How one derives significance test for pearsons correlation coefficient? I am exploring statistics a

groupweird40

groupweird40

Answered question

2022-05-22

How one derives significance test for pearsons correlation coefficient?
I am exploring statistics and probability. What upsets me, only ready to use algorithms are present in the books. But no example how one derives a significance test, where from the test statistics come from etc. At the moment I am interesten in Pearsons coefficient significance test, but really derivation of any popular test will be helpful for me.

Answer & Explanation

Madisyn Avery

Madisyn Avery

Beginner2022-05-23Added 12 answers

Generally, any hypothesis test is derived using a very basic strategy:
1. Formulate the null hypothesis H 0 as a statement about a statistic
2. Pick an underlying distribution for the data (or decide you are doing a nonparametric test)
3. Determine the sampling distribution of the statistic if we assume H 0 is true.
4. Determine the rejection region from the sampling distribution.
How do you choose a test statistic? That is the art of designing a good test, and always an area of active research!

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