The initial analysis of variance calculated from the block deviations from the overall mean. the treatment
effects and the final residuals is


 SS df MS


Blocks 35350 3 11783
Treatments 543798 14 38843
Error 135209 14 9653


Note that there are only 14 df for the treatment SS because one treatment effect, the four factor interaction,
is identical with the difference between blocks (1-2+3-4).

For the second stage of the analysis we consider the treatment means in systematic order.


 Treatment Effect Treatment Combination(ABCD)


 +20 +90 +18 +236 1111 1112 1121 1122
 -60 +38 -72 +262 1211 1212 1221 1222
 -208 -104 -182 +55 2111 2112 2121 2122
 -72 -105 -55 +138 2211 2212 2221 2222


The means for the two levels of factor A are:

Level 1 (+20 +90 +18 +236 -60 +38 -72 +262)/8 = +66
Level 2 (-208 -104 -182 +55 -72 -105 -55 +138)/8 = -67.

The SS for the Main Effect of A is (662 + 672)x16= 141512
and we subtract the means from the treatment effects to get:


-46 +24 -48 +170
-126 -28 -138 +196
-141 -37 -115 +122
 -5 -38 +12 +205


The means for the two levels of factor B are -9 and +10, the SS for the Main Effect of B is 2888 and the
reduced effects are


-37 +33 -39 +179
-136 -38 -148 +186
-132 -28 -106 +131
-15 -48 +2 +195