<html><head></head><body><div style="font-family: Verdana;font-size: 12.0px;"><div>Thank you very much Wolfgang! </div>
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<div style="margin:0 0 10px 0;"><b>Gesendet:</b> Montag, 24. August 2020 um 10:16 Uhr<br/>
<b>Von:</b> "Viechtbauer, Wolfgang (SP)" <wolfgang.viechtbauer@maastrichtuniversity.nl><br/>
<b>An:</b> "t.saueressig@gmx.de" <t.saueressig@gmx.de><br/>
<b>Cc:</b> "r-sig-meta-analysis@r-project.org <r-sig-meta-analysis@r-project.org>" <r-sig-meta-analysis@r-project.org><br/>
<b>Betreff:</b> RE: RE: [R-meta] Data Extraction</div>
<div name="quoted-content">This is easily derived based on basic principles (e.g., <a href="https://en.wikipedia.org/wiki/Algebra_of_random_variables#Variance_algebra_for_random_variables" target="_blank">https://en.wikipedia.org/wiki/Algebra_of_random_variables#Variance_algebra_for_random_variables</a>). In particular, we know:<br/>
<br/>
SD[x1-x2]^2 = SD[x1]^2 + SD[x2]^2 - 2*r*SD[x1]*SD[x2]<br/>
<br/>
and now if we assume SD[x1] = SD[x2] = SD, we get<br/>
<br/>
SD[x1-x2]^2 = 2*SD^2 - 2*r*SD^2<br/>
= SD^2 * 2 * (1-r)<br/>
<br/>
so:<br/>
<br/>
SD[x1-x2] = SD * sqrt(2*(1-r))<br/>
<br/>
If you need a reference, you could cite:<br/>
<br/>
Morris, S. B., & DeShon, R. P. (2002). Combining effect size estimates in meta-analysis with repeated measures and independent-groups designs. Psychological Methods, 7(1), 105-125.<br/>
<br/>
Best,<br/>
Wolfgang<br/>
<br/>
>-----Original Message-----<br/>
>From: t.saueressig@gmx.de [mailto:t.saueressig@gmx.de]<br/>
>Sent: Sunday, 23 August, 2020 19:05<br/>
>To: Viechtbauer, Wolfgang (SP)<br/>
>Cc: R-sig-meta-analysis<br/>
>Subject: RE: RE: [R-meta] Data Extraction<br/>
><br/>
>Hello,<br/>
><br/>
>One more question from me. From which equation does one derive this? Ist<br/>
>there a citation for this?<br/>
><br/>
>Thank you in advance.<br/>
><br/>
>Regards<br/>
><br/>
>Tobias<br/>
><br/>
>Am 18.08.2020 08:24 schrieb "Viechtbauer, Wolfgang (SP) "<br/>
><wolfgang.viechtbauer@maastrichtuniversity.nl>:<br/>
>Please always cc the mailing list.<br/>
><br/>
>You can include the study if you know (or can guestimate) the pre-post<br/>
>correlation.<br/>
><br/>
>SD of the change scores = SD * sqrt(2*(1-r)),<br/>
><br/>
>where SD is the pre or post treatment SD (this assumes that the SD is the<br/>
>same before and after the treatment). So if you know r, you can easily<br/>
>recover the SD and standardize in the usual manner.<br/>
><br/>
>Best,<br/>
>Wolfgang<br/>
><br/>
>>-----Original Message-----<br/>
>>From: Tobias Saueressig [mailto:t.saueressig@gmx.de]<br/>
>>Sent: Tuesday, 18 August, 2020 7:40<br/>
>>To: Viechtbauer, Wolfgang (SP)<br/>
>>Subject: Aw: RE: [R-meta] Data Extraction<br/>
>><br/>
>>Dear Wolfgang,<br/>
>><br/>
>>you are my hero. Thank you.<br/>
>><br/>
>>I am a bit sad that I cannot include the study because it is based on<br/>
>change<br/>
