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The phrase "average effect sizes" is correct and usable in written English.
You could use it when discussing the outcomes of a study that used empirical data to measure the differences between two groups. For example, "The study showed that the average effect sizes for the two groups were statistically significant."
Exact(38)
High presurgery emotional distress levels were associated with significantly more postsurgical pain, analgesic use, and impairment after surgery, with small to medium average effect sizes.
Youth-focused components designed to encourage more positive family relationships and a positive orientation toward the future emerged as key factors predicting larger than average effect sizes.
When we estimated average effect sizes separately for the two continents, the averages were moderate, consistent (Zr = 0.23 0.27), and significantly > 0.
Weighted average effect sizes (SMD, random-effects) and heterogeneity (Q and I 2 statistics) of the intervention-induced changes of tendon stiffness, Young's modulus, and CSA were calculated.
When we combined studies from North America and Eurasia, average effect sizes for timber harvest (Zr = 0.24) and tree size (Zr = 0.25) were similar in strength and both significantly > 0.
While a panel data fixed effects model also enables to capture time invariant heterogeneity across countries, it only yields average effect sizes of the variables of interests on acreage.
Similar(22)
Between 1992 and 1997, the average effect size shrank by eighty per cent.
Findings demonstrated statistically significant but small average effect size and evidence of heterogeneity among studies.
Most importantly, their students' learning showed significant improvement (p < .01, average effect size d = 0.47).
Effect sizes differed dramatically among studies and the average effect size was close to zero (Zr = 0.04).
The average effect size estimate across all outcomes was small-to-moderate, Cohen's d = 0.38 (range = 0.00 to 0.88).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com