# Choosing a Data Transformation with the Box-Whisker Plot

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This Demonstration shows the effect of a power data transformation,

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Contributed by: Ian McLeod (March 2011)

Open content licensed under CC BY-NC-SA

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Data transformations such as square-root and logs are often used in statistics to improve the model assumptions. See [1] for examples, with actual data, of the use of box-and-whisker plots to choose a transformation.

Using *Mathematica*'s built-in functions Manipulate and BoxWhisker with the family of power transformations provides a simple and effective method for choosing a suitable transformation with real data. For comparison and for pedagogical purposes, we have included skewness and maximum likelihood methods for choosing .

[2] discusses the use of maximum likelihood estimation for in the family of power transformations,

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[3] discusses choosing a power transformation by minimizing absolute skewness. The robust skewness statistic computed using QuartileSkewness is sometimes called Bowley skewness (Wolfram *MathWorld*).

The use of the relative likelihood function for statistical inference is discussed in the books [4] and [5].

References:

[1] W. S. Cleveland, *Visualizing Data*, Summit, NJ: Hobart Press, 1993.

[2] G. E. P. Box and D. R. Cox, "An Analysis of Transformations," *Journal of the Royal Statistical Society B*, 26(2), 1964 pp. 211–252.

[3] D. V. Hinkley, "On Power Transformations to Symmetry,” *Biometrika*, 62, 1975 pp. 101–111.

[4] A. Azzalini, *Statistical Inference*, Boca Raton, FL: Chapman & Hall/CRC, 1996.

[5] D. A. Sprott, *Statistical Inference in Science*, New York: Springer, 2000.

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