Control level in an experiment
In many experiments with a single factor, all factor levels are of equal status and none is of particular interest. There is no reason to design such experiments with different replicates for the different factor levels.
However sometimes experiments have one factor level that is special in some way.
The 'special' level for the factor is called a control level and we are more interested in comparing other levels to the control than to make comparisons between these other levels. In order to estimate the differences between the control and other levels more accurately,
We often design experiments with more replicates of the control level.
Designs with a control level
To illustrate the advantages that can arise from using more replicates for an experiment's control level, we will consider estimation of two types of contrast:
The diagram below describes experiments about the effect of a feed supplement on the weight gained chickens in their first three weeks. Four supplements are being assessed against a control level for which the chickens get no supplement. The experiment will be conducted on 50 chickens (experimental units).
The slider at the top of the diagram adjusts the number of replicates for the control level (and therefore also for the other factor levels since we are limited to 50 experimental units). The two columns at the bottom of the diagram show the standard errors of esimates of six contrasts.
The top two on the left are for the differences in mean weight gain between chickens getting particular supplements and those getting no supplement. The bottom standard error on the left is for the difference between the mean weight gain over all supplements and the control level. Observe that:
Contrasts involving the control level are more accurately estimated (lower standard errors) if there are a few more replicates for the control than the other levels.
The benefits of more accurate comparisons between the control and other levels come at a cost. Since there are fewer replicates for the non-control levels,
Contrasts comparing the non-control levels are less accurate if there are more replicates for the control level.
The decision on how much to increase the replicates for the control level depends largely on the objectives of the experiment.
Randomisation
As with all other experiments, random allocation of treatments to experimental units is critically important. The diagram below illustrates.
In the diagram above, click Randomise experiment to randomly allocate the treatments used to experimental units.
Use the pop-up menu to increase the number of replicates for the control treatment. Randomisation of the allocation of treatments works in exactly the same way as in experiments with equal replicates.