Common Transforms

 

Menu location: Data_Transforming and Deriving_Common Transforms.

 

This section deals with some common transforms for continuous variables:

• Log (natural)
• Log (base 10)
• Logit
• Probit
• Angular
• Cumulative
• Ladder of powers
• Empirical cumulative distribution
• Z scores

 

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.