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  1. Joshua W. Madsen

Published Online: 30 JAN 2010

DOI: 10.1002/9780470479216.corpsy1047

Corsini Encyclopedia of Psychology

Corsini Encyclopedia of Psychology

How to Cite

Madsen, J. W. 2010. Z-Score. Corsini Encyclopedia of Psychology. 1–3.

Author Information

  1. VA San Diego Healthcare System

Publication History

  1. Published Online: 30 JAN 2010


Z-scores, also known as standard scores, represent a transformation of raw data that is typically expressed as “Something minus its mean divided by its standard deviation.” The “something” in this statement is typically either a raw data point within a set of observations or the observed mean of a sample of data. When such a transformation is applied to all observations within a data set, the first step of subtracting the mean from each individual observation has the effect of recentering the distribution at a mean of zero. Because dividing all observations within a data set by a constant results in the standard deviation of the distribution similarly being reduced by that constant, the second step in the transformation results in a standard deviation of 1 for the distribution of z-scores. Thus, when a distribution of scores is converted to z-scores, the resulting distribution is centered at a mean of 0 with a standard deviation of 1.


  • central limit theorem;
  • standard normal distribution;
  • statistical inference;
  • z-score