Common Transforms

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This section deals with some common transforms for continuous variables:

Please note that other transformations can be achieved by applying a function to a column of data as described below.

Transforming a variable changes its measurement scale. Reasons for transformation include stabilizing variance, linearising relationships, normalizing distributions and making data easier to handle numerically (Armitage and Berry, 1994; Bland and Altman, 1996c). Details of the above transformations are discussed under their own titles, here we consider how to deal with other transformations, for example a power transform:

Power

Example, for square root apply function v1^.5 or sqr(v1), for standardized version (v1^.5-1)/.5

Limitation, v1 must be ≥ 0.

Standardized form: y = (x^c-1) / c

For c = 0.5 (square root):

Variance of x can be stabilized especially with Poisson distributed data.

For c = -1 (reciprocal):

Variance of x can be stabilized with distant high outliers, e.g. very long survival times compared with mainly shorter ones.

For c = 2 (square):

Variance can be stabilized when var(x) decreases with increasing x and with negatively skewed x.