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Reliability of gain scores under realistic assumptions about properties of pre‐test and post‐test scores
Author(s) -
Zimmerman Donald W.,
Williams Richard H.
Publication year - 1998
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1998.tb00685.x
Subject(s) - test (biology) , reliability (semiconductor) , context (archaeology) , statistics , classical test theory , econometrics , mathematics , computer science , psychology , item response theory , psychometrics , paleontology , power (physics) , physics , quantum mechanics , biology
For many years, psychometricians working in the context of classical test theory have questioned the reliability of measures of gains and growth. Many tables and figures in textbooks and journal articles have suggested that the reliability of these measures is far below that of the pre‐test and post‐test scores from which they are determined. Previous findings reported by the present authors have shown that under special conditions, gain scores can be much more reliable, especially when variances of pre‐test and post‐test scores are unequal and at the same time the reliability coefficients of pre‐test and post‐test scores are unequal with the same directionality. The present paper explores a novel approach to derivation of formulae for the reliability of gain scores in classical test theory. This approach reveals not only that gain scores can be reliable, but also that their reliability coefficients are intermediate between those of the pre‐test and the post‐test in a large proportion of practical testing applications.