Split-split-plot and more experimental designs

Split plot and strip plot (or split block) designs are commonly used in the agronomy, however, they don’t stop there.  We quite often have limited resources and may add on a factor or two on top of our current trial.  This blog post and session will expand on the Split-plot and the Strip-plot (split-block) designs.


We have 3 experimental units with 3 differing sizes.  The whole plot, the sub-plot, and the sub-sub-plot.  This link contains a PDF document that displays the Split-split plot design and also contains the Statistical model.

Factor A is the Whole plot – with two levels: A1 and A2.  A1 and A2 are randomly assigned within a block (or rep).  In this illustration we have 2 Blocks (Reps).Main plot of a Split split plot design

The WHOLE plot is now divided into SUB Plots.  Factor B, which has 3 levels is randomly assigned to each level of Factor A in the WHOLE plots.Sub plot of a Split split plot design

The SUB plot is now divided into SUB-SUB Plots.  Factor C, which has 5 levels is randomly assigned to each level of Factor B in the SUB plots.Sub Sub plot of a Split split plot design

Let’s build the model for the Split-Split plot design as modeled above:

Statistical model for a SPlit SPlit plot design

Definition of the Statistical model for the Split split plot design

Split-split-split plot

An extension of the split-split-plot, with a 4th experimental unit.  Same as above 4 differing experimental unit sizes, and therefore 4 errors to be aware of.

Split-plot x Split-block (strip-plot)

The combinations do not seem to end.  The more we look into these designs, the more I realize that many trials that we currently conduct may not be what we think they are.

In this case we are looking at the Split-block or Strip-plot design and within each row/column combination we are adding a third factor within this experimental unit and will aim to randomly assign them – leading us to a Split-plot x split-block design.

I will update with a picture of a design and the statistical model that accompanies it.



After working through these three examples, which design do you think you truly have?

I propose for the last workshop session in April, that we review Latin Square designs, and the combination of Split-plot and latin squares, as I suspect this will talk to a few researchers 🙂


3 thoughts on “Split-split-plot and more experimental designs”

  1. C’est vraiment simple à comprendre merci beaucoup mais j’ai une question: quelles sont les avantages du dispositif split split plot

    1. Sorry for the very late response – the design you choose depends on your experimental units and treatments and how you can apply them. If you want more info email me and we can chat

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