Z Scores, Standard Scores, and Composite Test Scores Explained

Abstract

Patients may be assessed using a battery of tests where different tests yield scores in different units, where different tests have different minimum and maximum scores, and where higher or lower scores mean different things in different tests. Therefore, a composite test score cannot be obtained by simple addition or averaging of scores in the individual tests. However, if performances in individual tests are converted to Z scores, the Z scores can be added or averaged to yield a composite score that can be interpreted or processed using conventional statistical methods. This article explains in simple ways how Z scores are calculated, what the properties of Z scores are, how Z scores can be interpreted, and how Z scores can be converted into other standard scores.

Keywords: Statistics; T score; Z score; composite score; standard score; stanine score; sten score.