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I am trying to understand hypothesis testing for correlation coefficient.

T = r√(n-2) / √(1-r^2)

It is known that the statistics follow t-distribution. I saw the many similar questions but many of them direct the link which is broken for now.

https://onlinecourses.science.psu.edu/stat414/node/254

Can someone explain why the equation above follow t-distribution?

Many thanks!

Sungmin Son
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  • By *definition,* the correlation is the dot product of two standardized vectors. "It is known that" is true only when those vectors are standard Normal. In that case, https://stats.stackexchange.com/questions/85916/distribution-of-scalar-products-of-two-random-unit-vectors-in-d-dimensions/85977#85977 fully answers your question. – whuber May 10 '21 at 14:52

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