On the base-free measure of change proposed by Tucker, Damarin and Messick

Abstract

base-free measure of change, difference scores, measuring change,

Surveying predictors of late-life longitudinal change in daily activity energy expenditure

“…To adjust for baseline variance, residualized values were created using a linear regression of follow-up on baseline values. Residualized values are referred to as “baseline-free” measures of change that help combat “regression to the mean” in change analyes [ 36 , 37 , 38 ]. There were two steps in creating change groups.…”

The Reliability of Linear Gain Scores as Measures of Student Growth at the Classroom Level in the Presence of Measurement Bias and Student Tracking

“…Standardized tests are increasingly used to calculate gain scores in an effort to measure student learning and evaluate teacher performance. Prior research has examined the reliability of measures of growth and change (e.g., Bond, 1979; Cronbach & Furby, 1970; Tucker, Damarin, & Messick, 1966; Zimmerman & Williams, 1998). Some special cases of a broader class of linear gain scores (LGS) have become popular measures of student learning as researchers and decision makers attempt to quantitatively evaluate the impact of teachers on students (Battauz, Bellio, & Gori, 2011; Lockwood, McCaffrey, Mariano, & Setodji, 2007; McCaffrey, Lockwood, Koretz, Louis, & Hamilton, 2004; Woodhouse, Yang, Goldstein, & Rasbash, 1996).…”

Denoting the Base‐free Measure of Change

“…Educational Testing Service Bond (1979) pointed out a presumably incorrect derivation in the Tucker, Damarin, and Messick (1966) presentation of a base-free measure of change. As a consequence, Bond argued that properties attributed to a (the coefficient for the regression of true scores from the second testing on true scores from the first testing) were instead properties of b, the corresponding regression coefficient for observed scores.…”

“…Using the Tucker et al (1966) notation which was also followed by Bond (1979), as well as standard relationships from classical test theory, the basefree measure of change (y) is defined as a true independent change score: Tucker et al (1966) and formula (14) in Bond (1979) give the correlation between an observed difference score and any other variable k, one to determine the difference score and one to correlate with the difference score, eliminates the negative bias in P d produced by correlated errors Xl (Thorndike, 1966), Equation (4) then becomes, with inserts from equation (3), (6) is algebraically equivalent to equation (63) in Tucker et al (1966), which gives the correlation between observed initial position and the observed difference score corrected for correlated errors. It is clear from equation (6) that PX'd is positive when a > 1, is zero when a = 1, and is negative when a < 1.…”