Power transform

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This article discusses the Modified Power Transform family.

In statistics, the Power transform refers to a family of transformations that map data to from one space to another using power functions. This is a useful data (pre)processing technique used to reduce data variation, make the data more Normal Distribution-like, improve the correlation between variables and for other data stabilization procedures.

1 Definition
2 Usage of the Power transform
3 Power transform activities
4 Power transform properties
5 See also
6 References
7 External links

[edit] Definition

The power transformation is defined as a continuously varying function, with respect to the power parameter $λ$ , in a piece-wise function form that makes it continuous at the point of singularity ( $λ = 0$ ). For all arguments $y > 0$ , the analytic form of the power transform function is expressed as

$y^{(\lambda)} = \left\{ \begin{array}{cc} {(y^{\lambda}-1)} / {\lambda} , &\mbox{ if } if \lambda \neq 0 \\ \log{y} , &\mbox{ if } \lambda = 0 \end{array}\right.$

[edit] Usage of the Power transform

Power transforms are ubiquitously used in various fields. For example, multi-resolution and wavelet analysis, statistical data analysis, medical research, modeling of physical processes, geochemical data analysis, epidemiology and many other clinical, environmental and social research areas.

[edit] Power transform activities

The SOCR resource pages contain a number of hands-on interactive activities with the Power Transform using Java applets and charts.

[edit] Power transform properties

To be continued

[edit] See also

[edit] References

Carroll, RJ and Ruppert, D. On prediction and the power transformation family. Biometrika 68: 609-615.
Handelsman, DJ. Optimal Power Transformations for Analysis of Sperm Concentration and Other Semen Variables. Journal of Andrology, Vol. 23, No. 5, September/October 2002.
Gluzman, S and Yukalov, VI. Self-similar power transforms in extrapolation problems. Journal of Mathematical Chemistry, Volume 39, Number 1 / January, 2006, DOI 10.1007/s10910-005-9003-7, 47-56.
Howarth, RJ and Earle, SAM. Application of a generalized power transformation to geochemical data Journal Mathematical Geology, Volume 11, Number 1 / February, 1979, DOI 10.1007/BF01043245, Pages 45-62.
Peters, JL Rushton, L, Sutton, AJ, Jones, DR, Abrams, KR, Mugglestone, MA. (2005) Bayesian methods for the cross-design synthesis of epidemiological and toxicological evidence. Journal of the Royal Statistical Society: Series C (Applied Statistics) 54 (1), 159–172, doi:10.1111/j.1467-9876.2005.00476.x