Standard errors for estimates
In the design of an experiment, the decision to vary a factor at block level instead of at the level of the experimental units should not be taken lightly.
If a factor is varied at block level in an experiment, its effect will be estimated less accurately than if it had been varied within blocks.
Researchers should therefore vary factors at the finest level that is practical in an experiment.
Illustrative example
The diagram below shows 54 experimental units blocked into groups of 6. The sliders above the scatterplot adjust the amount of variability between the blocks and within the blocks and the scatterplot shows the response values that might have been obtained if no factors were varied in the experiment.
We now consider a split-plot experiment using the same experimental units in which factor A (with 3 levels) is varied at block level and factor B (also with 3 levels) is varied at unit level.
The two standard errors under the table describe the accuracy of estimates of the differences between the mean response at levels 1 and 2 of each factor.
Adjust the sliders and observe that: