topic Re: Custom Split Plot Design Replicates in Discussions

Custom Split Plot Design Replicates

BenoitM — Mon, 03 Nov 2025 21:44:27 GMT

Hi everyone — I’m planning BioLector (a 48 well bioreactor platform) runs and need advice on implementing my design in JMP. I should note up-front that biological triplicates are applied at the subplot (treatment) level (i.e., three biological replicate wells/runs for each unique combination of the subplot factors A–D within a whole-plot temperature setting).

Experiment context (what I want to do)

Temperature must be constant during a BioLector run, so it is a hard-to-change / whole-plot factor.
Four additional factors A, B, C, D are easy to change and are subplot factors.
The analysis model should include all two-way interactions among the five factors and second-order (quadratic) terms for continuous factors (building a RSM).
I will use biological triplicates at the subplot level (three biological replicates of each A–D treatment combination inside each whole plot / temperature run).
I plan to use JMP Custom Design → split-plot → 6 whole plots (two for each temperature level)and 5 subplots per whole plot, but I noticed the Replicate option in “Augment Design” is greyed out for custom split-plot designs.

What I'd love some guidance on

How to include biological triplicates at the subplot level, given that the usual replicate augment option isn’t available for split-plot designs.
Any general advice or common pitfalls to watch out for. Are there more suitable alternatives out there for my specific case.

Any help is very much appreciated!

Re: Custom Split Plot Design Replicates

Victor_G — Tue, 04 Nov 2025 12:28:09 GMT

Hi @BenoitM,

Welcome in the Community !

I see at least two options that could lead to a design appropriate for your needs:

You could add a 3-levels categorical "Hard-to-change" factor for subplot replicate (A, B and C or 1, 2 and 3 levels), adding the main effect for this subplot replicate factor in the model panel, changing Temperature as "Very Hard to Change" factor, checking the option "Hard to change factors can vary independently of Very Hard to change factors", and specify an appropriate number of whole plots (depending on the number of bioreactor platforms you want to use) and number of subplot (multiple of 3, I choose 3 so that each subplot experiment is replicated 2 times, like you want). This design will create replicate runs in the subplots, but there is no certainty that each run of each subplot will be triplicated.
You could also design first the subplot matrices, by creating 6 RSM designs for 4 factors with 16 runs, and then replicating them each up to 48 runs with the Augment Designs. After this step, you can combine the designs (by concatenating the tables), adding a Whole Plot factor column and applying Temperature factor levels to each of the 6 Whole Plots, and it should lead to the design you want. This option is perhaps more tedious, but it is sure that the replicates constraint will be enforced by having each run of each subplot triplicated. Make sure at the end of this process to randomize order of the runs inside each whole plot, using the workaround found here by using Create a Subset Data Table with sampling rate of 1, and then sort the datatable by whole plot order to keep the split-plot structure.

Either one or the other option should create a design that respect your needs, you may only have to change the assumed model from the "Model" script in the datatable (to remove any effects linked to "subplot replicate" factor and the subplot random effect for option 1 for example).
Please find attached an example of such design, with 288 total runs, 48 runs per whole plot, and 3 replicates for each subplot experiment for both options. Some scripts are also saved in the datatable with the corresponding model assumed "Model (refined)" and some visualization of the design structure.

The comparison of the two designs performance shows similar results:

Power analysis:
Prediction variance and FDS:
Correlation map and design diagnostics:

Hope this answer will help you,

Re: Custom Split Plot Design Replicates

BenoitM — Tue, 04 Nov 2025 14:16:55 GMT

Hi @Victor_G

Thank you so much for the detailed explanation and the example designs! I think I need to clarify my situation a bit better to make sure we're on the same page:

I’m working with three bacterial species (M. sporium, M. buryatense, and M. acidophila). So far, I’ve been creating separate DOE files for each species (I’ve attached these in case that’s useful). Within each whole plot, I have the five subplot treatment combinations. I’m planning three biological replicates per subplot treatment. Across all three species, that gives me a total of 45 treatment conditions (5 subplots × 3 replicates × 3 species) for 1 out of 6 whole plots — which fits well into a single 48-well BioLector plate.

My Main Questions:

How do my 45 wells (15 wells per species) compare to your 48 wells per whole plot? I'm trying to understand if we're talking about the same thing or if there's a fundamental difference in our design structures.
How does having 3 separate species affect the split-plot design? Should "Species" be treated as an additional factor in the design, or is it acceptable to keep them as completely separate designs?
Can I keep my three DOE files separate, or do they need to be combined into a single design file?

