Further documentation is available here. While the analysis of variance reached fruition in the 20th century, antecedents analysis of binary data cox pdf centuries into the past according to Stigler. These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model.
It also initiated much study of the contributions to sums of squares. By 1827 Laplace was using least squares methods to address ANOVA problems regarding measurements of atmospheric tides. An eloquent non-mathematical explanation of the additive effects model was available in 1885. His first application of the analysis of variance was published in 1921.
Randomization models were developed by several researchers. One of the attributes of ANOVA which ensured its early popularity was computational elegance. The structure of the additive model allows solution for the additive coefficients by simple algebra rather than by matrix calculations. In the era of mechanical calculators this simplicity was critical. The determination of statistical significance also required access to tables of the F function which were supplied by early statistics texts. The analysis of variance can be used as an exploratory tool to explain observations.
A dog show provides an example. A dog show is not a random sampling of the breed: it is typically limited to dogs that are adult, pure-bred, and exemplary. A histogram of dog weights from a show might plausibly be rather complex, like the yellow-orange distribution shown in the illustrations. Suppose we wanted to predict the weight of a dog based on a certain set of characteristics of each dog. 1 is young, short-haired dogs, group 2 is young, long-haired dogs, etc. The heaviest show dogs are likely to be big strong working breeds, while breeds kept as pets tend to be smaller and thus lighter.
As shown by the second illustration, the distributions have variances that are considerably smaller than in the first case, and the means are more distinguishable. Grouping dogs according to a coin flip might produce distributions that look similar. An attempt to explain weight by breed is likely to produce a very good fit. All Chihuahuas are light and all St Bernards are heavy. The difference in weights between Setters and Pointers does not justify separate breeds.