Blocking (statistics)

However, the different methods share the same purpose: to control variability introduced by specific factors that could influence the outcome of an experiment.

The foundational concepts of blocking date back to the early 20th century with statisticians like Ronald A. Fisher.

His work in developing analysis of variance (ANOVA) set the groundwork for grouping experimental units to control for extraneous variables.

To address nuisance variables, researchers can employ different methods such as blocking or randomization.

Blocking involves grouping experimental units based on levels of the nuisance variable to control for its influence.

Randomization helps distribute the effects of nuisance variables evenly across treatment groups.

[5] The blocks method helps proving limit theorems in the case of dependent random variables.

By blocking on sex, this source of variability is controlled, therefore, leading to greater interpretation of how the diet pills affect weight loss.

However, depending on how you assign treatments to blocks, you may obtain a different number of confounded effects.

[3] with Suppose engineers at a semiconductor manufacturing facility want to test whether different wafer implant material dosages have a significant effect on resistivity measurements after a diffusion process taking place in a furnace.

That would increase the experimental error of each resistivity measurement by the run-to-run furnace variability and make it more difficult to study the effects of the different dosages.

By extension, note that the trials for any K-factor randomized block design are simply the cell indices of a k dimensional matrix.