2
$\begingroup$

We are trying to create a table of standardised effects and standardised errors to compute for a meta-analysis. And I had a few questions around this

  1. Can you get a standard error for pearson correlation, and if so can it be back calculated knowing the sample size, and r value. Or what other information do you need.

  2. In a regression output I see people report unstandardised coefficients, standard error, and standardised coefficient. Is this standard error the standard error of the standardised coefficient or the unstandardised?

  3. How do you back calculate a standardised error if you have a standardised coefficient, p value, and n?

$\endgroup$
3
$\begingroup$

Q1 The usual suggestion for meta-analysis of correlation coefficients is to transform them first. Although it is possible to calculate a standard error for the Pearson product moment statistic it is only really useful for very large sample sizes and population values of $r$ close to zero. The question linked to by @Glen_b in a comment Expected value and variance of sample correlation gives more details.

The usual transformation suggested first by Fisher is the hyperbolic arctangent $$ z = \frac{1}{2} \log \left(\frac{1 + r}{1 - r}\right) $$ with standard error $\frac{1}{\sqrt{N - 3}}$ where $N$ is the sample size. Note this is strictly only correct for bivariate normals but it is widely used nonetheless. It does of course have the advantage of mapping from [-1,1] to [$-\infty,\infty$]

Q2 I would assume the standard error was for the unstandardised coefficient but that is a wild assumption. You really need to ask the authors.

Q3 first back-calculate the value ot $t$ or $z$ corresponding to that $p$ and $n$. Then since you know that $t$ = coeff / se you can work out se.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.