Wrong. Factorial design will work here if I understand your description correctly. See Montgomery Design and Analysis of Experiments available in the z-library for download. Thinking in terms of regression rather than ANOVA should be of help to you. Best wishes David Booth PS follow up with Response surface methods to see if you can optimize your design.

Oops forgot to mention that you will want some type of logistic regression if your DVs are nominal. BTW this may take a bit of research to handle your DVs. Good luck with your research. D Booth

Hi David Eugene Booth ,

Thank you for your suggestions. After some study I think I have a better idea in what is needed to design experiments for nominal response variables.

You are correct that logistic regression is a useful tool for fitting nominal response. However, we need more than a factorial test to determine the factor effects. For example, for a case of 2 factors, the design space is a square and we use the most basic regression function z=a+b1*x1+b2*x2. x1 and x2 are the factors. In order to know how signficant x1 and x2 have on the response, we need to find the line in the design space that on one side of this line the response is likely a pass while on the other side is likely a fail. If one factor has much more significant effect on the other, this line will be close to a horizontal line or a vertical line in the design space (a square if you use the coded variable). On the other hand, if the two factors have equal effects on the response, the line should be parallel to the diagonal of the design space. Factorial test cannot find this line because all the tests are located in the four corners of the design space. However, if we have a grid of tests in the design space, there will be a much better chance in finding the line.

That is all very nice but rest of the model is already known. See Montgomery's Design and Analysis of experiments which is available in the z-library. Good luck David Booth and I believe you have forgotten the interaction terms please read about factorial experiments in the book I have suggested.t

A good course in experimental design would be helpful too. Best wishes David Booth

Just another usefull link for DOE:

5.Process Improvement https://www.itl.nist.gov/div898/handbook/

BTW if you are interested in screening designs you might look at Response surface methods. A section of Montgomery:s book introduced the topic. David Booth

Response surface methods are included in the attached search. D .Booth

This is for binary outcomes.