How to code a split plot design in JMP Pro 15

[#1]

Hello,

I need advice on how to properly model a split-plot design in jmp pro 15. I think it needs to have random effects, so an LME model probably will work best I think?

I have three main effects: Temperature(Categorical), Cultivar(Categorical), Cultivar*Temperature.

Response Variable - (Continuous) Germination %

The experiment was conducted on (1)thermal gradient table. The cultivars were randomized in each subplot. (It is listed as 1-5 in order, but they are randomized at that level). The whole plot is the temperature. The split-plot would be the cultivars I believe. (See picture below for table layout.)

My model in jmp was going to look like this:

Fixed Effects:
Cultivar

Temperature

Cultivar*Temp

Random Effects:
Reps[Tempearture]

Does this account for the right error terms in jmp?

[#2]

You should not include Rep in the model. It is automatically used to estimate the error variance. You need a new column called Whole Plot perhaps to indicate when the whole plot factor was reset. This variable will be used to estimate the whole plot variance while the Temperature variable will be used to estimate the fixed effects.

It looks like your design has Temperature as very hard to change and Cultivar as hard to change. That is, you did not randomize with one of these two factors. So you might want to select DOE > Custom Design and define these two factors this way. Select the option for nested levels to match what you did. This way will be easier, I think, than starting with a new JMP data table and creating all the data columns and meta-data to get the best analysis.

The design you made will unfortunately not support estimating and testing the interaction effect. You need to use a larger design in which you reset the temperature.

You could alternatively assume that the whole plot variance is zero and remove the Whole Plot random effect from the model, but that is likely not realistic.

[#3]

Great, thank you for taking the time to answer my question.

This is my first experience with JMP, so I'm not sure what all that means. I'll look through the website and see if I cant find some material to help me get there.

Thank you,
Michael

[#4]

The JMP documentation is a good place to start. See the DOE Guide.

How did you make this design in the first place?

[#5]

Great, I'll look into that. This is actually someone else's data. I was asked to analyze it. The experiment I'm designing is similar, but it will use 3 tables, not just one.

I see you have temperature as a continuous variable. Each temperature was fixed, I.e. temperature 1 = 130°c, 2 =°22 etc... so I've been coding them as categorical.

Many of my peers have split-plot designs too, so I've been trying to figure out how to do this in jmp for all our sakes.

-Michael

[#6]

The modeling type is a choice about how you imagine the effect of the factor. Of course, the temperature levels are fixed by the design. You are only observing the response at a few levels, but the effect of continuous. That is the philosophical consideration.

The practical consideration is about the available degrees of freedom For example, if the effect of temperature is linear then modeling it as a categorical factor requires 4 parameters and 4 degrees of freedom from the data. On the other hand, modeling it as a continuous factor requires only 1 parameter and 1 degree of freedom.

[#7]

This design seems to be putting cultivars in homogenous subplots. I believe the subplots have all 5 cultivars in them (randomized). Temp 4 Whole plot 1 Cultivar 5 in subplot 1

[#8]

Welcome to the community.  mark has already posed some thoughts for you.  I have some additional questions of a more practical nature:

1. Why would you consider temperature categorical?  It doesn't matter that the temps are coded, they can still be continuous and treated as fixed effects in the model.  Also why 4 levels?  Is temperature really hard to change?  Why?

2. It looks like you only have two factors (main effects) in the experiment:  Temperature and Cultivar. And you are suspicious of an interaction effect.  Why 3 reps of the subplot?

3. How adequate is your measurement system (% germination)?

4. One look might appear like you have 4 blocks and you are confounding temperature with the block.  This I would not recommend as you confound noise with a design factor.

5. If temperature is hard to change, then the design you describe has no way to estimate the whole plot error.  If this is the case, you might want to reduce the 3 reps you have of the sub-plots to 2 and then replicate the entire design (then you have a replicate x whole plot term to be used as the error term to compare temperature effects to).

6. I don't know where you are in your investigation? I'm not sure if this investigation is meant to understand the causal structure or to pick a winner?  Why not start with screening 2 levels of temp (extreme) and 2 levels of Cultivars (extreme).  Get an estimate of the first order model and then iterate to expand the space.

For an excellent paper on split plots:

Box, G.E.P., Stephen Jones (1992), “Split-plot designs for robust product experimentation”, Journal of Applied Statistics, Vol. 19, No. 1