Browsing by Author "Zimmerman, Donald W."
Now showing 1 - 4 of 4
- Results Per Page
- Sort Options
Item Are simple gain scores obsolete?(1996) Williams, Richard H.; Zimmerman, Donald W.It is widely believed that measures of gain, growth, or change, expressed as simple differences between pretest and posttest scores, are inherently unreliable. It is also believed that gain scores lack predictive validity with respect to other criteria. However, these conclusions are based on misleading assumptions about the values of parameters in familiar equations in classical test theory. The present paper examines modified equations for the validity and reliability of difference scores that describe applied testing situations more realistically and reveal that simple gain scores can be more useful in research than commonly believed. Index terms: change scores, difference scores, gain scores, measurement of growth, reliability, test theory, validity.Item Commentary on the Commentaries of Collins and Humphreys(1996) Williams, Richard H.; Zimmerman, Donald W.The critiques of Collins (1996) and Humphreys (1996) certainly throw light on properties of gain scores and difference scores that have led to controversies in the past. Collins’ examples reveal that familiar formulas for the reliability of differences do not adequately reflect the precision of measures of change, because they do not allow for intraindividual change. Some additional examples are provided here, and a similar argument is applied to the reliability of a single test. As Collins implies, these arguments indeed disclose flaws, not only in the conventional approach to the reliability of gains and differences, but also in the basic concept of reliability in classical test theory. Index terms: change scores, classical test theory, difference scores, gain scores, intraindividual differences, measurement of growth, reliability, test theory, validity.Item Reliability of measurement and power of significance tests based on differences(1993) Zimmerman, Donald W.; Williams, Richard H.; Zumbo, Bruno D.The power of significance tests based on difference scores is indirectly influenced by the reliability of the measures from which differences are obtained. Reliability depends on the relative magnitude of true score and error score variance, but statistical power is a function of the absolute magnitude of these components. Explicit power calculations reaffirm the paradox put forward by Overall & Woodward (1975, 1976)-that significance tests of differences can be powerful even if the reliability of the difference scores is 0. This anomaly arises because power is a function of observed score variance but is not a function of reliability unless either true score variance or error score variance is constant. Provided that sample size, significance level, directionality, and the alternative hypothesis associated with a significance test remain the same, power always increases when population variance decreases, independently of reliability. Index terms: difference scores, error of measurement, power, significance tests, t test, test reliability, true scores.Item Reliability, power, functions, and relations: A reply to Humphreys(1993) Zimmerman, Donald W.; Williams, Richard H.; Zumbo, Bruno D.Index terms: difference scores, error of measurement, power, significance tests, t test, test reliability, true scores.