The model term is not significant, why not delete it ?

[#1]

[#2]

I'm not sure why you are directing this question to the JMP community?  You should inquire with the author (Doug Montgomery). There are a number of reasons to include an "insignificant" term in the model, for example:

1. Heredity: the other factors in the interaction are still in the model

2. Hierarchy: higher order terms are in the model

3. Statistical significance is conditional, therefore removing a term can change the significance of other terms in the model

4. Utility: The experimenter may need to take advantage of this for practical purposes (vs. statistical)

[#3 · Accepted solution]

Hi @Rily_Maya,

If you take a look at the design and factors used, you will see that zi variables are noise variables, and xi variables are controllable variables.

The aim of the design is to find the right settings of xi variables that enable to handle as efficiently as possible the noise variables, so you need to estimate these interactions (and the DoE has been created to do so). If you don't introduce these interaction terms in the model, then noise variables are independant of the controllable variables, so you can't have any actions to lower the experimental noise thanks to process variables. In this case, you want to reduce as much as possible the noise influence on the outcomes by varying the process factor in optimal settings, so you're more in a predictive/robustness objective than a screening (using statistical significance metrics like p-values) objective.

Besides the other reasons mentioned by @statman, keeping the xi * zi variables interactions enable to have curvature effects on the responses. Removing such interaction (even if non significant) could remove a little curvature effect, and perhaps "over-simplify" the system understanding and system robustness to noise.

Hope this answer might help you,