Randomization with Blocks

[#1]

Hello

I have a Definitive Screening Design and, as JMP suggests, I selected blocks with center points to estimate quadratic effects. This results in two blocks (Block 1 and Block 2). Now I want to randomize. JMP suggests randomizing only within the blocks. I believe this is correct. However, the blocks are then not interleaved during execution (e.g., 1 1, then 2 2, then again 1 1, then 2 2, etc.), but instead, all runs from Block 1 are performed first, followed by all runs from Block 2. Is that still acceptable?

Regards Klaus

[#2]

Blocking is a strategy to handle noise in experimentation. It accomplishes 2 things:

1. Increases the inference space, hopefully allowing conclusions to be extrapolated into the future

2. It increases the precision of the experiment.

This is because the noise confounded with the block is constant within the block (reducing the effect of noise),  The noise constant within the block is then purposely changed between the blocks and is therefore assignable to the block effect.

Randomization is a strategy to handle noise that has not been identified by the experimenter.

"Block what you can, randomize what you cannot." G.E.P. Box

[#3]

Hi @NominalGemsbock3,

Blocking is a technique for dealing with nuisance factors.

A nuisance factor is a factor that has some effect on the response, but is of no interest to the experimenter; however, the variability it transmits to the response needs to be minimized or explained.

Blocking is the arranging of experimental units that are similar to one another in groups (blocks). The intent of blocking is to prevent large differences in the experimental units from masking differences between treatment effects, while at the same time allowing the treatments to be examined under different experimental conditions.
Practical situations involving blocks could be the use of different batches for raw materials, different operators, devices, or a practical constraint for running the experiments (for example, being able to run only 4 experiments per day). In all these situations, the use of blocking enables to have similar blocks of experiments, that help take into account this "constraint" without reducing the possibility to detect the effects of interest.

So blocking will force a specific order for running the experiments, to reduce the nuisance factor(s) behind it. You should not randomize the order of runs between blocks, the randomization is only set within blocks.

To learn more about blocking:
https://www.stat.purdue.edu/~zhanghao/STAT514/Lecture_Notes/LectureNotes13-Complete-Block-Design-.ht...
https://online.stat.psu.edu/stat503/lesson/4

Hope this complementary answer will help you,

[#4]

Thank you for the answers. In general, I do understand the purpose of blocks, but I don’t understand how introducing blocks into a DSD is supposed to help detect quadratic effects more effectively. How does that work?