Variability in the Results of Meta-Analysis as a Function of Comparing Effect Sizes Based on Scores from Noncomparable Measures: A Simulation Study

• Published in: Educational and psychological measurement Vol. 77; no. 3; pp. 449 - 470
• Main Author: Nugent, William R
• Format: Journal Article
• Language: English
• Published: United States SAGE Publications 01.06.2017
• Subjects: Comparative Analysis; Effect Size; Meta Analysis; Monte Carlo Methods; Scores; Simulation; meta-analysis; effect sizes; measurement and meta-analysis; standardized mean difference; effect size comparability
• ISSN: 0013-1644; 1552-3888
• DOI: 10.1177/0013164416654517

Meta-analysis is a significant methodological advance that is increasingly important in research synthesis. Fundamental to meta-analysis is the presumption that effect sizes, such as the standardized mean difference (SMD), based on scores from different measures are comparable. It has been argued that population observed score SMDs based on scores from different measures A and B will be equal only if the conjunction of three conditions are met: construct equivalence (CE), equal reliabilities (ER), and the absence of differential test functioning (DTF) in all subpopulations of the combined populations of interest. It has also been speculated the results of a meta-analysis of SMDs might differ between circumstances in which the SMDs included in a meta-analysis are based on measures which all met the conjunction of these conditions and that in which the conjunction of these conditions is violated. No previous studies have tested this conjecture. This Monte Carlo study investigated this hypothesis. A population of studies comparing one of five hypothetical treatments with a placebo condition was simulated. The SMDs in these simulated studies were based on true scores from six hypothetical measures. The scores from some of these measures met the conjunction of CE, ER, and, the absence of DTF, while others failed to meet CE. Three meta-analyses were conducted using both fixed effects and random effects methods. The results suggested that the results of meta-analyses can vary to a practically significant degree when the SMDs were based on scores from measures failing to meet the CE condition. Implications for future research are considered.