# The theory and application of transformation in statistics

 dc.contributor.author Kanjo, Anis Ismail en dc.contributor.department Statistics en dc.date.accessioned 2021-10-26T20:10:33Z en dc.date.available 2021-10-26T20:10:33Z en dc.date.issued 1962 en dc.description.abstract This paper is a review of the major literature dealing with transformations of random variates which achieve variance stabilization and approximate normalization. The subject can be said to have been initiated by a genetical paper of R. A. Fisher (1922) which uses the angular transformation Φ = 2 arcsin√p to deal with the analysis of proportions p with E(p) = P. Here it turns out that Var Φ is almost independent of P and so stabilizes the variance. Some fourteen years later Bartlett introduced the so-called square-root transformation which achieves variance stabilization for variates following a Poisson distribution. These two transformations and their ramifications in theory and application are fully discussed. along with refinements introduced by later writers, notably Curtiss (1943) and Anscombe (1948). Another important transformation discussed is one which refers to an analysis of observations on to a logarithmic scale, and here there are uses in analysis of variance situations and theoretical problems in the field of estimation: in the case of the latter, the work of D. J. Finney (1941) is considered in some detail. The asymptotic normality of the transformation is also considered. Transformations primarily designed to bring about ultimate normality in distribution are also included. In particular, there is reference to work on the chi-square probability integral (Fisher), (Wilson and Hilferty (1931)) and the logarithmic transformation of a correlation coefficient (Fisher (1921)). Other miscellaneous topics referred include i. the probability integral transformation (Probits), with applications in bioassay: ii. applications of transformation theory to set up approximate confidence intervals for distribution parameters (BIom (1954)): iii. transformations in connection with the interpretation of so-called 'ranked' data. en dc.description.degree M.S. en dc.format.extent vii, 185 leaves en dc.format.mimetype application/pdf en dc.identifier.uri http://hdl.handle.net/10919/106196 en dc.language.iso en en dc.publisher Virginia Polytechnic Institute en dc.relation.isformatof OCLC# 22247167 en dc.rights In Copyright en dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ en dc.subject.lcc LD5655.V855 1962.K364 en dc.subject.lcsh Transformations (Mathematics) en dc.title The theory and application of transformation in statistics en dc.type Thesis en dc.type.dcmitype Text en thesis.degree.discipline Statistics en thesis.degree.grantor Virginia Polytechnic Institute en thesis.degree.level masters en thesis.degree.name M.S. en

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