[R-meta] Question about Cohen's d and meta-regression

Angeline Tsui angelinetsui at gmail.com
Wed Jan 3 20:07:04 CET 2018

```Hello all,

I have some questions about effect sizes and meta-regression.

1) I am using between-subject Cohen's d (but this effect size is converted
from a within-subject d based on Morris and Deshan (2002) for my
meta-analysis. The main reason of the conversion is to make this mean
effect size comparable to other meta-analysis in my field, especially when
some other meta-analysis may also report between-subject Cohen's d.
However, I have concerns of interpreting the magnitude of the mean effect
size.

When I interpret the mean Cohen's d, I use the Cohen (1988) rule of thumb:
0.2 -> small, 0.5 -> medium and 0.8 -> large. However, a concern of
applying this Cohen's values rule of thumb to the current meta-analysis is
that it is not "context-specific". For example, a small effect size of 0.3
can be regarded as large effect size in some other contexts.

In this case, what other metrics would you recommend me to use to report
the mean effect size magnitude? I have searched some resources online and
see recommendation about the use of Cohen's U3 index or Common language
effect size statistics (CLES)? From what I understand, both U3 index is a
percentile index whereas CLES is a probability index. But I am not familiar
with these two metrics, can someone give me recommendation which index is
better?

Finally, if I change my effect size to hedge's g because the sample size of
each study is small and I need to correct it by converting Cohen's d to
hedge's g. Can I still convert the mean hedge's g using the same formula of
Cohen's U3 or CLES for interpreting the percentile/probability of the mean
effect size?

2) I ran a meta-regression model with which include a number of moderators.
My concern is the minimum sample size needed for each moderator level. I
was not able to find resources for recommendation of sample size for
moderator analysis. I did learn something from my teacher, she told me that
the rule of thumb is at least 6 studies for a moderator analysis level
(e.g., Gender is a moderator. Then I need to have at least 6 studies that
examined male and at least 6 studies that examined female). Is this true? I
again was not able to find this rule of thumb from books.

Thanks,
Angeline

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