[R-meta] Best choice of effect size

[Viechtbauer, Wolfgang (SP)]

Hi Luke,

Yes, treating the mean proportions as means is ok -- after all, they are means. As long as n is not too small (and the true mean proportion not too close to 0 or 1), then the CLT will also ensure that the sampling distribution of a mean proportion is approximately normal.

We have analayzed such mean proportions in these articles:

McCurdy, M. P., Viechtbauer, W., Sklenar, A. M., Frankenstein, A. N., & Leshikar, E. D. (2020). Theories of the generation effect and the impact of generation constraint: A meta-analytic review. Psychonomic Bulletin & Review, 27(6), 1139-1165. https://doi.org/10.3758/s13423-020-01762-3

Vachon, H., Viechtbauer, W., Rintala, A., & Myin-Germeys, I. (2019). Compliance and retention with the experience sampling method over the continuum of severe mental disorders: Meta-analysis and recommendations. Journal of Medical Internet Research, 21(12), e14475. https://doi.org/10.2196/14475

In these articles, we did not compute standardized mean differences based on the mean proportions, but one could do so.

For the data below:

escalc(measure="SMD", m1i=0.45, m2i=0.17, sd1i=0.17, sd2i=0.11, n1i=20, n2i=19)

If I understand you correctly, the second type are means of counts (i.e., there is a count for each subject and for example 4.5 is the mean of those counts). Again, while an individual count might have other distributional properties (e.g., Poisson or negative binomial), once you take the mean, it's a mean and the CLT 'kicks in'. So I would again say: yes, you can treat these as 'regular' means and compute SMDs based on them.

For the data below:

escalc(measure="SMD", m1i=4.5, m2i=4.7, sd1i=1.12, sd2i=1.59, n1i=17, n2i=18)

I might be inclined to code a moderator that distinguishes these different types, to see if there is some systematic difference between them.

Best,
Wolfgang

>-----Original Message-----
>From: Luke Martinez [mailto:martinezlukerm using gmail.com]
>Sent: Thursday, 30 September, 2021 0:32
>To: R meta
>Cc: Viechtbauer, Wolfgang (SP); James Pustejovsky
>Subject: Re: Best choice of effect size
>
>Dear All,
>
>To further clarify, the proportion types (my previous email) are used
>to score each study participant's performance on the text. Then, each
>study reports the "mean" and "sd" of a proportion type for control and
>experimental groups (to then compare them with t-tests and ANOVAs).
>
>For example, a study using proportion_type1 (see my previous email)
>can provide the following for effect size calculation:
>
>               Mean    SD     n
> group1   0.45      0.17  20
> group2   0.17      0.11  19
>
>The same is true for studies that use raw frequencies to score each
>study participant's performance on the text. In such studies, often,
>"mean" and "sd" of the  # of corrected items (numerator of the
>proportions in my previous email) for control and experimental groups
>(to then compare them with t-tests and ANOVAs).
>
>For example, a study using (raw) # of corrected items can provide the
>following for effect size calculation:
>
>               Mean    SD   n
> group1   4.5      1.12  17
> group2   4.7      1.59  18
>
>My question is that can I calculate SMD across all such studies given
>their intent is to measure the same thing?
>
>Thank you,
>Luke
>
>On Wed, Sep 29, 2021 at 12:12 PM Luke Martinez <martinezlukerm using gmail.com> wrote:
>>
>> Dear All,
>>
>> I'm doing a meta-analysis where the papers report only "mean" and "sd"
>> of some form of proportion and/or "mean" and "sd" of corresponding raw
>> frequencies. (For context, the papers ask students to read, find, and
>> correct the wrong words in a text.)
>>
>> By some form of proportion, I mean, some papers report actual proportions:
>>
>> proportion_type1 = # of corrected items / all items needing correction
>>
>> Some paper report a modified version of proportions:
>>
>> proportion_type2 = # of corrected items / (all items needing
>> correction + all wrongly corrected items)
>>
>> There are other versions of proportions and corresponding raw
>> frequencies as well. But my question is given that all these studies
>> only report "mean" and "sd", can I simply use a SMD effect size?
>>
>> Many thanks,
>> Luke