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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?

FunctionBlock
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  • $p$-value has nothing to do with $H_0$ being true. Check https://stats.stackexchange.com/questions/31/what-is-the-meaning-of-p-values-and-t-values-in-statistical-tests for a start or this recent thread https://stats.stackexchange.com/questions/347653/is-the-sum-of-p-value-and-specificity-1 – Tim May 24 '18 at 11:58
  • 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? – FunctionBlock May 24 '18 at 12:33
  • $P(X|H_0) \ne P(H_0|X)$ – Tim May 24 '18 at 12:34
  • Thanks Tim. If I edit my question as this way, does it make more sense? – FunctionBlock May 24 '18 at 12:42
  • 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. – FunctionBlock May 24 '18 at 13:13
  • Can I say 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 – FunctionBlock May 25 '18 at 14:29
  • what do you mean by strength of significance ? Are you making a reference to any thing different from level of significance ? –  Aug 09 '18 at 14:00

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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

FunctionBlock
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  • To me, the rejection region shows the proportion of area under normal curve that accommodates values of Z beyond that of normal distribution. –  Aug 09 '18 at 14:24
  • 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 . –  Aug 16 '18 at 11:40