Three way Factorial arrangement on a RCB
Sometimes 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
- 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.
Different colors represent different combinations of treatments; each drawn box represents a block. There are 3 blocks (I-III) and combinations of 3, 2, & 2 treatments (A-C, changes in red intensity; 1-2, changes in green intensity; and a-b, changes in blue intensity) in this example.
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
ANOVA table format:
|First factor (X)
|Second factor (Y)
|Third factor (Z)
|First X Second (XxY)
|First X Third (XxZ)
|Second X Third (YxZ)
|First X Second X Third (XxYxZ)
|awhere x=number of treatments in the first factor, y=number of treatments in the second factor, z=number of treatments in the third factor and b=number of blocks or replications.|
Sample ANOVA table:
|First X Second
|First X Third
|Second X Third
|First X Second X Third
|aF test with 2,22 degrees of freedom at P=0.05 is 3.44|
bF test with 1,22 degrees of freedom at P=0.05 is 4.30
Sample SAS GLM statements:
CLASS BLOCKS FIRST SECOND THIRD;
MODEL WHATEVER = BLOCKS FIRST SECOND FIRST*SECOND FIRST*THIRD
Washington State University
Tree Fruit Research and Extension Center
1100 N. Western Ave.
Wenatchee WA 98801
Copyright © Washington State University
WSU Electronic Publishing and Appropriate Use Policy
Comments concerning this page to
Thursday, August 24, 2000