Randomisation for balanced incomplete block designs
There are several stages to the choice and randomisation of a design.
Simple lattice designs
The first step above should be modified to generate a simple (unbalanced) lattice design.
Groups of blocks
In some designs, the blocks can be grouped into two or more sets of blocks, each of which contains equal numbers of all treatments. In particular, lattice designs separate into groups of r blocks. If the physical blocks can be grouped into 'super-blocks' in this way, the allocation of rows of the design to the physical blocks should be modified:
Illustration of randomisation
The diagram below shows the last three steps for randomisation of a balanced incomplete block design for 7 treatments in 7 blocks of size 4. The basic design that is shown below was obtained from tables.
Click Permute treatments to randomise the treatments and Permute blocks to randomly allocate rows from the basic design to the physical blocks.
Now click the checkbox Allocate to units then the button Randomise to randomly allocate the treatments within each block to its experimental units.
Further analysis
The analysis described in this section does not use all of the information available in the data about differences between the treatments.
In the next chapter, we will show that independent information about the differences between the treatments can be obtained from the block totals.
This analysis is however more complex.