SOLAR software can, at the discretion of the user, apply a rank-based inverse-normal transformation to the data using the command
inormal. This transformation is the one suggested by Van der Waerden (1952) and is given by:
where is the transformed value for observation , is the probit function, is the ordinary rank of the -th case among observations.
This transformation is a particular case of the family of transformations discussed in the paper by Beasley et al. (2009). The family can be represented as:
where is a constant and the remaining variables are as above. The value of varies for different proposed methods. Blom (1958) suggests , Tukey (1962) suggests , Bliss (1967) suggests and, as just decribed, Van der Waerden suggests .
Interesting enough, the Q-Q plots produced by Octave use the Bliss (1967) transformation.
An Octave/matlab function to perform these transformations in arbitrary data is here: inormal.m (note that this function does not require or use SOLAR).
- Van der Waerden BL. Order tests for the two-sample problem and their power. Proc Koninklijke Nederlandse Akademie van Wetenschappen. Ser A. 1952; 55:453–458.
- Blom G. Statistical estimates and transformed beta-variables. Wiley, New York, 1958 (page 71).
- Tukey JW. The future of data analysis. Ann Math Stat. 1962; 33:1–67.
- Bliss CI. Statistics in biology. McGraw-Hill, New York, 1967 (pages 117–120).
- Beasley TM, Erickson S, Allison DB. Rank-based inverse normal transformations are increasingly used, but are they merited? Behav Genet. 2009; 39(5):580-95.
- 23.Jul.2011: First public release.
- 19.Jun.2014: Added ability to deal with ties, as well as NaNs in the data.