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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.

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  • $\begingroup$ 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
    Commented Aug 14, 2018 at 1:14
  • $\begingroup$ Ah, got you. Thanks! Post as an answer? $\endgroup$
    – Chx
    Commented Aug 14, 2018 at 1:17

1 Answer 1

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

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