Skip to main content
Mail a PDF copy of this page to:
(Your email address will not be added to a mailing list)
Show menu

Power transformation

Next selectPower transformation


Allows to create a new variable containing a power transformation of a numeric variable. The transformation is defined by a power parameter λ (Lambda):

x(λ) = xλ when λ ≠ 0
x(λ) = log(x)  when λ = 0

Optionally, you can select the Box-Cox transformation. The Box-Cox power transformation is defined as (Armitage et al., 2002; Box & Cox, 1964):

x(λ) = (xλ - 1) / λ  when λ ≠ 0
x(λ) = log(x)  when λ = 0

When some of the data are negative, a shift parameter c needs to be added to all observations (in the formulae above x is replaced with x+c).

Required input

Power transformation, Box-Cox transformation

Click OK to proceed. The selected column in the spreadsheet is filled with the power-transformed data.

Interpretation of the power transformation

When you do not select Box-Cox transformation and the shift parameter c is zero then the power transformation is easy to interpret for certain values of lambda, for example:

λ = 0 logarithmic transformation
λ = 0.5 square root transformation
λ = -1 inverse transformation
λ = 1 no transformation!


See also

Recommended book

Book cover

Statistical Methods in Medical Research
Peter Armitage, Geoffrey Berry, J. N. S. Matthews

Buy from Amazon

Although more comprehensive and mathematical than the books by Douglas Altman and Martin Bland, "Statistical Methods in Medical Research" presents statistical techniques frequently used in medical research in an understandable format.