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Randomize Treatments Within Block

Lovy_Singh

Hi SE Community,

Had a question from a customer on how to randomize all treatments within a block.

DOE has 2 discrete numeric factors with 3 levels. So there are 9 possible treatments. Customer wants to do 3 replicates of each treatment, so total of 27 runs.

They want the runs to be in 3 blocks - 9 runs per block. But for each block to contain all 9 treatments randomized.

Currently when doing the setup JMP will randomize the runs within the whole table. The issue this causes is that each block has repeat treatments at times (see image).

Does anyone know how to make it so each block has all possible treatments, but randomized within the blocks?

thank you!

Accepted answers

DonMcCormack

OK. This is ugly but I think it should always work. A problem with using Custom Design is that you're not guaranteed of having all nine combinations. Use Full Factorial Design under DOE > Classical. Specify 2 Discrete Numeric factors and 2 Replicates. Leave Run Order Randomized.

Screenshot 2025-02-14 at 4.34.59 PM.png

Create the table. Add a column with the sequential row numbers (I've called it Run in the attached table). Create a categorical column Block with this formula

Screenshot 2025-02-14 at 4.38.00 PM.png

where X1 and X2 are your factors. Add it as a random factor to the model.

Screenshot 2025-02-14 at 4.40.37 PM.png

Replace the Model table script with this.

Would probably be a good idea to test this out to make sure it works for you and I didn't overlook anything.

RCBD with 3 reps.jmp

Jed_Campbell

This might be a bit of a hack, but:

DOE > Classical > Full Factorial
Add 2 3-level continuous factors
Click "Make Table" 3 times
Tables > Concatenate those 3 tables, checking the "Create source column" checkbox
Change Table name column to Block, maybe do some checking of numbering to be sure (Checksum column)

I think this results in what you want, but involves some extra steps. Table attached.

3 full randomized repeats.jmp

All comments

DonMcCormack

Screenshot 2025-02-14 at 4.34.59 PM.png

Create the table. Add a column with the sequential row numbers (I've called it Run in the attached table). Create a categorical column Block with this formula

Screenshot 2025-02-14 at 4.38.00 PM.png

where X1 and X2 are your factors. Add it as a random factor to the model.

Screenshot 2025-02-14 at 4.40.37 PM.png

Replace the Model table script with this.

Would probably be a good idea to test this out to make sure it works for you and I didn't overlook anything.

RCBD with 3 reps.jmp

DonMcCormack

Should have added to sort by Block when you're done so the runs are organized by block.

Byron_JMP

Maybe this is a Replicated Randomized Complete Block Design?

DonMcCormack

Yes, it is a replicated RCBD. It has two factors, though. BIBD only let's you have one.

Jed_Campbell

This might be a bit of a hack, but:

DOE > Classical > Full Factorial
Add 2 3-level continuous factors
Click "Make Table" 3 times
Tables > Concatenate those 3 tables, checking the "Create source column" checkbox
Change Table name column to Block, maybe do some checking of numbering to be sure (Checksum column)

I think this results in what you want, but involves some extra steps. Table attached.

3 full randomized repeats.jmp

Lovy_Singh

thanks Don, clever way to use the colrank formula....haven't done it like that before

Lovy_Singh

Hi Jed,

this what I was thinking of doing as well....also never knew about checksum formula, thanks for that