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The phrase "a moderate effect size" is correct and usable in written English.
It can be used in statistical or research contexts to describe the magnitude of an effect in a study or experiment.
Example: "The results indicated a moderate effect size, suggesting that the intervention had a meaningful impact on participants' outcomes."
Alternatives: "a medium effect size" or "an average effect size".
Exact(60)
The three clusters showed significant differences in the three communication variables, with a moderate effect size (Cohen, 1988).
We found a marginally significant difference between the two interfaces with a moderate effect size (d = 0.63).
*Denotes a moderate effect size difference (0.60 to 1.20) between the high- and low-standard playing groups.
Evaluations of pre- and post-treatment measures pointed to a moderate effect size, relatively greater in the within-subject and single-subject studies.
There was a statistically significant (t(20) = 2.74, p = 0.013, d = 0.50) improvement toward more reformed responses on the survey with a moderate effect size.
A significant negative correlation was found between rating scores on the YMRS and the RAVLT trial 1 (p = .033) with a moderate effect size (r = − .333).333
Fact: Hyde's meta-analysis indicated that there was a moderate effect size for women when it came to smiling during conversations.
This difference had a moderate effect size.
Bolded symbols denote a moderate effect size.
This is equivalent to a moderate effect size [ 27].
The estimated sample size was 52 subjects per group for a moderate effect size [ 35].
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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