>>scores and I have used postintervention only.<br/>
>><br/>
>>Gesendet: Montag, 17. August 2020 um 22:33 Uhr<br/>
>>Von: "Viechtbauer, Wolfgang (SP)"<br/>
>><wolfgang.viechtbauer@maastrichtuniversity.nl><br/>
>>An: "Tobias Saueressig" <t.saueressig@gmx.de>, "r-sig-meta-analysis@r-<br/>
>>project.org" <r-sig-meta-analysis@r-project.org><br/>
>>Betreff: RE: [R-meta] Data Extraction<br/>
>>Dear Tobias,<br/>
>><br/>
>>The difference between the upper and lower CI bounds divided by the<br/>
>>appropriate critical t-value should be *twice* the SE. So:<br/>
>><br/>
>>SE <- (9.3 - -5.7) / (2*1.99)<br/>
>><br/>
>>should be the SE of the difference in the mean change between the two<br/>
>>groups. Dividing this by sqrt(1/n1 + 1/n2) should give you the SD of the<br/>
>>change scores (assuming homoscedasticity of the change variances in the two<br/>
>>groups), so:<br/>
>><br/>
>>SD <- SE / sqrt(1/30 + 1/36)<br/>
>><br/>
>>Hence:<br/>
>><br/>
>>1.8/SD<br/>
>><br/>
>>yields approximately 0.12. Sure you can apply the bias correction, but this<br/>
>>is hardly relevant here.<br/>
>><br/>
>>More importantly, this d-value standardizes the difference between the two<br/>
>>groups based on the (pooled) SD of the change scores. This is not<br/>
>comparable<br/>
>>to d-values that use the SD of a single time point for the standardization.<br/>
>><br/>
>>Best,<br/>
>>Wolfgang<br/>
>><br/>
>>>-----Original Message-----<br/>
>>>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces@r-<br/>
>>project.org]<br/>
>>>On Behalf Of Tobias Saueressig<br/>
>>>Sent: Monday, 17 August, 2020 12:03<br/>
>>>To: r-sig-meta-analysis@r-project.org<br/>
>>>Subject: [R-meta] Data Extraction<br/>
>>><br/>
>>>Hello,<br/>
>>><br/>
>>>I have a problem to extract data from one study. I want to calculate<br/>
>>hedges<br/>
>>>g.<br/>
>>><br/>
>>>I have the following information (2 groups):<br/>
>>><br/>
>>>Between-group change score from baseline to follow-up (9 months) is 1.8(-<br/>
>>>5.7,9.3) (mean and 95%CI) and p-value 0.64<br/>
>>><br/>
>>>Sample size is n1 = 30; n2 = 36 (two group RCT).<br/>
>>><br/>
>>>Link: <a href="https://linkinghub.elsevier.com/retrieve/pii/S1063458420309882" target="_blank">https://linkinghub.elsevier.com/retrieve/pii/S1063458420309882</a> (TABL<br/>
>E<br/>
>>>2 HOOS ADL)<br/>
>>><br/>
>>>I would do it the following way:<br/>
>>><br/>
>>>Calculate a SD for both group from the CI. _> SE = (Upper limit-lower<br/>
>>>limit)/t-statistic (~2) => SD = SE/squ(1/n1 + 1/n2)<br/>
>>><br/>
>>>Then g = d = MD/SD<br/>
>>><br/>
>>>g* = (1-3/(4*(n1+n2)-9) * g<br/>
>>><br/>
>>>e.g.<br/>
>>><br/>
>>>SE = (9.3+5.7)/1.99 = 7.54 => SD = 7.54/squ(1/30+1/36) = 7.54/0.25 = 30.16<br/>
>>><br/>
>>>g = 1.8/30.16 = 0.06<br/>
>>><br/>
>>>g* = 0.06 * (1-3/255) = 0.06 * 0.99 = 0.0594<br/>
>>><br/>
>>>Is that correct?<br/>
>>><br/>
>>>Best regards<br/>
>>><br/>
>>>Tobias</div>
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