<P> Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among group means in a sample . ANOVA was developed by statistician and evolutionary biologist Ronald Fisher . In the ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation . In its simplest form, ANOVA provides a statistical test of whether the population means of several groups are equal, and therefore generalizes the t - test to more than two groups . ANOVA is useful for comparing (testing) three or more group means for statistical significance . It is conceptually similar to multiple two - sample t - tests, but is more conservative, resulting in fewer type I errors, and is therefore suited to a wide range of practical problems . </P> <P> While the analysis of variance reached fruition in the 20th century, antecedents extend centuries into the past according to Stigler . These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model . Laplace was performing hypothesis testing in the 1770s . The development of least - squares methods by Laplace and Gauss circa 1800 provided an improved method of combining observations (over the existing practices then used in astronomy and geodesy). It also initiated much study of the contributions to sums of squares . Laplace knew how to estimate a variance from a residual (rather than a total) sum of squares . By 1827 Laplace was using least squares methods to address ANOVA problems regarding measurements of atmospheric tides . Before 1800 astronomers had isolated observational errors resulting from reaction times (the "personal equation") and had developed methods of reducing the errors . 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 . An eloquent non-mathematical explanation of the additive effects model was available in 1885 . </P>

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