Matched groups to compare 3 or more factor levels
The idea of using matched pairs of experimental units to give more accurate comparisons of two factor levels can be generalised to experiments with 3 or more factor levels.
The experimental units can be grouped into collections of similar units whose size equals the number of factor levels. The different factor levels are randomly allocated to the units within each such matched group.
Again, this type of experiment results in more accurate estimates of the differences between the factor levels than a completely randomised experiment.
Three diets and beef from cows
The diagram below simulates experiments using a herd of 21 calves of varying weights. An experiment is to be conducted to compare a standard diet and two new diets (3 different factor levels).
Initially click Accumulate then click Conduct experiment several times to see the variability in the three estimates of the differences between the three diets in a completely randomised experiment. Observe that the estimates are all very inaccurate.
Now select Grouped by calf weight from the pop-up menu. In this experimental design, the calves are grouped into matched groups of three with similar weights before the experiment is started, illustrated by the vertical bands on the scatterplot. In each of these matched groups of calves, exactly one is randomly chosen to get each of the diets.
Repeat this experiment several times and observe that estimates of the differences between the diets are much more accurate than with the earlier completely randomised experimental design.