I hope this is clear. Thanks again for taking the time to explain this!

Benoît

Re: Custom Split Plot Design Replicates

Victor_G — Tue, 04 Nov 2025 15:31:05 GMT

Indeed, I had some infos missing from the first post and question. I'm not entirely sure to follow :
How many factors do you have in total ? :

Temperature (Continuous, 3 levels, Hard to change),
Species (Categorical, 3 levels, Easy to change),
pH (Continuous, 3 levels, Easy to change),
TN (Continuous, 3 levels, Easy to change),
TN/TP (Continuous, 3 levels, Easy to change),
C/N (Continuous, 3 levels, Easy to change) ?

Do you confirm you would like to create a design with maximum 288 runs with 6 whole plots of 48 runs each ?

The designs options I have posted contained Temperature and 4 continuous factors (pH, TN, TN/TP and CN), but not the "species" factor.

Even if "bacterial species" is missing in my design option 2, you can still use the process used to create your final design:

Create individual subplot matrices for the 5 Easy-to change factors, specifying a model for each matrix with 16 (or 15) runs, and replicate each subplot design to get to the 45/48 subplot parts.
Concatenate the subplot parts to get the final design structure.
Link 2 whole plots to each temperature conditions.
Make sure all column properties and model script are ready for analysis (whole plot random effect column and attribute in model, Hard to change property for Temperature, etc...).

Concerning your two other questions:

@BenoitM wrote:
How does having 3 separate species affect the split-plot design? Should "Species" be treated as an additional factor in the design, or is it acceptable to keep them as completely separate designs

Yes, if species is an easy to randomize/change factor, I think it should be included in the subplot designs matrices. This way, it will make sure that the individual species are facing different levels of the other factors in a randomized way. However, if you want to triplicate each run of your subplot runs, you won't be able to have a full RSM model in only 16 runs with these 5 factors (minimum is 25). You might have to change the estimability of some higher order terms to "If Possible" and/or delete some model terms to reduce the number of runs to 16/15.

@BenoitM wrote:
Can I keep my three DOE files separate, or do they need to be combined into a single design file?

It depends on what you want to do in terms of objectives, modeling/statistical analysis, and practical realization of the experiments.
Will the DoEs be run independantly ? Or by batches ? Do you want to learn/analyze from them globally ? Or incrementally, "DoE by DoE" ? By species or globally ?

The design(s) structure(s) and analysis should reflect your objectives and goals.

Hope this follow-up answer will help you,

Re: Custom Split Plot Design Replicates

BenoitM — Tue, 04 Nov 2025 21:07:18 GMT

To answer some of your questions.

1) How many factors do I have in total?

Whole-plot (hard-to-change): Temperature — continuous (3 target levels).
Subplot (easy-to-change, per-species DoE): four continuous factors — pH, TN, TN/TP, C/N.
Species: I have 3 bacterial species, but I do not want species as a subplot factor, since I would like to analyze each species independently. So, per-species design/model will include Temperature + the four subplot factors (and their two-way interactions / quadratic terms as planned).

2) How the DoEs will be run

The DoEs will not be run independently. Each BioLector run takes roughly a week and will complete a single whole plot (at a fixed temperature) that contains one species block (5 subplots x 3 replicates = 15 wells) from each of the three species’ DoEs for a total of 45 wells (48 is max capacity).
After all runs are complete, I will analyze by species.
I do not want subplot treatments randomized across species, if that makes sense.

Given this setup, I think my question boils down to: Can I keep the attached DoEs separate for each species? If so, what is the most efficient way to include the biological triplicates? Would it be reasonable to simply copy each subplot row twice (to get three replicates per treatment) and then randomize only within each species block on the plate?

I hope this additional context helps in answering my question.

Benoît

Re: Custom Split Plot Design Replicates

Victor_G — Wed, 05 Nov 2025 09:24:46 GMT

Ok, I think I understand what you want to design.
In fact, the three replicates are each allocated to one bacterial species, and that's why you want the runs to be triplicated in each whole plot, to make the visualization and comparison easier.

So using the design option 2 shared before, I have added a column for bacterial species in order to identify the "triplicates" so that each run is allocated to one different species. If you want to create the design from scratch, you can follow the process of design option 2, but keep the replicate runs identification to save some time at the end and be able to attribute the replicates to each species.

