Standard error for comparing means in the table:


 q(2(135209/14)/8) = 49

The two-way table of means for factors C and D is constructed in the same manner:


Factor D Factor C

 1 2 Mean


 1 455 462 459
 2 515 708 613

 Mean 485 585


The standard errors are exactly as for the table for factors A and B

Example 3 Incomplete Block Design

When each block contains a different set of treatments the result of sweeping, first by blocks and then by
treatments. will not leave residuals which sum to zero both for each block and for each treatment. Consider
a very simple example with four treatments in four blocks, arranged so that each block includes only three
of the treatments.


 Block
 1 2 3 4

Treatment
 A 410 260 360
 B 510 370 320
 C 640 590 430
 D 510 640 430


To understand the process better we shall consider first the situation where all 16 combinations are
available.


 Block
 1 2 3 4

Treatment
 A 410 260 360 190
 B 510 370 480 320
 C 640 470 590 430
 D 650 510 640 430