Observation of the pattern in this table suggests that the four columns are each either all + or all -. This
corresponds to the CxD interaction (check with the original table of treatment combinations) and this
would seem to be the next effect to consider. The means for the four columns are +46, -46, -46 and +46.
and the reduced effects are:


+9 +19 -1 -27
-22 +16 -42 +48
-18 +26 0 -7
+31 -62 +40 -11


and are clearly now very small. The sum of squares of these reduced effects is now 27110 on 8 df and there
is clearly no point in searching for further effects. If we had wished to examine other effects we would use
the table of treatment combinations to identify the four sets of four values from which we should calculate
means.

The tables of means which we require to summarize the results are two-way tables for (1) factors A and B
and (2) factors C and D. The means are calculated from the mean effects previously calculated and the
overall mean. Thus for the four combinations of A and B the combination means are calculated:


Factor A B

Levels 1 1 535 +66 -9 +34 = 626
 1 2 535+66 +10-34 = 577
 2 1 535 -67 -9-34 = 424
 2 2 535-67+10+34 = 502

 1 Mean 535+66 = 601
 2 Mean 535 -67 = 469
 Mean 1 535 -9 = 526
 Mean 2 535 +10 = 545


The standard form of presentation for the two-way table is:


Factor B Factor A
 1 2 Mean

 1 626 577 526
 2 424 502 545

 Mean 601 469


Standard error for comparing marginal means:

 q(2(135209/14)/16) = 35