The positive square root of is called the standard error of measurement . Before considering test reliability, however, we summarize several results for parallel measurements. The correlation between the observed scores of any pair of parallel measurements equals the squared correlation of observed and true scores. This is a fundamental result in Classical Test Theory relating the precision of a measurement. An extremely important concept in CTT is the reliability of the measurement .
Reliability is a measure of the precision with which is measured.
Formally, is called the reliability coefficient for the measurement . In this sense, directly expresses the precision of a measurement in terms of how faithfully the observed score reflects the unknown true score. Alternatively, the equality demonstrates the inverse relationship of reliability and error. For error-free measurement, i.e., when , reliability equals one. As error increases, i.e., as approaches as a limiting value, reliability approaches zero.