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The Reliability of Difference Scores in Populations and Samples

Donald W. Zimmerman
Journal / Anthology

Journal of Educational Measurement
Year: 2009
Volume: 46
Issue: 1
Page range: 19-42

This study was an investigation of the relation between the reliability of difference scores, considered as a parameter characterizing a population of examinees, and the reliability estimates obtained from random samples from the population. The parameters in familiar equations for the reliability of difference scores were redefined in such a way that determinants of reliability in both populations and samples become more transparent. Computer simulation was used to find sample values and to plot frequency distributions of various correlations and variance ratios relevant to the reliability of differences. The shape of frequency distributions resulting from the simulations and the means and standard deviations of these distributions reveal the extent to which reliability estimates based on sample data can be expected to meaningfully represent population reliability.