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 available in 1885. 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.
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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. 4.2.3 Statistical models for observational data.4.1 Textbook analysis using a normal distribution.
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