Spearman's correction for attenuation (measurement error) corrects a correlation coefficient for measurement errors in either-or-both of two variables, and follows from the assumptions of classical test theory. Spearman's equation removes all measurement error from a correlation coefficient which translates into "increasing the reliability of…

A critical discussion of the assumption of uncorrelated errors in classical psychometric theory and its applications is provided. It is pointed out that this assumption is essential for a number of fundamental results and underlies the concept of parallel tests, the Spearman-Brown's prophecy and the correction for attenuation formulas as well as…

In adolescence research, the treatment of measurement reliability is often fragmented, and it is not always clear how different reliability coefficients are related. We show that generalizability theory (G-theory) is a comprehensive framework of measurement reliability, encompassing all other reliability methods (e.g., Pearson "r,"…

Recently, there has been an increasing level of interest in subscores for their potential diagnostic value. Haberman suggested a method based on classical test theory to determine whether subscores have added value over total scores. In this article I first provide a rich collection of results regarding when subscores were found to have added…

Recent policy has charged schools and districts with maintaining highly qualified teachers and differentiating among teachers in terms of their effectiveness (U.S. Department of Education, 2009). This emphasis has driven the development and implementation of teacher quality measures which are increasingly being used to evaluate teachers with…

Recently, there has been an increasing level of interest in subscores for their potential diagnostic value. Haberman (2008) suggested a method based on classical test theory to determine whether subscores have added value over total scores. This paper provides a literature review and reports when subscores were found to have added value for…

Subscores are reported for several operational assessments. Haberman (2008) suggested a method based on classical test theory to determine if the true subscore is predicted better by the corresponding subscore or the total score. Researchers are often interested in learning how different subgroups perform on subtests. Stricker (1993) and…

The majority of large-scale assessments develop various score scales that are either linear or nonlinear transformations of raw scores for better interpretations and uses of assessment results. The current formula for coefficient alpha (a; the commonly used reliability coefficient) only provides internal consistency reliability estimates of raw…

Uses classical test theory to show that it is the nature of the range restriction, rather than the nature of the available reliability coefficient, that determines the sequence for applying corrections for range restriction and unreliability. Shows how the common rule of thumb for choosing the sequence is tenable only when the correction does not…

In educational testing, subscores may be provided based on a portion of the items from a larger test. One consideration in evaluation of such subscores is their ability to predict a criterion score. Two limitations on prediction exist. The first, which is well known, is that the coefficient of determination for linear prediction of the criterion…

Evaluated coefficient alpha under violations of two classical test theory assumptions: essential tau-equivalence and uncorrelated errors through simulation. Discusses the interactive effects of both violations with true and error scores. Provides empirical evidence of the derivation of M. Novick and C. Lewis (1993). (SLD)

It has often been asserted that the reliability of a measure places an upper limit on its validity. This article demonstrates in theory that validity can rise when reliability declines, even when validity evidence is a correlation with an acceptable criterion. Whether empirical examples can actually be found is an open question. (SLD)

The reliability of a gain is determined by the reliabilities of the components, the correlation between them, and their standard deviations. Reliability is not inherently low, but the components of gains in many investigations make low reliability likely and require caution in the use of gain scores. (SLD)

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)

People can use a variety of different strategies to perform tasks and these strategies all have two characteristics in common. First, they can be evaluated in comparison with either an absolute or a relative standard. Second, they can be used at varying levels of consistency. In the present article, the authors develop a general theory of task…