I have modified the model script (to analyze by species) and some visualizations, this design should now meet your requirements ?

Let me know if I missed something,

Re: Custom Split Plot Design Replicates

statman — Wed, 05 Nov 2025 16:04:56 GMT

These discussions would be so much easier if the factor relationships with each other and noise were presented graphically.

Sanders, D., & Coleman, J. (2003). “Recognition and Importance of Restrictions on Randomization in Industrial Experimentation”. Quality Engineering, 15(4), 533–543

Bergerud, Wendy A. (1996) “Displaying Factor Relationships in Experimentation”, The American Statistician, Vol. 50, No. 3

Re: Custom Split Plot Design Replicates

BenoitM — Wed, 05 Nov 2025 16:31:18 GMT

Hi @Victor_G — thanks, this is very close and I really appreciate the changes (and the model-by-species script).

One small point I think we still need to clarify: in the current table, the species column nicely tags the three replicate rows, but it seems that the actual treatment conditions inside a single whole plot aren’t truly triplicated. For a given treatment combination within one whole plot, I don’t see three biological replicate rows of that same treatment — instead, the replicates are distributed across species.

To make sure we’re aligned, what I’d like is that for each unique subplot treatment combination, there are three rows of that same treatment (the three biological replicates), and those are labeled with the three species names.

This would mean that for every whole plot, there are only six unique treatment conditions per species (instead of eighteen). This might not be feasible in practice, but if that’s the case, I’m wondering why, when looking at a single species alone (as in my attached DOE files), it is possible to have only five subplots per whole plot (and six total whole plots) and still achieve decent power for all model terms.

Does combining the species into a single design inherently require a larger number of unique subplots per whole plot, or is there a way to preserve that smaller structure while keeping the three-species labeling?

Thanks again — this is getting very close to exactly what I need!

Re: Custom Split Plot Design Replicates

Victor_G — Wed, 05 Nov 2025 17:47:19 GMT

Hi @BenoitM,

Yes, I have understood (wrongly apparently) that the triplicates were used to allocate each treatment to each species, so that the comparison could be easier (and visualizations too). It seems you want in each whole plot same treatment combinations for each of the 3 species, as well as triplicates for each treatment combinations.

If yes, that means you would have only maximum 5 unique treatments of the 4 factors per whole plots, that would then be done for each of the three species (so 3x5 = 15 runs), which then would be triplicated (so ending at 15x3 = 45 runs). There won't be enough runs available to fit a RSM for the 4 easy-to-change factors in each whole plot, as a minimum of 15 unique treatment combinations would be needed.

One strategy would be to simplify the assumed model in each whole plot, so that it fit your requirements.

Another possibility is to use 2 whole plots to fit the RSM (since each level of Temperature is "seen" for 2 whole plots).
To do this, you need to create an I-optimal design with 4 continous factors and a blocking factor (5 runs per block, to allow triplicates for the 3 species), specify a RSM model, adjust the complexity of the model (you need a minimum of 20 runs with this blocking factor and full RSM model for the 4 continuous factors) by removing some terms or changing the estimability to "If Possible", and finally allocate the runs of the first block to the first whole plot of the same temperature, and the runs of the second block to the second whole plot of the same temperature. Then, you can multiply these 5 runs per block by 9, to get your 45 runs per whole plots, and having triplicates of the treatment combinations for each of the three species.

I put an example I have created of these 2 whole plots used to fit a Bayesian I-optimal design for the 4 factors. These 2 whole plots correspond to the same level of temperature, so the procedure would need to be done 2 more times to have the other "parts" of this design (for the 2 remaining Temperature levels).

A little visualization to appreciate the setting of this first part of the design:

Of course the runs need to be randomized inside each whole plot, I just let the order of the construction to facilitate the visualization.

Hope I did understand your needs correctly,

Re: Custom Split Plot Design Replicates

BenoitM — Wed, 05 Nov 2025 19:04:34 GMT

Hi @Victor_G quick follow-up:

If I just want to fit one RSM for the four continuous factors combined across all whole plots (and temperature included in the model, meaning five total factors) instead of a full RSM for every whole plot, would that be a sensible approach?

If yes, would it then be feasible using the 5 subplots per whole plot scheme I described earlier?

