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Our World Statistics Day conversations have been a great reminder of how much statistics can inform our lives. Do you have an example of how statistics has made a difference in your life? Share your story with the Community!
I constructed a definitive screening design for the filtration of particles under different conditions.
The particles express 3 different categorical surface types, C, R and V.
There are 4 different types of filters, HA, HV, Nylon and PES.
The continuous variables are pH and Salt, with centre points.
My responses are particle transmission and contaminant transmission as a percentage of a non-filtered control.
I initially designed the experiment with only pH and Salt with two blocks. As my experiment expanded I duplicated the same DoE for the different surface types and filters, eventually collating into one dataset and adding seperate columns to describe the new filter and surface types.
From this datset I am looking to evaluate the significant factors that impact transmission, identify the best conditions for each surface type and identify the best surface type in general.
I have attempted a full factorial of my categorical and continuous condtions, and response surface, but in my naivety I find reducing my model under effect summary can wildly differ my results.
First of all, this experiment does not seem appropriate for a definitive screening design because you have a small number of factors with which the essential principles of screening are unlikely to hold.
Second of all, the proper analysis depends on the actual run order and the pattern of resetting all factors. I suspect that this experiment is not fully randomized but the models that you mention assume that the experiment is randomized.
Third, I was able to fit separate models starting with the response surface model (all first-order terms and all second-order terms). I eliminated insignificant and unimportant terms before reducing the model to a reasonable, defensible size. There is a Particle Transmission outlier among all the runs:
The terms that I select for the model of Particle Transmission:
The terms that I selected for Contaminant Transmission are:
I optimized the desirably of both response to obtain these settings:
The shallow profile for the joint desirability in the bottom row indicates that there is not much difference in the choice of factor settings. Note that R square for the two models is 0.38 and 0.43, respectively.