[R-meta] Meta-analyzing studies that failed to account for their nested data

Fri Oct 1 22:27:24 CEST 2021

Mikkel,

Thank you. Is this new formula (with F-value) for the sampling variance of
g in the WWC procedures handbook? Would you please provide a reference?

Best regards,
Tim M

On Fri, Oct 1, 2021 at 3:22 PM Mikkel Vembye <mikkel.vembye using gmail.com>
wrote:

> When I have relevant F-values from ANCOVA and related models, I calculate
> vg_corrected = omega^2 * [(g_corrected^2/F-value) * eta +
> g_corrected^2/(2*h)]
>
> Have a nice weekend.
>
> Best,
> Mikkel
>
> Den fre. 1. okt. 2021 kl. 21.41 skrev Mikkel Vembye <
> mikkel.vembye using gmail.com>:
>
>> Sorry. I referred to an older version of the Appendix. I usually just
>> follow WWC's recommendation when I cannot obtain R2. This is
>>
>> "if R2 is not available, then WWC will take a cautious approach to
>> calculating the
>> standard error and assume a value of zero for R2. This cautious approach
>> will overestimate the
>> magnitude of the standard error but protects against type I error." (See
>> the WWC Procedure Handbook, p. E-5)
>>
>> https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-Procedures-Handbook-v4-1-508.pdf
>>
>>
>> Whether this approach is better, is more a James question.
>>
>> Mikkel
>>
>> Den fre. 1. okt. 2021 kl. 19.44 skrev Timothy MacKenzie <
>> fswfswt using gmail.com>:
>>
>>> Much appreciated, Mikkel. I saw that. BTW, there is no Table 5, it's a
>>> typo in the WWC document (I found other typos as well).
>>>
>>> But I have both ANOVAs and a few ANCOVAs from primary studies that did
>>> cluster assignment but ignored nesting structure, with barely any R^2
>>> reported in them.
>>>
>>> My understanding is that I should find a more general SE[g] that only
>>> requires icc, am I correct in thinking this way?
>>>
>>> Thanks,
>>> Tim M
>>>
>>> On Fri, Oct 1, 2021 at 12:32 PM Mikkel Vembye <mikkel.vembye using gmail.com>
>>> wrote:
>>>
>>>> Hi Tim,
>>>>
>>>> Glad that I/we can help. You find the ANCOVA examples (both uncorrected
>>>> and corrected) in Table 3.
>>>>
>>>> [image: image.png]
>>>>
>>>> I forgot to mention that you also can find some corrections to Hedges
>>>> (2007) in Table 5.
>>>>
>>>> All the best,
>>>> Mikkel
>>>>
>>>> Den fre. 1. okt. 2021 kl. 19.21 skrev Timothy MacKenzie <
>>>> fswfswt using gmail.com>:
>>>>
>>>>> Dear James and Mikkel,
>>>>>
>>>>> Thank you both. In my case, the primary studies have used AN(C)OVAs
>>>>> with (non-)random assignment of classes to conditions. I have the
>>>>> Means and SDs of student-level data for conditions.
>>>>>
>>>>> Based on:
>>>>> https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-41-Supplement-508_09212020.pdf
>>>>> , I should use the unbiased version of equation E.5.1 to compute the
>>>>> SMD effect size (g):
>>>>>
>>>>> g = wb / s * sqrt(  1 - (2*(n-1)*icc / N - 2)  ) ; s = pooled standard
>>>>> deviation; n = ave. cluster size; N = n_t + n_c;  w = hedges'
>>>>> correction factor
>>>>>
>>>>> Based on the same document, the standard error of g (SE[g]) for
>>>>> cluster-assignment studies is (equation E.7.1 under "Cluster
>>>>> assignment"):
>>>>>
>>>>> SE[g] = w * sqrt(  (SE_uc / s )^2 * eta + (g^2 / (2*h))  ); eta =  1 +
>>>>> (n - 1)*icc; h = ( [(N-2)-2*(n-1)*icc ]^2 ) / ((N-2)*(1-icc)^2 +
>>>>> 2*(N-2*n)*icc*(1-icc)  )
>>>>>
>>>>> where SE_uc = regression coefficient standard errors uncorrected for
>>>>> clustering in the primary studies.
>>>>>
>>>>> Am I pointing to the correct formulas? If yes, I don't have SE_uc in
>>>>> my primary studies, what should I do?
>>>>>
>>>>> Thanks,
>>>>> Tim M
>>>>>
>>>>>
>>>>> ------ Forwarded Message ------
>>>>> From: Mikkel Vembye <mikkel.vembye using gmail.com>
>>>>> Date: Fri, Oct 1, 2021 at 6:54 AM
>>>>> Subject: Re-re: [R-meta] Meta-analyzing studies that failed to account
>>>>> for their nested data
>>>>> To: <fswfswt using gmail.com>, <r-sig-meta-analysis using r-project.org>
>>>>>
>>>>>
>>>>> Hi Tim,
>>>>>
>>>>> Just to follow up on James, WWC do also have a nice description of how
>>>>> they handle cluster trials and quasi-experiments:
>>>>>
>>>>> https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-41-Supplement-508_09212020.pdf
>>>>>
>>>>> Mikkel
>>>>>
>>>>>
