On the Appropriateness of Fixed Correlation Assumptions in Repeated-Measures Meta-Analysis: A Monte Carlo Assessment

Vasileios Papadopoulos ()
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Vasileios Papadopoulos: Laboratory of Anatomy, Department of Medicine, Democritus University of Thrace, GR-68100 Alexandroupolis, Greece

Stats, 2025, vol. 8, issue 3, 1-9

Abstract: In repeated-measures meta-analyses, raw data are often unavailable, preventing the calculation of the correlation coefficient r between pre- and post-intervention values. As a workaround, many researchers adopt a heuristic approximation of r = 0.7. However, this value lacks rigorous mathematical justification and may introduce bias into variance estimates of pre/post-differences. We employed Monte Carlo simulations (n = 500,000 per scenario) in Fisher z-space to examine the distribution of the standard deviation of pre-/post-differences ( σ D ) under varying assumptions of r and its uncertainty ( σ r ). Scenarios included r = 0.5, 0.6, 0.707, 0.75, and 0.8, each tested across three levels of variance ( σ r = 0.05, 0.1, and 0.15). The approximation of r = 0.75 resulted in a balanced estimate of σ D , corresponding to a “midway” variance attenuation due to paired data. This value more accurately offsets the deficit caused by assuming a correlation, compared to the traditional value of 0.7. While the r = 0.7 heuristic remains widely used, our results support the use of r = 0.75 as a more mathematically neutral and empirically defensible alternative in repeated-measures meta-analyses lacking raw data.

Keywords: correlation coefficient; repeated measures; meta-analysis; variance estimation; Monte Carlo simulation; paired data; heuristic methods; evidence synthesis (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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