Matched pairs

The experimental units are sometimes naturally grouped into pairs, as in twin studies. However we can use any available information — numerical, categorical or even subjective judgement — to create pairs.

When the blocks (pairs of similar units) are created in this way, they are called matched pairs. If the number of expeirmental units is n = 2g, we therefore have g of these matched pairs.

Estimated effect of the factor

As in a completely randomised design, a randomised block design applies each factor level to half of the experimental units. Therefore the best estimate of the factor's effect is again the difference between the mean response at the two factor levels.

This estimated factor effect (difference between the level means) is less variable in a randomised block design.

The factor effect is estimated more accurately in a randomised block design than in a completely randomised experiment with the same experimental units.


Feed supplement and beef from cows

The diagram below simulates experiments using a similar herd of calves that were used to show the effect of variable experimental units in the previous section. We now assume that the initial variability in calf weights is unavoidable.

Initially click Accumulate then click Conduct experiment several times to see the variability in the estimate of the feed supplement's effect in a completely randomised experiment. Observe that the estimate is very inaccurate.

Now select Paired by calf weight from the pop-up menu. In this experimental design, the calves are grouped into matched pairs with similar weights before the experiment is started, as illustrated by the vertical bands on the scatterplot. In this randomised block design, exactly one calf from each matched pair is given the feed supplement.

Repeat this experiment several times and observe that the estimate of the effect of the feed supplement is much less variable (more accurate) with the randomised block design than in the earlier completely randomised experiment.