0
$\begingroup$

I don't quite understand the explanation of an answer in my textbook.

Data are collected on the height of a cake and the temperature. When a hypothesis test is conducted to test for positive correlation, the p-value is $0.032$. Is this evidence of positive correlation at the $5%$ significance level? (Yes)

If the correlation coefficient increases, does this increase or decrease the p-value? Justify your answer.

In the explanation of the answer, the textbook says:

If $r$ increases then it becomes less likely that this is a chance result from a population with $ρ = 0$. So the p-value decreases.

Improve this question
$\endgroup$
2
  • $\begingroup$ If $r$ increases, it means that deviation from $\rho = 0$ has become more extreme. Since more extreme observations are less likely, $p$-value decreases. $\endgroup$
    – Mr K
    Aug 14, 2018 at 1:14
  • $\begingroup$ Ah, got you. Thanks! Post as an answer? $\endgroup$
    – Chx
    Aug 14, 2018 at 1:17

1 Answer 1

Reset to default
1
$\begingroup$

If $r$ increases, it means that deviation from $\rho=0$ has become more extreme. Since more extreme observations are less likely, $p$-value decreases.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.