<div dir="ltr"><div>No it isn't. I mainly have it from James and his blog (see link below), and then I added the correction from WWC. <br></div><div><a href="https://www.jepusto.com/alternative-formulas-for-the-smd/">https://www.jepusto.com/alternative-formulas-for-the-smd/ <br></a></div><div><br></div><div>James, please let me/us know if this approach is viable. :) <br></div><div><br></div><div>Mikkel <br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Den fre. 1. okt. 2021 kl. 22.27 skrev Timothy MacKenzie <<a href="mailto:fswfswt@gmail.com">fswfswt@gmail.com</a>>:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr">Mikkel, <div><br></div><div>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?</div><div><br></div><div>Best regards,</div><div>Tim M</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, Oct 1, 2021 at 3:22 PM Mikkel Vembye <<a href="mailto:mikkel.vembye@gmail.com" target="_blank">mikkel.vembye@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>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)]</div><div><br></div><div>Have a nice weekend.<br></div><div><br></div><div>Best,</div><div>Mikkel<br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Den fre. 1. okt. 2021 kl. 21.41 skrev Mikkel Vembye <<a href="mailto:mikkel.vembye@gmail.com" target="_blank">mikkel.vembye@gmail.com</a>>:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>Sorry. I referred to an older version of the Appendix. I usually just follow WWC's recommendation when I cannot obtain R2. This is<br></div><div> <font size="2"><span style="font-family:arial,sans-serif"><br></span></font></div><div><font size="2"><span style="font-family:arial,sans-serif">"<span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid6"><span role="presentation" dir="ltr">if </span></span><span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid11"><span role="presentation" dir="ltr">R</span><span role="presentation" dir="ltr">2</span></span><span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid7"><span role="presentation" dir="ltr"> is not available, then WWC will take a cautious approach to calculating the </span></span></span></font></div><div><font size="2"><span style="font-family:arial,sans-serif"><span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid7"></span></span></font></div><font size="2"><span style="font-family:arial,sans-serif"><span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid7"><span role="presentation" dir="ltr">standard error and assume a value of zero for </span></span><span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid12"><span role="presentation" dir="ltr">R</span><span role="presentation" dir="ltr">2</span></span><span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid8"><span role="presentation" dir="ltr">. This cautious approach will overestimate the </span><br role="presentation"></span></span></font><div><font size="2"><span style="font-family:arial,sans-serif"><span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid8"><span role="presentation" dir="ltr">magnitude of the standard error but protects against type I error." (See the WWC Procedure Handbook, p. E-5) <br></span></span></span></font></div><div><font size="2"><span style="font-family:arial,sans-serif"><span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid8"><span role="presentation" dir="ltr"><br></span></span></span></font></div><div><font size="2"><span style="font-family:arial,sans-serif"><span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid8"><span role="presentation" dir="ltr"><a href="https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-Procedures-Handbook-v4-1-508.pdf" target="_blank">https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-Procedures-Handbook-v4-1-508.pdf </a><br></span></span></span></font></div><div><font size="2"><span style="font-family:arial,sans-serif"><span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid8"><span role="presentation" dir="ltr"><br></span></span></span></font></div><div><font size="2"><span style="font-family:arial,sans-serif"><span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid8"><span role="presentation" dir="ltr">Whether this approach is better, is more a James question. <br></span></span></span></font></div><div><font size="2"><span style="font-family:arial,sans-serif"><span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid8"><span role="presentation" dir="ltr"><br></span></span></span></font></div><div><font size="2"><span style="font-family:arial,sans-serif"><span id="gmail-m_-3605924293969833316gmail-m_6960763470629103385gmail-m_4520656011407347308gmail-m_8891246733792076375gmail-m_-386697204492361036gmail-page124R_mcid8"><span role="presentation" dir="ltr">Mikkel <br></span></span></span></font></div>
</div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Den fre. 1. okt. 2021 kl. 19.44 skrev Timothy MacKenzie <<a href="mailto:fswfswt@gmail.com" target="_blank">fswfswt@gmail.com</a>>:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr">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). <div><br></div><div>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. </div><div><br></div><div>My understanding is that I should find a more general SE[g] that only requires icc, am I correct in thinking this way?</div><div><br></div><div>Thanks,</div><div>Tim M</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, Oct 1, 2021 at 12:32 PM Mikkel Vembye <<a href="mailto:mikkel.vembye@gmail.com" target="_blank">mikkel.vembye@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>Hi Tim,</div><div><br></div><div>Glad that I/we can help. You find the ANCOVA examples (both uncorrected and corrected) in Table 3.</div><div><br></div><div><img src="cid:ii_ku8n4rmg0" alt="image.png" width="541" height="93"><br></div><div><br></div><div>I forgot to mention that you also can find some corrections to Hedges (2007) in Table 5.</div><div><br></div><div>All the best,</div><div>Mikkel<br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Den fre. 1. okt. 2021 kl. 19.21 skrev Timothy MacKenzie <<a href="mailto:fswfswt@gmail.com" target="_blank">fswfswt@gmail.com</a>>:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Dear James and Mikkel,<br>
