I want to test a number of supplements added to cell culture flasks - basically a screening experiment + or - 7 different factors. Each supplement will be tested at 1 concentration on top of the control process, but I don't want to add more than 2 to any flasks at a time. So I have 7 supplements and I want to look at effects of individual supplements and 2-way interactions among them. Is there an easy way to make this design? Everything I try makes some conditions with 3 or more factors added at once. The only thing I have found that seems like it would work is "disallowing combinations" but I have to disallow lots of them, so I'm hoping there's an easier way. Or maybe I'm looking at this the wrong way altogether??
I'd appreciate any advice. Thanks!
Have you considered using a Mixture Design approach. It sounds like you are making a formulation. Try a 7 factor Simplex Lattice with number of levels=2. That would give you experiments with 100% of each main effect supplement and the binary blends.
Thanks for the suggestion. I did consider that (and looked into it again since you suggested it), although it's not a formulation experiment. The problem is the supplements I'm adding don't make up a major component of the total composition of the mixture (maybe 5-10% total) so I'm not sure if this approach makes sense. For each supplement I wouldn't be adding half as much when there are 2, I would be adding both at the full concentration. And since they are such a small proportion of the total, I would assume little affect of adding 2 versus 1 on the proportion of the other. I don't know if I'm explaining this well... It's more of a +/- experiment, rather than concentration based.
If it isn't a mixture design then why wouldn't you go with the settings recommended to delineate your desired model? The whole basis of DOE is to vary the factors in such a way so that you are able to make statements about the impact of those factors. This gives settings that varies them in such a way so as to keep the terms orthogonal so that the factors are independent.
Contrast the above to a design where you are investigating 7 factors and restricting it to only two factors being changed together at any one given time you would obtain the following diagnostics
Perhaps however you may only be interested in understanding a 21 level categorical experiment where you are examining all the pairs of supplements (AB, AC, AD, AE, AF, AG, BC, BD, BE, BF, BG, CD, CE, CF, CG, DE, DF, DG, EF, EF and FG).
Thanks for you help! I thought maybe I was approaching the whole question wrong. I ended up dividing the factors up into groups by type of supplement and doing a 3x3x4 factorial design. Basically I rethought my approach to the experiment.