Analysis of DoE model with center points

Question

Hello,

I have a d-optimal design with 6 center point experiments. While performing the model building, does JMP take the mean of the 6 center points as a datapoint to fit the model? Or does it take all 6 points as individual points?

What is the correct way to build the model?

In addition, I have one scenario where the variation from the center point replicates is comparable to the variation from the DoE factor variation. In such case, can we conclude that the factors may not be explaining the variation in the response?

Variance from center points= 2.03

Variance from all data points excluding the center points = 2.54

I usually contact @martindemel  for JMP related questions. However, he is away during this week. Hence, posting the question here.

Thank you.

Victor_G · Answer

Both, depending on what you're looking at in the model :

* For the estimation of terms coefficient in the model, the average value of the replicates is used to calculate them (like an ANOVA would do). This enable to have a more precise estimation of effect terms in the model.
* The individual points are used for the estimation of the model variance and to estimate the variance of terms coefficients.

Replication enables the experimenter to obtain an estimate of experimental error, see Key Principles of Experimental Design | Statistics Knowledge Portal | JMP. Replicate experiments are not repeats, even if you can have a similar effect on terms estimation between repeats (conducting the same measurement on the same unit multiple times help reduce measurement error, but not experimental error) and replicates in the model (it will improve the effects estimation), it won't improve statistical significance of terms and of the model or variance reduction, as you need a higher number of degree of freedoms brought by independant experiments (like replicates).

As an example, here is the modeling result from "Bounce Data" in JMP with an unreplicated Box-Behnken design:

By augmenting the design and adding two replicates of this initial design (so that each runs from the original design is independantly present three times in the augmented design), here are the results:

You can see that parameter estimates haven't changed a lot (I just used similar response values for the replicate runs), but the standard error of each effect estimates has largely decreased (and p-values too) in the augmented version, as well as the error of the model (Root Mean Square Error), thanks to this additional degree of freedom brought by the replicates.

Hope this answer will help you,

statman · Answer

Just to be clear, there is a difference between repeats and replicates (yes, words matter).  Repeats are multiple datapoints (e.g., multiple measures of the same experimental unit) while the treatment combination is constant.  Replicates are multiple experimental units for the same treatment combination.  Replicates increase the DF's in the study, repeats do not as they are not independent events.  So do you mean repeats or replicates?

What JMP will do depends on how you set-up the table.  If the repeated data points are in separate rows, JMP will "think" those are independent "events" and will consider them additional DF's.  If you record the repeated data points as separate columns, JMP will "think" those are additional Y's.  You will have to summarize the repeats before doing the analysis of the experiment.  One additional thought is to first determine if it is appropriate to summarize the data points before determining the appropriate statistic.  In other words, are there any unusual data points?  Do the repeats seem consistent within treatment?  If so, then you can calculate the mean and also the variation of the repeated data points.  The variation estimate can be treated as an additional Y.  Therefore you can determine if your model effects impact both the mean AND the variation.

Coverbird30 · Answer

Hello,

Thanks a lot for your reply. It has addressed a lot of my querries. I have one remaining question. In JMP DoE, I got the design from the software. While building the model (All interactions and quadratic effects included) , does the model take the experimental repeats as individual points? Or does it take an average value of the repeats for building the model?