Editing Analysis of variance (section)

==History==
While the analysis of variance reached fruition in the 20th century, antecedents extend centuries into the past according to [[Stephen Stigler|Stigler]].<ref>Stigler (1986)</ref> These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. [[Pierre-Simon Laplace|Laplace]] was performing hypothesis testing in the 1770s.<ref>Stigler (1986, p 134)</ref> Around 1800, Laplace and [[Carl Friedrich Gauss|Gauss]] developed the least-squares method for combining observations, which improved upon methods 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.<ref>Stigler (1986, p 153)</ref> By 1827, Laplace was using [[least squares]] methods to address ANOVA problems regarding measurements of atmospheric tides.<ref>Stigler (1986, pp&nbsp;154–155)</ref> Before 1800, astronomers had isolated observational errors resulting 
from reaction times (the "[[personal equation]]") and had developed methods of reducing the errors.<ref>Stigler (1986, pp&nbsp;240–242)</ref> The experimental methods used in the study of the personal equation were later accepted by the emerging field of psychology <ref>Stigler (1986, Chapter 7 – Psychophysics as a Counterpoint)</ref> which developed strong (full factorial) experimental methods to which randomization and blinding were soon added.<ref>Stigler (1986, p 253)</ref> An eloquent non-mathematical explanation of the additive effects model was available in 1885.<ref>Stigler (1986, pp&nbsp;314–315)</ref>

[[Ronald Fisher]] introduced the term [[variance]] and proposed its formal analysis in a 1918 article on theoretical population genetics, ''[[The Correlation between Relatives on the Supposition of Mendelian Inheritance|The Correlation Between Relatives on the Supposition of Mendelian Inheritance]]''.<ref>''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)</ref> His first application of the analysis of variance to data analysis was published in 1921, ''Studies in Crop Variation I''.<ref>{{cite journal | title=) Studies in Crop Variation. I. An Examination of the Yield of Dressed Grain from Broadbalk | first1=Ronald A. | last1=Fisher | journal=Journal of Agricultural Science | volume=11  | pages=107–135| year=1921 | issue=2 | doi=10.1017/S0021859600003750 | hdl=2440/15170 | s2cid=86029217 | hdl-access=free }}</ref> This divided the variation of a time series into components representing annual causes and slow deterioration. Fisher's next piece, ''Studies in Crop Variation II'', written with [[Winifred Mackenzie]] and published in 1923, studied the variation in yield across plots sown with different varieties and subjected to different fertiliser treatments.<ref>{{cite journal | title=) Studies in Crop Variation. II. The Manurial Response of Different Potato Varieties | first1=Ronald A. | last1=Fisher | journal=Journal of Agricultural Science | volume=13  | pages=311–320| year=1923 | issue=3 | doi=10.1017/S0021859600003592 | hdl=2440/15179 | s2cid=85985907 | hdl-access=free }}</ref>  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 [[Jerzy Neyman]] in 1923.<ref>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.")</ref>