So we have arrived at last! The error SS is calculated as usual by summing the squares of the final residuals

 (+5)2 +(+3)2 +(-9)2 +...+(+18)2 + (-17)2 1094.

The analysis of variance needs some care because the SS for blocks and treatments depend on the order in
which they are fitted. If, as in the procedure above, we first fit blocks (ignoring treatments) the block SS is
calculated from the block totals or means. The treatment SS is calculated from the change in the sum of
squares of the residuals from those obtained after sweeping for blocks (the first time) to those after the
sweeping is completed. Thus

the block SS is((64)2 +(-76)2 +(74)2 +(.63)2)x4 = 78468,

the SS of residuals after sweeping blocks only = 110667,

the SS of residuals after the final sweeping = 1094,

and the treatment SS(adjusting for blocks) = 109573.

Hence we have the analysis of variance


 SS df MS


Blocks (ignoring treatments) 78468 3 26156
Treatments (adjusting for blocks) 109573 3 36524
Error 1094 5 219


The block and treatment effect estimates are built up from the results of the repeated sweeps. Thus for
blocks we have


Block 1 2 3 4


1st sweep +64 -76 +76 -63
2nd sweep +31 +24 -10 -44
3rd sweep +3 +3 -1 -5
4th sweep +1 0 0 0

Total +99 -49 +65 -112



Treatment 1st 2nd 3rd Total


 A -133 -15 -2 -150
 B -31 -4 0 -35
 C +72 +8 +1 +81
 D +92 +10 +1 +103