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Running a split-plot design on two days

BenGengenbach

Hi,

this is actually a follow up question to this post and the related experiment.

I want to keep this very generic that's why I wont go into too much detail.

We want to transfer a particles suspension from a reservoir with varying fill height in which the particles are being agitated.
We have 3 easy-to-change transfer factors, 2 hard to change particle agitation factors and the very hard to change reservoir fill height factor. Hard and very hard can not vary independently.

The anticipated model has been reduced to be in line with our assumptions regarding interactions and general complexity. In order to achieve adequate precision we most likely need 8 whole and 16 subplots but the number of runs required exceeds our daily capacity so we want to run the experiment on two days.

We are not specifically interested in the actual day-to-day effect because this is surely random.

Now can we simply run the first half of the split-plot design on day 1 (whole plot 1-4) and the second half on day 2 (whole plot 5-8) without the need to introduce another Day Blocking factor?

Also should anything keep us from analyzing the first half to check if we might already have achieved sufficient precision and only run the second half if the results of day 1 are inconclusive?

regards ben

Accepted answers

Victor_G

Hi @BenGengenbach,

There are still missing informations about the model terms you want to estimate in your model (or I might have skipped this information), but I will try to help you best. I have created a design with the factors description you mentioned, number of whole plots (8)/sub plots (16) and a model with only main effects (48 runs) in order to have more informed and illustrative answers that correspond to your problem.

First, no problem about the fact that "Hard" and "Very hard to change" factors can not vary independently, this is already an option in JMP during design creation when introducing these types of factors (as you mention):

Concerning your questions :

"Now can we simply run the first half of the split-plot design on day 1 (whole plot 1-4) and the second half on day 2 (whole plot 5-8) without the need to introduce another Day Blocking factor?" : One useful way to look at a randomized block experiment is to consider it as a collection of completely randomized experiments, each run within one of the blocks of the total experiment. Inside each whole plots there is a randomization of the factor levels for easy-to-change factors. Hard-to-change factors levels are grouped in subplots. When looking at the distributions of the factors levels for the first 4 whole plots (or first 8 subplots), you can see that the levels repartition is balanced for all factors :

I would have think the same as Phil to add a blocking variable "Day" would help, but in this case whole plots and subplots effects are already treated as random effects (so you can already estimate the variance of your response(s) from whole plots to whole plots and from subplots to subplots), and adding a blocking variable here would mess the structure of whole plots and subplots (as you already show) :

"Also should anything keep us from analyzing the first half to check if we might already have achieved sufficient precision and only run the second half if the results of day 1 are inconclusive?" : Same answer as Phil, you can absolutely have a look at your first initial results. Just keep in mind that analyzing only half of your results means that you'll have a lower power to detect effects, so a non-significant effect from the analysis of day1 results may become significant when all results are present. Here are screenshots of the power analysis of day1 datatable vs. complete datatable :

The biggest change for detecting effects can be seen for main effects involving hard/very hard to change factors.

I hope these answers will help you.

Please find attached the datatable used for illustration in my answer.

Custom Design_example.jmp

All comments

Phil_Kay

I would say it depends on how concerned you are that something that is outside of your control will have changed that will significantly impact the process between day 1 and day 2. Even then, the fact that you are running this as a split plot means that the model will capture variation between whole plots. Strictly speaking this should probably include a blocking / random effect for day. I can't think of a reason not to add that, other than it will consume an extra degree of freedom.

I am slightly concerned by your description that "Hard and very hard can not vary independently." This makes it sound like all your hard- and very-hard-to-change factors are completely correlated with each other. I suspect that is not what you mean.

And I would say that you absolutely can and should look at your results from day 1. Be aware that this will of course be an incomplete design, so it will probably not be possible to estimate everything that you designed the experiment to test. And precision and power will be much lower. Adding a day blocking factor in the design stage will help to minimise these problems.

I hope that helps,
Phil

BenGengenbach

Hi Phil,

thx for the swift response.

I am sorry but I am not sure if you are saying the extra day blocking effect is not necessary since I am already capture variation between whole plots or that I should add it because such as split plot design should have an extra day blocking factor?

And adding an extra day blocking factor to a Split-Plot design practically means adding another categoric very hard to change factor at two levels and then sorting the design by that categoric day factor? If I include that day categoric factor as a main effect in the model the power hardly changes but fds goes slightly up.

When I try to add a "blocking" factor from the drop down during design generation (with 1/2 of my runs per block) the resulting block structure breaks apart my already existing whole and subplot structure.

"Hard and very hard can not vary independently."

That means I did not check the box during design generation and my blocking factors are nested.

From JMP help:
Checking this option creates a two-way split-plot design. If this option is not checked, the design is treated as a split-split-plot design, with nesting of factors at the two levels.

cheers ben

Victor_G

Hi @BenGengenbach,

Concerning your questions :

"Now can we simply run the first half of the split-plot design on day 1 (whole plot 1-4) and the second half on day 2 (whole plot 5-8) without the need to introduce another Day Blocking factor?" : One useful way to look at a randomized block experiment is to consider it as a collection of completely randomized experiments, each run within one of the blocks of the total experiment. Inside each whole plots there is a randomization of the factor levels for easy-to-change factors. Hard-to-change factors levels are grouped in subplots. When looking at the distributions of the factors levels for the first 4 whole plots (or first 8 subplots), you can see that the levels repartition is balanced for all factors :

"Also should anything keep us from analyzing the first half to check if we might already have achieved sufficient precision and only run the second half if the results of day 1 are inconclusive?" : Same answer as Phil, you can absolutely have a look at your first initial results. Just keep in mind that analyzing only half of your results means that you'll have a lower power to detect effects, so a non-significant effect from the analysis of day1 results may become significant when all results are present. Here are screenshots of the power analysis of day1 datatable vs. complete datatable :

The biggest change for detecting effects can be seen for main effects involving hard/very hard to change factors.

I hope these answers will help you.

Please find attached the datatable used for illustration in my answer.

Custom Design_example.jmp

BenGengenbach

Thank you @Victor_G and thank you @Phil_Kay .

Your answers perfectly complemented each other and now I know what I need.