Analysis of CCD resultsHi everyone,
I am trying to study a chemical behavior of a solid. I did screening desing and steepest ascent which showed me a saddle point. Then, I conducted experiment (ordinary central composite design) on this area to capture the curvature. But I don't know how to analyse the results, my model isn't significant with quadratic terms and the lack of fit is significant (the model only become significant when I raise my model to the power of 4).
Could someone please help me to understand more?
I attached my file
| xT | xt | xN | Temperature | Time | L/S | Responses |
| 0 | 0 | 0 | 178 | 3.7 | 4.9 | 61.32 |
| -1 | -1 | -1 | 176 | 3.5 | 4.62 | 59.49 |
| -1 | 1 | -1 | 176 | 3.9 | 4.62 | 70.17 |
| -1 | -1 | 1 | 176 | 3.5 | 5.15 | 53.69 |
| 1 | -1 | -1 | 180 | 3.5 | 4.62 | 69.95 |
| 1 | 1 | -1 | 180 | 3.9 | 4.62 | 63.31 |
| 1 | -1 | 1 | 180 | 3.5 | 5.15 | 49.51 |
| 0 | 0 | 0 | 178 | 3.7 | 4.9 | 65.88 |
| 1 | 1 | 1 | 180 | 3.9 | 5.15 | 70.5 |
| 0 | 0 | -1.68 | 178 | 3.7 | 4.4 | 72.39 |
| 0 | 0 | 1.68 | 178 | 3.7 | 5.4 | 66.82 |
| 0 | -1.68 | 0 | 178 | 3.4 | 4.9 | 67.99 |
| 0 | 1.68 | 0 | 178 | 4 | 4.9 | 68.89 |
| 1.68 | 0 | 0 | 182 | 3.7 | 4.9 | 92.75 |
| -1.68 | 0 | 0 | 175 | 3.7 | 4.9 | 74.25 |
| -1 | 1 | 1 | 176 | 3.9 | 5.15 | 69.57 |
| 0 | 0 | 0 | 178 | 3.7 | 4.9 | 71.74 |
DOERe: Analysis of CCD resultsHi, Aaron
It seems that temperature is an important factor.
From the 3D plot, the curve composed of any two dimensions does not look like a parabola. Therefore, the effect of second-order fitting will be bad, and high-order fitting will cause over-fitting.
Similarly, if the temperature is taken as the Z axis and the remaining two parameters are taken as the X and Y axes, a parabolic surface (imagine a mountain) cannot be seen. So the response surface should not be very good.
High-order fitting will achieve better R-squared, but it is likely to be over-fitting.
Hope it can help you.
Re: Analysis of CCD resultsI'm not seeing much as being significant here either. In fact, I do NOT see a significant lack of fit as the p-value for that test with the full response surface model is 0.2195. The main issue seems to be that there is not a large change in the response over the ranges you have selected.
Even removing the axial points from the design and fitting a full factorial model does not show any significant effects (and does not show a lack of fit either). I think that the variability on your center points (standard deviation = 5.22) is large relative to the standard deviation in the rest of the data. I will say that the ranges for your variables are not very wide. Typically, you want ranges to be wide enough to be able to detect an effect. A seven degree swing from the low axial point to the high and only a four degree difference between the -1 and +1 levels is not very large.
Re: Analysis of CCD resultsI agree with @Dan_Obermiller . The factors do not seem to have much effect on the response over the ranges that you have used. As a chemist, the temperature range does seem very narrow - intuitively I would not expect to see a big change in the response if I change the temperature from 175 to 182 degrees.
This might be a good thing, if this is a robustness study. The results here tell you that you could vary the factors over these ranges and get a consistent response.
But it sounds more like this was an optimisation study. In which case you will have to experiment more boldly to obtain a useful model. You could use Augment Design in the DOE menu to add runs from an expanded factor range.
An option is that you could include the data from your screening design. The combined data set will probably not be balanced but I expect it will include data from a wider factor space and might enable you to build a more useful model.
I have attached you data as a JMP data table.
I hope this all helps.
Phil
Re: Analysis of CCD resultsThank you very much for your replyRe: Analysis of CCD resultsThank you very much @Phil_Kay and @Dan_Obermiller for your insightful comments. Given that I did steepest ascent with 9 steps and saddle point was shown between step 3 and 4 which correspond to my range (176-180°C) (the response decrease from 4 to 9). Is it possible that this is only a local optimum?
