intercept was lower than where it should be. This was informative but not as useful.
2 analysis) Using the Screening Platform, significant coefficients are C and C*C. I run the model using C and C*C, the result make sense. Biologically, this also expected because I was not surprise that the responding result is a curvature. Also, the intercept is where its should be. The resulting model is logical and more useful to me.
So, my co-worker argue that my initial design was not a surface respond design. It is basically a blocking full factorial DoE, therefore, I can not have a model that is a square(curvature). Since I don't fully understand the screening platform to fully explain the C*C in a report, I should take a more conservative approach and use the first analysis which is classical but a less informative model.
If my co-worker is correct, why would the Screening Platform give me a C^2 when my initial design was not mean to detect it. Is there a way to justify the resulting square coefficient?
It fit a curvature and scientifically I have no doubt that it is a curvature. Is my co-worker point correct that my initial design was not a surface respond design, therefore I can not have a C^2 result?
You are both right....
If you are being a detective then perhaps if C is significant and no other terms are significant and there is lack of fit (since you mentioned that you repeated the center point in each block) then perhaps C*C is possible but realize that it is confounded with other possible terms (B*B and C*C).
To truly elucidate the active terms one could augment the experiment with 5 additional runs to fit the RSM.
I think you haven't given us quite enough information about the design.
Did you create the original design in JMP? If so, which design generator did you use (e.g. Custom, Screening, etc.)?
5 runs in one block, and 5 runs in the next block. One control in each block.
How many runs total does this add up to? 10 or 12? What A, B and C settings did you use for the "Control" run?
The Screening platform is a very simple platform. It assumes that you are in a screening situation so that the screening principles hold. effect sparsity, effect hierarchy, effect heredity, and projection). It is not clear that this experiment is, in fact, screening, no matter which design platform in JMP was used. So the results from Screening might be suspect.
The Screening platform creates contrasts based on these principles until the model is saturated. So it enters the largest additive effect first, then the second largest and so on based on the effect hierarchy principle. After all the main effects are in the model, it starts to add the second order effects (e.g., interactions and quadratic terms) using the main effects in order of significance based on the effect heredity principle. It continues until it has used all of the degrees of freedom (i.e., 10 terms in your case). The idea is that saturating the model increases the chance that effect sparsity holds and increases the validity of the pseudo-standard error used in the t-tests. Since C entered as the most significant main effect, then it would enter early in a second order term, such as A*C or C^2, based on effect heredity principle. Because you have only a center point, the assignment of curvature is going to be to C, the most significant main effect based on the effect heredity principle. There is, in fact, no data in your experiment to actually determine which factors are responsible for curvature in the response.
I would hate the answer that I have not gained any information after 10 runs. There is a problem with no replicates i.e. no pure error estimate - one extra center point in each block would be better. On the other hand you should have a normal plot of the effects, and if it as you say, you should have a clear graphical indication of C as the active effect ( C deviating from a straight line). If C is the only active effect the rest is noise. C is a three level factor as you have a center point with plus minus in a one dimensional factor space. The 0.7 levels are risks as the orthogonality of the design is somewhat questionable and assets when estimating a C square coefficient. If the model residuals are ok the chances are you have built the strength of the "C only active" hypothesis against any other model considerably. The next step could be a validation experiment.