## Three way Factorial arrangement on a RCBSometimes the researcher will want to look at the effect of three different factors superimposed on each other. This is often handled with a 3-way factorial arrangement (but also look at the split-split plot design). The 3-way can also be applied to the CRD and Latin square designs.
- Treatments are combinations of three factors, such as chemical compositions and methods of applying chemicals. This is an arrangement of treatments within a RCB design.
- Treatments are assigned at random within blocks of adjacent subjects, each treatment once per block.
- The number of blocks is the number of replications.
- Any treatment can be adjacent to any other treatment, but not to the same treatment within the block.
Block I Block II Block III C1a B2a C2a C1a B2a B1a B1a A2a C1b B1a B2b A2a A2b A1a B2b A2a A2b A1a B1b B2b A1b A1a C1b C2b A1b C2a B1b A2b C1a A1b C2b C1b C2b B2a B1b C2a
PROC GLM; CLASS BLOCKS FIRST SECOND THIRD; MODEL WHATEVER = BLOCKS FIRST SECOND FIRST*SECOND FIRST*THIRD SECOND*THIRD FIRST*SECOND*THIRD; RUN;
- Randomized Complete Block (RCB): Treatments are from a single set.
- Two-way Factorial arrangement on a RCB: treatments are combinations of two sets of factors.
- Split-split Plot on a RCB: one set of treatments is assigned at random to experimental units; a second set is assigned to at random to sub-units; and a third set to sub-units of the second.
- Split-block design: one set of treatments is randomized in one directios; a second set is randomized in a second direction.
- Regression--comparing trends from different treatments: a set of treatments from a quantitative range are crossed on treatments from a qualitative set.
- RCB repeated in time: one set of treatments is examined at different times.
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