The theory and application of transformation in statistics

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Polytechnic Institute

Year dc:date.issued

1962

Author dc:creator

• Kanjo, Anis Ismail

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10919/106196

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/106196