<br>
Thank you both. In my case, the primary studies have used AN(C)OVAs<br>
with (non-)random assignment of classes to conditions. I have the<br>
Means and SDs of student-level data for conditions.<br>
<br>
Based on: <a href="https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-41-Supplement-508_09212020.pdf" rel="noreferrer" target="_blank">https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-41-Supplement-508_09212020.pdf</a><br>
, I should use the unbiased version of equation E.5.1 to compute the<br>
SMD effect size (g):<br>
<br>
g = wb / s * sqrt( 1 - (2*(n-1)*icc / N - 2) ) ; s = pooled standard<br>
deviation; n = ave. cluster size; N = n_t + n_c; w = hedges'<br>
correction factor<br>
<br>
Based on the same document, the standard error of g (SE[g]) for<br>
cluster-assignment studies is (equation E.7.1 under "Cluster<br>
assignment"):<br>
<br>
SE[g] = w * sqrt( (SE_uc / s )^2 * eta + (g^2 / (2*h)) ); eta = 1 +<br>
(n - 1)*icc; h = ( [(N-2)-2*(n-1)*icc ]^2 ) / ((N-2)*(1-icc)^2 +<br>
2*(N-2*n)*icc*(1-icc) )<br>
<br>
where SE_uc = regression coefficient standard errors uncorrected for<br>
clustering in the primary studies.<br>
<br>
Am I pointing to the correct formulas? If yes, I don't have SE_uc in<br>
my primary studies, what should I do?<br>
<br>
Thanks,<br>
Tim M<br>
<br>
<br>
------ Forwarded Message ------<br>
From: Mikkel Vembye <<a href="mailto:mikkel.vembye@gmail.com" target="_blank">mikkel.vembye@gmail.com</a>><br>
Date: Fri, Oct 1, 2021 at 6:54 AM<br>
Subject: Re-re: [R-meta] Meta-analyzing studies that failed to account<br>
for their nested data<br>
To: <<a href="mailto:fswfswt@gmail.com" target="_blank">fswfswt@gmail.com</a>>, <<a href="mailto:r-sig-meta-analysis@r-project.org" target="_blank">r-sig-meta-analysis@r-project.org</a>><br>
<br>
<br>
Hi Tim,<br>
<br>
Just to follow up on James, WWC do also have a nice description of how<br>
they handle cluster trials and quasi-experiments:<br>
<a href="https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-41-Supplement-508_09212020.pdf" rel="noreferrer" target="_blank">https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-41-Supplement-508_09212020.pdf</a><br>
<br>
Mikkel<br>
<br>
<br>
On Thu, Sep 30, 2021 at 11:09 PM James Pustejovsky <<a href="mailto:jepusto@gmail.com" target="_blank">jepusto@gmail.com</a>> wrote:<br>
><br>
> 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.<br>
><br>
> To your second question, yes these adjustments are also important for quasi-experiments.<br>
><br>
> James<br>
><br>
> On Thu, Sep 30, 2021 at 10:53 PM Timothy MacKenzie <<a href="mailto:fswfswt@gmail.com" target="_blank">fswfswt@gmail.com</a>> wrote:<br>
>><br>
>> Dear James,<br>
>><br>
>> Many thanks for this information. Certainly this is serious.<br>
>><br>
>> I should add that a few of the (newer) studies in my pool say that<br>
>> they found their ICCs to be negligible and opted for the single-level<br>
>> analyses (maybe I should not adjust the sampling variances in these<br>
>> cases, correct?).<br>
>><br>
>> Also, I'm assuming that I can use these sampling variance adjustments<br>
>> for quasi-experiments where schools/centers themselves haven't been<br>
>> randomly recruited as well?<br>
>><br>
>> Thanks,<br>
>> Tim M<br>
>><br>
>> On Thu, Sep 30, 2021 at 9:40 PM James Pustejovsky <<a href="mailto:jepusto@gmail.com" target="_blank">jepusto@gmail.com</a>> wrote:<br>
>> ><br>
>> > Hi Tim,<br>
>> ><br>
>> > 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.<br>
>> ><br>
>> > 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:<br>
>> > <a href="https://training.cochrane.org/handbook/current/chapter-23#section-23-1" rel="noreferrer" target="_blank">https://training.cochrane.org/handbook/current/chapter-23#section-23-1</a><br>
>> > Hedges (2007; <a href="https://doi.org/10.3102/1076998606298043" rel="noreferrer" target="_blank">https://doi.org/10.3102/1076998606298043</a>) and (2011; <a href="https://doi.org/10.3102/1076998610376617" rel="noreferrer" target="_blank">https://doi.org/10.3102/1076998610376617</a>) provides slightly more elaborate methods that can be used if you have more details about the study designs. Hedges and Hedberg's Variance Almanac (<a href="http://stateva.ci.northwestern.edu/" rel="noreferrer" target="_blank">http://stateva.ci.northwestern.edu/</a>) is a helpful source for developing estimates of ICCs for educational outcomes.<br>
>> ><br>
>> > James<br>
>> ><br>
>> > On Thu, Sep 30, 2021 at 4:58 PM Timothy MacKenzie <<a href="mailto:fswfswt@gmail.com" target="_blank">fswfswt@gmail.com</a>> wrote:<br>
>> >><br>
>> >> Hello All,<br>
>> >><br>
>> >> I've noticed almost all the studies I have selected for meta-analysis<br>
>> >> have ignored the nested structure of their data (subjects nested in<br>
>> >> classrooms) and have conducted only single-level analyses.<br>
>> >><br>
>> >> I've extracted the condition-level summaries from those studies (i.e.,<br>
>> >> Means and SDs for C vs. T groups).<br>
>> >><br>
>> >> But I'm wondering if I can/should make any adjustment to my<br>
>> >> meta-regression model to account for the nested structure of the data<br>
>> >> in those studies AND if not, whether such a situation poses a<br>
>> >> limitation to my meta-analysis?<br>
>> >><br>
>> >> Thank you very much for your assistance,<br>
>> >> Tim M<br>
>> >><br>
>> >> _______________________________________________<br>
>> >> R-sig-meta-analysis mailing list<br>
>> >> <a href="mailto:R-sig-meta-analysis@r-project.org" target="_blank">R-sig-meta-analysis@r-project.org</a><br>
>> >> <a href="https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis" rel="noreferrer" target="_blank">https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis</a><br>
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