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Analysis of variance (ANOVA) is a collection of statistical models used to analyze the differences among group means and their associated procedures (such as "variation" among and between groups), 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 or not the means of several groups are equal, and therefore generalizes the ''t''-test to more than two groups. As doing multiple two-sample t-tests would result in an increased chance of committing a statistical type I error, ANOVAs are useful for comparing (testing) three or more means (groups or variables) for statistical significance. ==History== While the analysis of variance reached fruition in the 20th century, antecedents extend centuries into the past according to Stigler.〔Stigler (1986)〕 These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. Laplace was performing hypothesis testing in the 1770s.〔Stigler (1986, p 134)〕 The development of least-squares methods by Laplace and Gauss circa 1800 provided an improved method of combining observations (over the existing practices of astronomy and geodesy). It also initiated much study of the contributions to sums of squares. Laplace soon knew how to estimate a variance from a residual (rather than a total) sum of squares.〔Stigler (1986, p 153)〕 By 1827 Laplace was using least squares methods to address ANOVA problems regarding measurements of atmospheric tides.〔Stigler (1986, pp 154–155)〕 Before 1800 astronomers had isolated observational errors resulting from reaction times (the "personal equation") and had developed methods of reducing the errors.〔Stigler (1986, pp 240–242)〕 The experimental methods used in the study of the personal equation were later accepted by the emerging field of psychology 〔Stigler (1986, Chapter 7 - Psychophysics as a Counterpoint)〕 which developed strong (full factorial) experimental methods to which randomization and blinding were soon added.〔Stigler (1986, p 253)〕 An eloquent non-mathematical explanation of the additive effects model was available in 1885.〔Stigler (1986, pp 314–315)〕 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''.〔''The Correlation Between Relatives on the Supposition of Mendelian Inheritance''. Ronald A. Fisher. ''Philosophical Transactions of the Royal Society of Edinburgh''. 1918. (volume 52, pages 399–433)〕 His first application of the analysis of variance was published in 1921.〔On the "Probable Error" of a Coefficient of Correlation Deduced from a Small Sample. Ronald A. Fisher. Metron, 1: 3-32 (1921)〕 Analysis of variance became widely known after being included in Fisher's 1925 book ''Statistical Methods for Research Workers''. Randomization models were developed by several researchers. The first was published in Polish by Neyman in 1923.〔Scheffé (1959, p 291, "Randomization models were first formulated by Neyman (1923) for the completely randomized design, by Neyman (1935) for randomized blocks, by Welch (1937) and Pitman (1937) for the Latin square under a certain null hypothesis, and by Kempthorne (1952, 1955) and Wilk (1955) for many other designs.")〕 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「analysis of variance」の詳細全文を読む スポンサード リンク
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