Published Online: 30 JAN 2010
Copyright © 2010 John Wiley & Sons, Inc. All rights reserved.
Corsini Encyclopedia of Psychology
How to Cite
Madsen, J. W. 2010. Z-Score. Corsini Encyclopedia of Psychology. 1–3.
- 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;