# [R-meta] Dependant variable in Meta Analysis

Tarun Khanna kh@nn@ @end|ng |rom hert|e-@choo|@org
Thu Jun 4 14:15:50 CEST 2020

```Thank you for your reply Wolfgang.

The "beta coefficients" that I refer to are not standardized regression coefficients but the relevant regression coefficients in the original studies. Would it be correct to direcly meta analyze the coefficients even when they are not standardized? How to we take into account the standard error of the coefficients? I have seen meta analysis in the literature that use the tranformation beta coefficient/ (sample size)^1/2 but I don't see how that takes into account the associated standard error.

I have instead been calculating r coefficients using the t values of the relevant coefficients and the sample size using the following formula.

r = ( t^2 / (t^2 + sample size) )^1/2

I have been using the r to Fisher's Z transformation that you mentioned. Unfortunately, like you mentioned most of the studies employ multivariate analysis and so the transformation is not accurate. What would be the correct way to handle this?

Best

Tarun

Tarun Khanna

PhD Researcher

Hertie School

Friedrichstraße 180

10117 Berlin ∙ Germany
khanna using hertie-school.org ∙ www.hertie-school.org<http://www.hertie-school.org/>

________________________________
From: Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
Sent: 04 June 2020 13:56:59
To: Tarun Khanna; r-sig-meta-analysis using r-project.org
Subject: RE: Dependant variable in Meta Analysis

Dear Tarun,

What exactly do you mean by 'beta coefficient'? A standardized regression coefficient? In the (very unlikely) case that the model includes no other predictors and is just a standard regression model, then the standardized regression coefficient for that single predictor is actually identical to the correlation beteen the predictor and the outcome and converting this correlation via Fisher's r-to-z transformation is fine (and then 1/(n-3) can be used as the corresponding sampling variance). However, if there are other predictors in the model, then the standardized regression coefficient is not a simple correlation and while one can still apply Fisher's r-to-z transformation to the coefficient, it will not have a variance of 1/(n-3) and assuming so would be wrong.

Why don't you just meta-analyze the 'beta coefficients' directly? If these coefficients reflect percentage change, it sounds like they are 'unitless' and comparable across studies. Then you get the pooled estimate of the percentage change directly from the model.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org]
>On Behalf Of Tarun Khanna
>Sent: Thursday, 04 June, 2020 13:41
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] Dependant variable in Meta Analysis
>
>Dear All,
>
>I am conducting a meta analysis of reduction in energy consumption in
>households that have been exposed to certain behavioural interventions in
>trials. The beta coefficients in the regressions in my the original studies
>can ususally be interpreted as percentage change in electricity consumption.
>To do the meta analysis I am converting these beta coefficients to Fisher's
>Z. My problem is that Fisher's Z is not as easy to interpret as percentage
>change in energy consumption.
>
>Question 1: Is it possible to do the meta anlysis using the beta
>coefficients coming from the original studies so that the results remain
>easy to interpret?
>
>Question 2: Is it sensible to convert the final Fisher's Z estimates back to
>the dependant variable coming from the studies?
>
>Sorry if this question sounds too basic.
>
>Best
>
>Tarun
>Tarun Khanna
>PhD Researcher
>Hertie School
>
>Friedrichstraße 180
>10117 Berlin ∙ Germany
>khanna using hertie-school.org ∙ www.hertie-school.org<http://www.hertie-school.org>

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