[R-meta] Negative r value for effect sizes within studies

[Reza Norouzian]

Dear Stefanou,

In short, it depends on whether you have a single outcome or, if you
have more than one outcome, whether the outcomes run in opposite
directions or not.

In the former case, regardless of the direction of the single outcome
in question (e.g., whether the higher is better or lower is better),
the effect size estimates can be shown to be positively correlated
within studies.

In the latter case, if the outcomes run in opposite directions, then,
the effect size estimates obtained across the opposing outcomes can be
shown to be negatively correlated within studies.

That said, when possible, it is common to sync the direction of the
outcomes by reversing the sign for some of them, in which case, again,
you end up expecting positively correlated effect size estimates
within studies.

The syncing of outcome directions is especially helpful when things
can get a little bit complicated within studies. For example, in the
presence of multiple treatment groups being compared to a common
control, effect size estimates for the treatment groups on each
outcome (regardless of its direction) are again positively correlated.
But effect size estimates for the "same treatment groups" across the
opposing outcomes tend to have a negative correlation.

The same thing happens if we add a longitudinal aspect to the studies.
Effect size estimates obtained at each time point are positively
correlated on each outcome (regardless of its direction). But then,
these effect size estimates for "same treatment groups" are negatively
correlated with their counterparts obtained on opposing outcomes
within studies.

Of course, if you have a single treatment group compared to a control
group on two opposing outcomes in a study, then you can use a single
negative r value:

impute_covariance_matrix(..., r = -.6)

But as I mentioned above, in most realistic situations, opposing
outcomes make it a bit challenging to simply provide a single negative
r value (consider syncing!)

Best,
Reza



On Fri, Sep 3, 2021 at 11:47 AM Stefanou Revesz
<stefanourevesz using gmail.com> wrote:
>
> Dear All,
>
> This may be too basic to ask. But can the r value chosen to represent
> the common correlation among effect sizes within studies be a negative
> one?
>
> For example, is there a situation where I would need to use the following?
>
> impute_covariance_matrix(..., r = -.6)
>
> Thank you,
> Stefanou
>
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