Thanks again for your guidance,

Benoît

Re: Custom Split Plot Design Replicates

Victor_G — Thu, 06 Nov 2025 07:59:46 GMT

Hi @BenoitM,

Of course, it is a sensible approach and make the design generation a lot easier.
Here are the steps I followed:

Create a split-plot design with Temperature (Hard to change), 4 continuous factors (Easy to change), specify a RSM model, and create 6 whole plots with 30 runs in total.
Copy-paste this design 2 times, to enter the Bacterial species factor in the design as a new column and allocate one initial design per species.
Copy-paste the previous design by species 2 times, to get the final design with triplicates for the three species in the final design. You should get at the end a 270 runs DoE with 6 Whole plots, each Whole plots with 45 runs (15 runs by species, and each species having triplicates of 5 unique treatments).
Make sure to randomize the runs inside each whole plot, and to order the runs by Whole plots, to respect the restriction randomization.

Here is how the final design looks like with a Cell plot visualization and a Parallel plot (unrandomized, just sorted by Whole Plots to better understand the pattern repetition accross species and Whole Plots):

Please find attached the design proposed with all scripts (visualizations, models, and randomized version of the DOE).

Hope this answer will finally help you get to your final design,

Re: Custom Split Plot Design Replicates

BenoitM — Thu, 06 Nov 2025 12:33:43 GMT

Hi @Victor_G,

Thanks a lot, this is exactly what I needed! :)

One last detail I forgot to mention: the pH levels differ between species (4 - 5.5 - 7 for M. acidophila ; 8 - 9 - 10 for M. buryatense ; 6.5 - 7.5 - 8.5 for M. sporium). I assume it’s fine if I just manually adjust those pH values in the data table for each species?

My sincere thanks again for all your help. I really appreciate the time you’ve taken to guide me through this!

Benoît

Re: Custom Split Plot Design Replicates

Victor_G — Thu, 06 Nov 2025 12:44:59 GMT

Is the pH a factor you would (and could) like to vary for each (or some) species ? Or is it a characteristic of the species ?

In the latter case, pH and species will be confounded, so you can still record the value, but it won't impact the analysis (each species has its pH value).
In the first case, depending on how you can vary this factor (independantly like any other subplot factor, or it's a "result" of the different factors combination), you can either treat it as a factor during design generation (independant factor) or record the values in a new column and treat is as Uncontrolled factor in the analysis/modeling (dependant factor of the other conditions).

If the ranges of pH are different for the species but you can still control it, this pH factor can be introduced in the design as a nested factor within species. You can use the method presented in to build your design with a nested factor, or use a candidate set approach: create all possible combinations of factors, remove the unfeasible ones, and let the Custom design platform choose the relevant and most informative treatments to create your design.

The candidate set approach has been extensively discussed on various use cases in this forum, here are some links to know more:

...

Hope this answer may help you,

Re: Custom Split Plot Design Replicates

BenoitM — Thu, 06 Nov 2025 16:16:13 GMT

Hi @Victor_G,

Thanks again for the detailed explanation.

Just to clarify, I’ll actually be fitting separate models for each species, so I don’t need to estimate cross-species effects. Given that, I assume I don’t need to set up any nesting in the design? My understanding is that nesting would only be necessary if I wanted to create one combined design (and single model) that enforces species-specific pH ranges within the same design table.

Since I’ll analyze each species independently, I suppose I can simply define the pH range differently in each species’ design and keep everything straightforward, does that sound right? Given this context, does it make more sense to simply replace the pH values with the species-specific levels, as I mentioned earlier?

The final design would then be the one you proposed earlier ("Custom Split Plot Design Replicates_F.jmp"), where the pH levels 4 – 5.5 – 7 are kept for M. acidophila, replaced with 6.5 – 7.5 – 8.5 for M. sporium, and with 8 – 9 – 10 for M. buryatense.

Thanks again for all your help,
Benoît

Re: Custom Split Plot Design Replicates

Victor_G — Thu, 06 Nov 2025 16:30:58 GMT

Hi @BenoitM,

Exactly, if you plan to analyze the results separately by species, you won't need any nesting in the design, as there will be separate models and pH ranges ( and/or any other factors ranges) for each species. So you can simply replace the values for pH by the ones used for each specific species. You can then modify the last design proposed "Custom Split Plot Design Replicates_F.jmp" with the actual values for each species.

If you plan on generalizing your analysis and seeing different impacts of pH variations depending on species and other factors, you can then use nesting in the model.

All the best for your experimentation and analysis !