Reduce Full factorial Seed Saftey DOE with categorical factors

Question

Hi,

my customer has to make sure new treatments do not harm the seeds. Therefore they store seeds with different treatments (untreated, base treatment BT and 5 other treatments combining the base treatment with A1, A2 or B (while A1 and A2 cannot be at the same time means BT+A1, BT+A2, BT+C, BT+A1+C, BT+A2+C). They have in addition 9 different varieties they want to test on. The storage measurements are after the treatment and after 6, 12 and 18 months.

The response should behave the same over time for the 2-3 treatments in focus compared to the base treatments and best to untreated.

Currently they do a full factorial design to get all combinations and especially to be able to see all possible measurements in a graph builder plot. I could briefly see his table and saw 1900 rows, which is a lot and results from measurements on replicates (2-4) on each of the 4 time points.

The goal is to understand especially for the few treatments in focus if they harm the seeds more than the current standard (untreated and Base Treatment). I wonder if we could get less runs and still have most information at least for the treatments in focus?

What would be your best approach to handle this problem? two factors - one with 6 and one with 9 levels, including main effects and interaction effect - OR 1 factor with 9 levels for variety and 3 factors for the treatment (A1, A2 and B each active/not active, with a disallowed combination of A1 and A2 at the same time)? Or some different approach? And does this allow for aximum information for e.g. Treatment BT+A2 and/or BT+A1+C?

Thanks,

Martin

PS: they have to show to customers afterwards that the reults show that there is no difference on the harm effect on seeds with or without the treatment in focus

malcolm_moore1 · Answer

Thanks for the update Martin. It appears the factors are:

* Treatment with 7 levels
* Variety with 9 levels
* Storage time with 4 levels

We will need to understand how the seeds are stored, e.g. does a large batch of seeds get treated with one of the 56 combinations of Treatment x Variety then this large batch of seeds is put in storage and a sample of seeds selected from the batch for each storage test time?

There appear to be three responses: SG, AA and CT. What do we know about what they are calling the replicates for each of these responses? Are they repeat measurements on the same sample of seeds or are they measurements on a different sample of seeds from the larger batch of seeds in storage? What do these measurements represent? Presumably they are germinating the seeds and they are some measures of the resulting plant characteristics?

I'm still wondering where is the opportunity to streamline their current test process? I doubt they will want to reduce the number of test combinations for the Treatment x Variety interaction effects. Nor will they want to reduce the number of time points they sample from storage. The potential saving may therefore come from reducing the number of replicate measurements and understanding the relative size of this component of variance to understand whether 4 (or 2) replicate measurements are needed. If you can get answers to the above questions and their anonymised data, we'll be able to guide them appropriately. Also the information about the motivation to change from my previous reply to your message: what specific benefit do they get by reducing the amount of testing by e.g. 25% or 50% if they were to do this without significant loss of information?

Best,

Malcolm

martindemel · Answer

Hi Malcolm, will do so. Meanwhile here is more detail on the full factorial design:

There are different 7 treatments, 4 different intervals and 9 varieties.
But also, In that particular table we have 3 tests for each case (SG, CT, AA)
Each SG test includes 4 different runs.
Each CT or AA has 2 different runs:

malcolm_moore1 · Answer

Hi Martin,

I suggest the following as a way forward:

* Try and get more details about what it means to the users if they were to save 30 runs - your last paragraph says this would be amazing. What does saving 30 runs mean to them (or even 1 run)? The answer to this question should help motivate your users better.
* Try and get an anonymized version of their data. With that we could compare alternative designs vs their current design using compare designs (and even simulate data based on the model from their data) to determine what loss of information (if any) is obtained with a more efficient design alternative.

The other issues you mention such as nesting or constrained randomisation will become clearer if we can get an anonymized version of their data.

Best,

Malcolm