 
Summary: Zscores
Hervé Abdi1
1 Overview
A score by itself does not tell much. If we are told that we have ob
tained a score of 85 on a beauty test, this could be very good news
if most people have a score of 50, but less so if most people have
a score of 100. In other words a score is meaningful only relative
to the means of the sample or the population. Another problem
occurs when we want to compare scores measured with different
units or on different population. How to compare, for example a
score of 85 on the beauty test with a score of 100 on an I.Q. test?
Scores from different distributions, such as the ones in our ex
ample, can be standardized in order to provide a way of comparing
them that includes consideration of their respective distributions.
This is done by transforming the scores into Zscores which are
expressed as standardized deviations from their means. These Z
scores have a mean of 0 and a standard deviation equal to 1. Z
scores computed from different samples with different units can
be directly compared because these numbers do not express the
original unit of measurement.
