24-deep well plates with hard to change factors

[#1]

Hi,

I am setting up an experiment using 24-deep well plates, with 5 factors, among which 2 are temperature and time. These are hard to change factors, since the deep-well plate has to go to the freezer or to the heater for certain amount of time, while other 3 parameters can vary between deep wells across the plate.

I was just wondering if setting up a DoE using hard-to-change factors and ending up with a whole-plot DoE, inducing a random effect error, is necessary here? Alternatively, I could just put those factors as easy-to-change, and then sort the DoE table by temperature and time, ending up essentially in the similar DoE layout. I know that randomization would be "violated" in the latter case, but I suspect that this should not be an issue here, given that each plate will be filled separately anyway. So I guess the run order is not important, since there is no "memory effect".

The reason for avoiding hard-to-change factors is that the optimal number of runs (and consequently plates) increases, and I am quite limited. Furthermore, the DoE diagnostics (correlation matrix, prediction variance) looks worse. Also, the design with hard-to-change factors is not balanced, thus some combinations of factors do not appear, contrary to when using easy-to-change factors.

Any thoughts or comments would be appreciated. Thanks.

[#2]

Hi @aatw,

Yes, the setting of the DoE through a Split-plot configuration (with "Hard to change" factors) is necessary here for several reasons :

•  Creating the design directly through a Split-plot configuration ensures the runs are balanced between blocks and inside blocks. Rearranging the runs "manually" could lead to small imbalance between or inside blocks (and possibly the introduction of bias/noise by this manual arrangement) that would be less optimal than the runs arrangement proposed by the Split-plot design structure.
• More importantly, there are two "structures" in your experimental setup: one plate structure, where temperature and time are applied for a whole plate, and a well structure, where each well can receive a combination of the three "Easy to change" factors. This creates a strong difference in the degree of freedoms used for the analysis between "Hard to change" and "Easy to change" factors, that won't be taken into consideration if you're arranging the runs manually, as the analysis will be done wrongly with the same degree of freedom for every factor. So your estimates, confidence intervals and p-values for the "Hard to change" factors will be biased and falsely (optimistically) estimated.
• The random effect also ensure to capture any variation from plate-to-plate, which can help better estimate the "Easy to change" factors. If you don't use this random effect through a Split-plot design, the variance from plate to plate will be pooled with the rest of the unexplained variance, which may hide some effects. Split-plot design offers high precision in estimates, except for whole plot main effects. 

In your analysis, the main effects linked to "Hard to change" factors are left in the model anyway. Note that "Easy to change" factors and interactions between "Easy -" and "Hard to change" factors have higher power, resulting in better estimates.

For your specific use case, if you can afford 5 plates, each with 24-deep well, the evaluation of the design seems quite positive:

I attached the Split-plot design used if you want to evaluate it.

About your concern with some factors combination not appearing, is there a specific practical reason to include some of them ? If yes, you could prepare a Candidate set with all the combinations you would like to have in the design, and use it as Covariate factors: Design with Hard-to-Change Covariates
See the talk from Christopher Gotwalt about Candidate set approach : Candidate Set Designs: Tailoring DOE Constraints to the Problem (2021-EU-30MP-78... - JMP User Commu...

More infos about Split-plot designs:
Split-Plot Designs
Lecture_13
LinkedIn post about Split-plot designs 
Designs with Randomization Restrictions
Recording DOE Club with Jacqueline Asscher and Phil Kay - JMP User Community

Hope this answer will help you,