A test for curvature in a factorial experiment is the p-value of the centerpoint effect. It is calculated by getting the statistical significance of the difference between the centerpoint value and the average of the modeled corner points. I'd like a way to see this in an ANOVA table or a lack of fit table. I'd like a way for the model fit to exclude the center points. I'd like the model to not include effects that I'm pooling into the error. In other words, I'd like to get JMP to do what Minitab does.
This doesn't seem to be an option in the standard features of JMP 16. It I'm wrong about this, please point me to how to do it.
If I'm right, I still want to do it in JMP. My question is whether it would be a possible for a script to do it, or whether this would be impossible and I should just give up and do it by hand. The main challenge to me is I don't know how to use a script to extract sums of squares and degrees of freedom from a model report.
I could create a JMP script that would do this:
- For the centerpoint:
-- Calculate Ybar-center, the average response for rows that have a "0" in the "Pattern" column (center points)
-- Calculate Ybar-corner, the average response for rows that don't have a "0" in the "Pattern" column (corner points)
-- Determine the number of center points and corner points to get degrees of freedom, DFcenter = Number of centerpoints - 1
-- Calculate the sums of squares of error of the center point replication
--- SScenter-error = (sums of squares of differences between centerpoint values and Ybar-center)
-- Calculate the sums of squares for curvature effect
--- SScurvature = Ncorner * Ncenter / (Ncorner + Ncenter) * (Ybar-center - Ybar-corner)^2
-- Mean square of curvature effect
--- MScurvature = SScurvature / 1 degree of freedom.
Now I need the total mean square error. This error should include the pure error of any replicated center points as well as the error of replicated corner points and of the contribution of unmodelled effects.
- To get the sums of squares of error in the model and the degrees of freedom in the error, excluding all centerpoints, the script does this:
-- Exclude rows that have a "0" in the "Pattern" column
-- Show the model dialog so the user can select which effects to include
-- Create the model
-- Somehow extract the sums of square of error
--- SSmodel-error = (SSpure-error + SSlack-of-fit) and the degrees of freedom for error DFmodel-error
-- Add the sums of squares of error from the centerpoints to the sum of squares of error of the model.
--- SSerror-total = SScenter-error + SSmodel-error.
-- Then MSerror-total = SSerror-total / ( DFcenter-error + DFmodel-error)
-- Calculate F ratio for curvature effect = MScurvature / MEerror-total.
-- Then get p-value from the F distribution.
Will it work? What guidance could you give about the approach or the scripting? Any amount of canned automation would be welcome?
Thanks,
Mike