Properties of the Spearman correction for attenuation were investigated using Monte Carlo methods, under conditions where correlations between error scores exist as a population parameter and also where correlated errors arise by chance in random sampling. Equations allowing for all possible dependence among true and error scores on two tests at…

An alternative formula is presented for the reliability of a difference score that contains the correlation between true scores instead of the correlation between observed scores. This approach provides more useful information and yields values that are not as anomalous as those usually obtained. (SLD)

The reliability of differences between pretest and posttest measures with intervening experimental treatment can be highly reliable under some conditions. If the error components of pretest and posttest measures are correlated, the classical formula for the reliability of differences underestimates the actual reliability of gains. (Author/CM)

The correlation between bias components of test scores and unbiased observed scores is shown to be an effective predictor of changes in reliability and validity resulting from elimination of bias. Plausible assumptions about value of correlation and size of related variance components indicate that reducation in reliability and validity is a…

The usual formulas for the reliability of differences between two test scores are based on the assumption that the error scores are uncorrelated. Formulas are presented for the general case where this assumption is unnecessary. (Author/JKS)

Changes, like single scores, are demonstrated to be valid and reliable and potentially predictable by independent variables. Change and growth measures determined from individual examinees' test scores indicated excellent predictive value. (Author/PN)

A mathematical link between test reliability and test validity is derived, taking into account the correlation between error scores on a test and error scores on a criterion measure. When this correlation is positive, the "paradoxical" nonmonotonic relation between test reliability and test validity occurs universally. (Author/BW)

The critiques by L. Collins and L. Humphreys in this issue illustrate problems with the use of gain scores. Collins' examples show that familiar formulas for the reliability of differences do not reflect the precision of measures of change. Additional examples demonstrate flaws in the conventional approach to reliability. (SLD)

Using the concepts of conditional probability, conditional expectation, and conditional independence, the main results of the classical test theory model can be derived in a very few steps with minimal assumptions. The present effort explores the possibility that present classical test theories can be further condensed. (Author/RC)

The reliability of simple difference scores is greater than, less than, or equal to that of residualized difference scores, depending on whether the correlation between pretest and posttest scores is greater than, less than, or equal to the ratio of the standard deviations of pretest and posttest scores. (Author)