Known differences between the experimental units
When nothing is known about the differences between the experimental units before the experiment is conducted, we can do no better than to randomise allocation of treatments to the units. Randomisation avoids systematic over- or under-estimation of treatment effects. However...
When more is known about the differences between the experimental units, we can improve on this simple randomisation.
Randomised block designs
If information about the experimental units is know before the experiment is started, they can sometimes be grouped into blocks of similar units. More accurate results are obtained if a separate experiment is conducted within each block with treatments randomly allocated to the experimental units in the block. Although all data are analysed together, the lower variability of experimental units with each block means that differences between the treatments can be more accurately estimated.
Since treatments are randomly allocated within blocks, this design is called a randomised block design. Although it is not essential,
If possible, researchers usually try to define blocks that have equal size and use each treatment the same number of times within each block.
Effect of enzyme on production of corn syrup
Enzymes are used in the commercial production of corn syrup from the starch in milled corn (maize). A researcher wants to assess how the quantity of enzyme used affects the percentage of glucose in the resulting syrup. Three quantities of enzyme will be used to process batches of corn that have been obtained from three different suppliers.
We will initially examine a completely randomised design. The 36 pictures above represent the 36 batches of corn. Click Randomise treatments a few times to show how the 12 batches getting each level of enzyme are randomly selected from the 36 batches.
Since the batches have been obtained from three suppliers and there may be differences in corn quality between suppliers, we can use the suppliers to define blocks of batches. Select Randomised block from the pop-up menu to group the batches of corn by supplier.
Click Randomise treatments a few times to randomly allocate each of the treatments to 4 of the 12 batches within each block. Note that the randomisation is applied within each block.
The factor effects can usually be estimated more accurately from a randomised block experiment than a completely randomised one. However experimental units in industrial experiments usually have less prior structure than in agricultural or biological experiments, so we will not further examine the use of blocks in this e-book.
We refer readers to the companion e-book Experimental Design for Agriculture and Biology for examples of the use of blocks in experimental design.