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Correct me if I am wrong, The region of rejection is we picked up a significant level then use that to calculate rejection region while P value is the conditional probability of alternative hypothesis $Ha$ on $Ho$ is true then we compare with significant level?

Is significant level a conditional probability of Reject Ho on Ho is true?

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  • $\begingroup$ $p$-value has nothing to do with $H_0$ being true. Check stats.stackexchange.com/questions/31/… for a start or this recent thread stats.stackexchange.com/questions/347653/… $\endgroup$
    – Tim ♦
    May 24, 2018 at 11:58
  • $\begingroup$ Thanks. According to the link you refer, $P$($Samplemean$ ≥ 5ft 9inches|$Truevalue$=5ft7inches).Which the true value is $Ho$ is true which $u$ is population mean? I thought it is same as my understanding? $\endgroup$
    – FunctionBlock
    May 24, 2018 at 12:33
  • $\begingroup$ $P(X|H_0) \ne P(H_0|X)$ $\endgroup$
    – Tim ♦
    May 24, 2018 at 12:34
  • $\begingroup$ Thanks Tim. If I edit my question as this way, does it make more sense? $\endgroup$
    – FunctionBlock
    May 24, 2018 at 12:42
  • $\begingroup$ re-read/digest the link, my understanding is: region of rejection is by positioning $Z$ test result in the confidence interval, we can see whether the null hypothesis is rejected or not. Same conclusion can be obtained from $P$ value test. After calculate $P$ value from alternativehy pothesis $Ha$ on Null hypothesis $Ho$, if value is greater than significant level then we don't reject $Ho$, but if value is smaller, we reject it. $\endgroup$
    – FunctionBlock
    May 24, 2018 at 13:13

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the region of rejection test is using Z value. It just simply reject the result without showing the strength of significance? This is why we introduce P value

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  • $\begingroup$ To me, the rejection region shows the proportion of area under normal curve that accommodates values of Z beyond that of normal distribution. $\endgroup$
    – user10619
    Aug 9, 2018 at 14:24
  • $\begingroup$ It shows the area occupied by outliers (Z values more than the expected Z under the assumption of (say) alpha = .05 . The probability or alpha level for a given distribution of observed scores is usuailly calculated by simulation. If the calculated probability is less than or equal to say, assumed alpha (.05), we say that the effect-size is statistically significant at .05 . $\endgroup$
    – user10619
    Aug 16, 2018 at 11:40

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