CODEWITHSUNDEEP
rcorrelationvariancepearson-correlation
Patrick Gerbersmann
Patrick Gerbersmann

Reputation: 81

Calculating the variance of a correlation just from r for a meta-analysis

I am writing a meta-analysis atm and some of my papers only give me a correlation coefficient instead of means and standard deviations for a standardized mean difference(SMD).

So to calculate the SMD from r I can calculate that following Bornstein (2009), but I also need the variance of r, which is not given in the paper. I can not for the life of it find a good citeable source for the variance formula of a correlation coefficient. The only formula I found on non-quotable sites was Standard error of r . Now this is the standard error, not the standard deviation and I think I can not just square that to get the variance???

All I need is a valid source for calculating the variance of r, so I can transform r and its variance into a SMD and its variance. Thanks for the help.

Btw a way of doing it in R could be enough.

Upvotes: 0

Views: 782

Answers (2)

JRB
JRB

Reputation: 233

In Borenstein et al. (2009), the following formula is provided for the variance of the correlation coefficient:

Vr = (1 - r^2)^2 / n - 1

where n is the sample size.

Upvotes: 0

tester
tester

Reputation: 1692

See here https://www.jstor.org/stable/2277400?seq=1 and here https://stats.stackexchange.com/questions/226380/derivation-of-the-standard-error-for-pearsons-correlation-coefficient you can just square it.

set.seed(123)

n <- 100
x <- rnorm(n)
y <- rnorm(n) 

r <- cor(x, y)
r

se <- sqrt((1-r^2)/(n-2))
se

r_var <- se^2
print(r_var)

Upvotes: 0

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