Solved – How to test whether average of ten independent correlations is different from zero

correlationrepeated measurest-test

I have calculated the correlation between A and B for 10 different subjects. For averaging purposes, I've converted the r-values to z-values using Fisher's z-transformation. 

subj zvalue
s1 -0.04
s2 -0.14
s3 -0.29
s4 -0.20
s5 -0.37
s6 -0.01
s7 -0.09
s8  0.20
s9 -0.15
s10  0.09

I want to test if the correlation between A and B is significantly different from zero. Do I use a paired sample t-test against 0 with the z-values, then report the r-value converted from the mean z-value? Or should I convert each subject's z-value back to an r-value before doing the t-test?

Edit:
Critically, is a paired t-test against 0 appropriate to test if this correlation is significant across subjects?

Best Answer

Treat r (or Z) as any effect size and calculate its mean using a standard formula:

$\bar{r} = \Sigma r_iw_i$/$\Sigma w_i$

where $r_i$ is the $i$th value of r and $w_i$ is a weighting factor which is $1/s^2(r_i)$

The standard error of $\bar{r}$ is given by the square root of $1/\Sigma w_i$ and you can use this to construct confidence intervals around $\bar{r}$ and check whether they include 0 or not.

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