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The Pearson product-moment correlation coefficient is a measure of the linear relationship between two variables $X$ and $Y$, giving a value between +1 and −1.

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When testing Pearson's r, when should I use r-to-t transformation instead of [Fisher's] r-to...

At least two tests are common for testing the significance of a Pearson correlation coefficient. Comparing $t=\frac{\sqrt{r^2/(1-r^2)}}{\sqrt{\frac{1}{N-2}}}$ to Student's $t$-distribution with $N-2 …
Nils Enevoldsen's user avatar
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When testing Pearson's r, when should I use r-to-t transformation instead of [Fisher's] r-to...

That is correct. (The answer to my question was posted by another user as a since-deleted comment. I'm adding this comment so I can mark the question as answered.)
Nils Enevoldsen's user avatar