Fisher taught science to plan variation on purpose
Design of experiments builds procedures that show how changing some parts of a system shifts others. From Charles Peirce's 1880s blinded weight trials to Ronald Fisher's 1926 and 1935 agricultural manuals, the craft turned gut feeling into randomisation, blocking, and replication.
At simplest, experimenters manipulate independent (input) variables and watch dependent outcomes while controlling what they can. Validity, reliability, and replicability are core worries; documentation must be thick enough to repeat. DOE spans true experiments that impose treatments and quasi-experiments that select natural conditions. Applications run through natural science, engineering Quality by Design, marketing, and policy. Peirce stressed randomisation-based inference in 1877–1883 work and ran volunteers through blinded repeated measures on weight discrimination, seeding laboratory randomised traditions.
Fisher's Arrangement of Field Experiments (1926) and Design of Experiments (1935) systematised agricultural tests, including the lady tasting tea parable. Random assignment gives each unit equal chance of each condition, separating true experiments from weaker designs. Blocking groups similar units to quiet irrelevant noise; orthogonal contrasts keep comparisons uncorrelated under normality. Multifactor plans beat one-factor-at-a-time by revealing interactions via analysis of variance. Sequential designs, pioneered by Abraham Wald, let each stage depend on earlier results, including stopping rules. Replication of whole experiments helps separate treatment effects from measurement noise when every reading carries uncertainty.
A classic weighing puzzle attributed via Harold Hotelling and Frank Yates compares eight objects on a pan balance. Weighing each alone yields error variance σ² per estimate; a Hadamard-pattern scheme that mixes objects on both pans cuts that variance eightfold for the same eight weighings. Optimal design lineage includes Gergonne (1815), Peirce (1876), and Kirstine Smith's 1918 polynomial plans. The lesson is methodological: scarce measurements buy more truth when the layout itself is engineered. Comparisons against a control or standard treatment often beat absolute metrology when no shared measurement standard exists—another Fisher-era practical rule still taught in labs.
Source: Design of experiments
