Curiosity question: How can a DoE factor setting cube with 3 dimensions be explained.

Question

Dear JMP-expert,

I have a very general and maybe stupid question.

After a DoE plan is sketched I usually use the 3D scatterplot to check the  factor setting.

Its is easy to understand for 2 factors, that a 2 D plane can be used to visualize the experimental space and a cube can be used to visualize the experimental space for three factors.

Just theoretically: What is now the geometrical representation of a 4 factor design up to n-factor design?

Is simple 4 factor experimental design with two factor setting per factor (only  factorial points) a tesseract?

Hope this question is not too stupid, but it would help to explain experimental spaces to non DoE experts.

Thanks in advance!

SDF1 · Accepted Answer

Hi @DualARIMACougar ,

Well, since we can't actually generate plots of things that have more than 3 dimensions, it will be challenging to try and show larger dimensional DOEs, but I wouldn't consider a 4-factor DOE to be a tesseract because the three axes that make up the cube are three of the four factors in the DOE design space, so the extra cube in the cube is still in the DOE design space of those three dimensions.

In my opinion, especially when explaining DOEs to non-DOE experts, it's actually better to keep things as a 2D plot. So, if you have 3 factors, you'd plot X1 vs X2, X1 vs X3, and X2 vs X3. Similarly for 4 factors, it would be X1/X2, X1/X3, X1/X4, X2/X3, X2/X4, X3/X4, and so on for n-factor DOEs. You can see that as the number of factors increases, the number of plots goes up pretty quick. Most people often find two dimensional graphs to be more understandable, and sometimes 3D scatterplots can be a bit confusing and overwhelming for a viewer, especially when the graph is static and the person can't turn the scatterplot. 2D just makes things a lot easier to understand. The good thing is that with Graph Builder, you can put several different columns (factors) on either the X-axis or Y-axis, so you can have multiple plots in a single graphic.

Hope this helps!,

DS