# Test if correlations differ

This question is probably pretty basic but I don't know what key words I need to be googling to find the right answer.

I am running the same regression model on some data for two different years (the data is paired). I then calculate the correlation between the fitted values and residuals for each year. Now I would like to test if the difference in correlation coefficients is significant given the sample size.

What test should I use for this?

These are the data by the way :)

cor1 = 0.89 cor2 = 0.83 sample_size = 150

## 1 Answer

Read about the Fisher's transform. source

This transformation makes the Pearson's correlation coefficient Statistic (R) to be normally distributed no matter which R you are observing on your sample.

Just in case you did not know: if you observe a close to zero sample estimate of Pearson correlation, it is normally distributed, but when it moves to either side, the distribution becomes biased.

After making the transform you are also able to calculate the standard error for the Statistic. With these two components at hand you are able to say if there is a significant difference between the values.