The Randomized Complete Block (RCB) with subsampling
Field marks:
 Replications of treatments are assigned completely at random to independent groups of experimental subjects within blocks.
 Each treatment is repeated more than once per block.
Sample layout:
Different colors represent different treatments. Blocks are
arranged in vertical rows. There are 4 blocks (IIV) of 3 treatments (AC) with 3 subsamples (ac).
Aa Ab Ac + Ba Bb Bc + Ca Cb Cc + Ba Bb Bc
Ba Bb Bc + Aa Ab Ac + Ba Bb Bc + Aa Ab Ac
Ca Cb Cc + Ca Cb Cc + Aa Ab Ac + Ca Cb Cc
Block I + Block II + Block III + Block IV
ANOVA table format:
Source of variation 
Degrees of freedom^{a} 
Sums of squares (SSQ) 
Mean square (MS) 
F 
Blocks (B) 
b1 
SSQ_{B} 
SSQ_{B}/(b1) 
MS_{B}/MS_{E} 
Treatments (Tr) 
t1 
SSQ_{Tr} 
SSQ_{Tr}/(t1) 
MS_{Tr}/MS_{E} 
Experimental Error (E) 
(t1)*(b1) 
SSQ_{E} 
SSQ_{E}/((t1)*(b1)) 
MS_{E}/MS_{S} 
Sampling Error (S) 
t*b*(s1) 
SSQ_{S} 
SSQ_{S}/(t*b*(s1)) 

Total (Tot) 
t*b*s1 
SSQ_{Tot} 


^{a}where t=number of treatments, b=number of blocks and s=number of subsamples. 
Sample ANOVA table:
Source of variation 
Degrees of freedom 
Sums of squares (SSQ) 
Mean square (MS) 
F 
Blocks 
3 
64.32 
21.44 
2.16^{a} 
Treatments 
2 
201.86 
100.93 
10.17^{b} 
Experimental Error 
6 
59.53 
9.93 
1.64^{c} 
Sampling Error 
24 
145.18 
6.05 

Total 
35 
470.89 


^{a}F test with 3,6 degrees of freedom at P=0.05 is 4.76
^{b}F test with 2,6 degrees of freedom at P=0.05 is 5.14
^{c}F test with 6,24 degrees of freedom at P=0.05 is 2.51 
Sample SAS GLM statements:
PROC GLM;
CLASS BLOCKS TREATS;
MODEL WHATEVER = BLOCKS TREATS TREATS*BLOCKS;
TEST H = BLOCKS TREATS E = TREATS*BLOCKS;
RUN;
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Wednesday, August 16, 2000
