Design of experiments

The first statistician to consider a methodology for the design of experiments was Sir Ronald A. Fisher. He described how to test the hypothesis that a certain lady could distinguish by flavor alone whether the milk or the tea was first placed in the cup. While this sounds like a frivolous application, it allowed him to illustrate the most important ideas of experimental design:
 * Randomization
 * Replication
 * Blocking
 * Orthogonality
 * use of factorial experiments instead of the one-factor-at-a-time method

Analysis of the design of experiments was built on the foundation of the analysis of variance, a collection of models in which the observed variance is partitioned into components due to different factors which are estimated and/or tested.

In 1950, Gertrude Mary Cox and William Cochran published the book Experimental Design which became the major reference work on the design of experiments for statisticians for years afterwards.

Developments of the theory of linear models have encompassed and surpassed the cases that concerned early writers. Today, the theory rests on advanced topics in abstract algebra and combinatorics.

As with all other branches of statistics, there is both classical and Bayesian experimental design.