# Degrees of freedom when manually doing (Welch) T-test?

I have two samples A and B and want to test if the (Pearson) auto-correlation of A is greater than that of B. So far I've computed the two autocorrelations, $$r_a$$ and $$r_b$$ and found their standard deviations using $$\sigma_x = \sqrt{\frac{1 - r^2}{n_x - 2}}$$ (where $$x$$ denotes $$a$$ or $$b$$ and $$n_x$$ is the number of data points in each of the two samples).

It's been a while since I took statistics, but I seem to recall that the way to test for something like this is to compute a T value according to $$t = \frac{r_a - r_b}{\sqrt{\sigma_a^2 + \sigma_b^2}},$$ and then look up that value in a table and find the corresponding p-value (I believe this is the Welch test?). However, when I look up such tables, they have separate rows for the number of degrees of freedom, which I don't recall the meaning of or how to obtain. Making matters worse, I find different formulas for this, such as $$n_a + n_b - 2$$ here or sometimes a long complicated expression.

Can someone help me understand which is the correct one and what it means?

• Thanks, but... are you sure this works? That answers recommends using the Fisher transformation, which assumes independence. As I'm looking at autocorrelation, that seems wrong, right? Dec 18, 2018 at 13:12
• Good point. I hadn't checked the assumptions well enough. I'll remove my comments. Dec 18, 2018 at 15:11