>>>>> On Thu, Sep 30, 2021 at 11:09 PM James Pustejovsky <jepusto using gmail.com>
>>>>> wrote:
>>>>> >
>>>>> > For studies that claim to find negligible ICCs, I would guess that
>>>>> they base this judgement either on a) failing to reject a test of ICC = 0
>>>>> or b) a rule of thumb. a) is not a good justification because with few
>>>>> classes, the test will have little power. b) is arbitrary and even small
>>>>> ICCs (of say 0.02 or 0.04) can be consequential for estimating the variance
>>>>> of the effect size estimate. I would use the ICC adjustment regardless.
>>>>> >
>>>>> > To your second question, yes these adjustments are also important
>>>>> for quasi-experiments.
>>>>> >
>>>>> > James
>>>>> >
>>>>> > On Thu, Sep 30, 2021 at 10:53 PM Timothy MacKenzie <
>>>>> fswfswt using gmail.com> wrote:
>>>>> >>
>>>>> >> Dear James,
>>>>> >>
>>>>> >> Many thanks for this information. Certainly this is serious.
>>>>> >>
>>>>> >> I should add that a few of the (newer) studies in my pool say that
>>>>> >> they found their ICCs to be negligible and opted for the
>>>>> single-level
>>>>> >> analyses (maybe I should not adjust the sampling variances in these
>>>>> >> cases, correct?).
>>>>> >>
>>>>> >> Also, I'm assuming that I can use these sampling variance
>>>>> adjustments
>>>>> >> for quasi-experiments where schools/centers themselves haven't been
>>>>> >> randomly recruited as well?
>>>>> >>
>>>>> >> Thanks,
>>>>> >> Tim M
>>>>> >>
>>>>> >> On Thu, Sep 30, 2021 at 9:40 PM James Pustejovsky <
>>>>> jepusto using gmail.com> wrote:
>>>>> >> >
>>>>> >> > Hi Tim,
>>>>> >> >
>>>>> >> > One important issue here is that the sampling variance of the
>>>>> effect size estimate calculated from such a study will be
>>>>> inaccurate---possibly even an order of magnitude smaller than it should be.
>>>>> If you ignore this, the consequence will be to make the effect size
>>>>> estimates appear far more precise than they actually are.
>>>>> >> >
>>>>> >> > To properly correct the sampling variance estimate, you would
>>>>> need to know the intra-class correlation describing the proportion of the
>>>>> total variation in the outcome that is at the cluster level (in this case,
>>>>> what fraction of the total variance is between classes?). If this isn't
>>>>> reported, then it may be possible to develop a reasonable estimate based on
>>>>> external information. The Cochrane Handbook describes how to correct the
>>>>> sampling variance based on an imputed intra-class correlation:
>>>>> >> >
>>>>> https://training.cochrane.org/handbook/current/chapter-23#section-23-1
>>>>> >> > Hedges (2007; https://doi.org/10.3102/1076998606298043) and
>>>>> (2011; https://doi.org/10.3102/1076998610376617) provides slightly
>>>>> more elaborate methods that can be used if you have more details about the
>>>>> study designs. Hedges and Hedberg's Variance Almanac (
>>>>> http://stateva.ci.northwestern.edu/) is a helpful source for
>>>>> developing estimates of ICCs for educational outcomes.
>>>>> >> >
>>>>> >> > James
>>>>> >> >
>>>>> >> > On Thu, Sep 30, 2021 at 4:58 PM Timothy MacKenzie <
>>>>> fswfswt using gmail.com> wrote:
>>>>> >> >>
>>>>> >> >> Hello All,
>>>>> >> >>
>>>>> >> >> I've noticed almost all the studies I have selected for
>>>>> meta-analysis
>>>>> >> >> have ignored the nested structure of their data (subjects nested
>>>>> in
>>>>> >> >> classrooms) and have conducted only single-level analyses.
>>>>> >> >>
>>>>> >> >> I've extracted the condition-level summaries from those studies
>>>>> (i.e.,
>>>>> >> >> Means and SDs for C vs. T groups).
>>>>> >> >>
>>>>> >> >> But I'm wondering if I can/should make any adjustment to my
>>>>> >> >> meta-regression model to account for the nested structure of the
>>>>> data
>>>>> >> >> in those studies AND if not, whether such a situation poses a
>>>>> >> >> limitation to my meta-analysis?
>>>>> >> >>
>>>>> >> >> Thank you very much for your assistance,
>>>>> >> >> Tim M
>>>>> >> >>
>>>>> >> >> _______________________________________________
>>>>> >> >> R-sig-meta-analysis mailing list
>>>>> >> >> R-sig-meta-analysis using r-project.org
>>>>> >> >> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>>>>>
>>>>

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