DOE with whole plots and blocking factor - how to improve the design?

Lavik17

I am trying to make a DOE for an experiment where I have one continues variable and two discrete numeric variables that are very hard to change (more information in the image below).

 

 

 

My questions are:

1. I am running the test by columns in a 96 well plate, so is there a way to define that no matter how many runs are needed, a plot will always have up to 8 runs?

2. As is, even with 192 runs in 24 plots, I get a pretty low power for quad effects. Is there anything I can do to improve the design other than just adding more runs?

3. I would like to account for a blocking variable "Plate" as I need more than one plate for this experiment (8 runs in a plot X 12 plots in a plate). Should the blocking variable be set with 96 runs per block? How would the blocking variable affect the whole plot setting? 

Victor_G

Hello @Lavik17,

 

For your first question, there is a possibility to do this :
- Either you can add a blocking factor specifying 8 runs per block (add factor, blocking, 8 runs per block). This way, you can be sure that every plot will contain 8 runs (not recommended if you want to include "plate" later as a blocking factor).
- Either you specify the number of whole plots in order to have 8 runs per plot (in your 96 runs example, you specify 12 as the number of whole plot and you'll end with plot having each 8 runs).

For your second question, I will let experts answer you, but my guess is that any restriction on full randomization reduce the power for your effects. Concerning your quadratic effects, you can try increasing your number of experiments (from the start or by augmenting your design after a first DoE), maybe changing the optimality criterion (to I-optimal ?), change the estimability (from If possible to Necessary). These are just suggestions, and I'm sure experts in this community will have better ideas

For your third question, if you have 192 experiments, you can add a blocking factor "plate" (with 96 runs per block) and specify the number of whole plots to 24 (to have 8 runs per whole plots), in order to fulfill your two conditions. But this will also reduce the randomization, so it may have an effect on the effects power.

 

I hope it help you,