Can You Do a Design of Experiments with Different Levels for Different Factors?

Sure, it’s a 2 x 3 design

Experiment Factor A Factor B
1 -1 -1
2 1 -1
3 -1 0
4 1 0
5 -1 1
6 1 1


Thanks Katie(?), for correcting the design display on my first post. You can remove the second one if you wish.

Thanks Mike

Katie I think it is great you bring Michael every now and then. It keeps him occupied.

I don’t understand what you mean by “setup in Minitab 18.” The six point design is all there is and it would just be a matter of building the appropriate spreadsheet for the X’s and Y responses. If you go with just the six points you can build a model where Y is a function of A, B, AB, and B*B. If you toss in a single replicate of one of the design points you could also check A*B*B.

You would reduce the model to just the significant terms in the usual way – first plot the data and see what you see, run backward elimination and forward selection with replacement regression and check the final model using residual analysis. If all is well then you would confirm the validity of the final reduced model by using it to make predictions with certain combinations of A and B, run those combinations, and see if your final result was inside the prediction error limits associated with your prediction.

If you have more than one Y you would follow the above procedure for each of them and then you would use all of the equations together to predict a couple of optimum conditions (these will most likely be trade offs – most of the time you can’t get all of the Y responses simultaneously at their optimum level for a given level of A and B) and you would test the predictions in the same manner as above.

Hi Tino,

Get a copy of Design and Analysis of Experiments by Douglas Montgomery. Chapter 5 will introduce you to factorial designs with some very good examples. What you are asking about is rather straightforward and well-explained in Montgomery’s book.