Example 1: Randomized Complete Block Design


We stan with a RCBD example for eight varieties in three blocks (G.Edmeades Ghana data 83T1 sitel5).
We shall consider three components in our model:-

(1) the general mean
(2) the block effect
(3) the treatment effect

The separate consideration of the overall mean is not strictly necessary but is adopted to emphasize the
general principles.


 Block
 1 2 3

Varieties
 1 270 275 360
 2 390 360 425
 3 290 300 235
 4 250 305 240
 5 220 130 33;
 6 315 270 315
 7 365 290 285
 8 285 275 365

 298

 -28 -23 +62
 +92 +62 +127
 -8 +2 -63
 -48 +7 -58
 -78 -168 +32
 +17 -28 +17
 +67 -8 -13
 -13 -23 +67



Mean 0 -22 +21


We first calculate the overall average.

We now sweep out this average from each plot value.



The resulting residuals are the set of deviations
from the overall mean.


The sum of squares of these "residuals about
the overall mean" is the total sum of squares = 89951.

Next calculate the mean for each block
(note that apart from rounding error they sum to zero).