Normal rank transformation

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The normal rank transformation (also surface transformation or normalization ) is a statistical approach to convert a non-normal distribution in empirically collected data into a normal distribution . The process is widely used for the standardization of psychological tests used because the normal distribution hypothesis for many measured there features applies. Various standard value scales are used for this.

Based on the cumulative frequencies, the percentile ranks are converted into z-values or scales derived from them. The normal value is assigned to each measured raw value , which corresponds to its cumulative frequency in a standard normal distribution. This assignment can be made using the inverse distribution function of the normal distribution.

The "artificial" spread in areas of high frequency density can, however, lead to sham differentiations. In principle, the method should therefore only be used if the original distribution of the measured values ​​( raw values ) also approximately follows a normal distribution and any deviations are errors (e.g. restrictions on the representativeness of the standardization sample).

Individual evidence

  1. COD Encyclopedia of Psychology keyword normalization
  2. Representation in Moosbrugger u. a. (Ed.): Test theory and questionnaire construction

Web links

Online calculator for generating cumulative frequencies and performing a normal rank transformation