Suppose we wanted to predict the weight of a dog based on a certain set of characteristics of each dog. A histogram of dog weights from a show might plausibly be rather complex, like the yellow-orange distribution shown in the illustrations. A dog show is not a random sampling of the breed: it is typically limited to dogs that are adult, pure-bred, and exemplary. The analysis of variance can be used to describe otherwise complex relations among variables. The first was published in Polish by Jerzy Neyman in 1923. Randomization models were developed by several researchers. Analysis of variance became widely known after being included in Fisher's 1925 book Statistical Methods for Research Workers. His first application of the analysis of variance was published in 1921. Ronald Fisher introduced the term variance and proposed its formal analysis in a 1918 article The Correlation Between Relatives on the Supposition of Mendelian Inheritance. An eloquent non-mathematical explanation of the additive effects model was The experimental methods used in the study of the personal equation were later accepted by the emerging field of psychology which developed strong (full factorial) experimental methods to which randomization and blinding were soon added. Before 1800, astronomers had isolated observational errors resultingįrom reaction times (the " personal equation") and had developed methods of reducing the errors. By 1827, Laplace was using least squares methods to address ANOVA problems regarding measurements of atmospheric tides.
Laplace knew how to estimate a variance from a residual (rather than a total) sum of squares. It also initiated much study of the contributions to sums of squares. Around 1800, Laplace and Gauss developed the least-squares method for combining observations, which improved upon methods then used in astronomy and geodesy. Laplace was performing hypothesis testing in the 1770s. These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. While the analysis of variance reached fruition in the 20th century, antecedents extend centuries into the past according to Stigler.