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P value is explained very nicely in the link . But still i have not understood Why is P value interpreted under null hypothesis?

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zinnia
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    Your question has been asked before as http://stats.stackexchange.com/q/124084/22228 which got some good answers. – Silverfish Dec 02 '14 at 10:48

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If you do hypothesis testing, you always set up the distribution your estimator had under $H_0$ in the beginning. Now, you draw a sample from the real world and compute an estimate. Intuitively speaking, you will reject $H_0$ if your estimate is "very far" away from $H_0$. Since the p-values measures the probability of making an error when rejecting $H_0$, it is some sort of measure of this "very far". So, the smaller the p-value, the higher is the distance between $H_0$ and your estimate.

In general, the p-value tells you the probability to observe your estimate and values that are even more far away from $H_0$ than your estimate, if the true distribution was the one under $H_0$. Hence, $H_0$ is rejected if this probability is very low.

random_guy
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  • I have one more question.P=.23 means we have observed an event of obtaining the observed sample results or more extreme results for which the chance is 23 in 100 if the $H_0$ is actually true. In such case, we fail to reject $H_0$. But why as more i am getting extreme case than the null value , it is more likely to support $H_0$? Doesn't it imply inconsistency with $H_0$ when i am getting more extreme case than the null value ? – zinnia Dec 02 '14 at 15:16
  • I am not sure whether I understood your question but I try to answer it anyway. P=0.23 means the probability that you get such an estimate or values that differ even more from your estimate is 23% if $H_0$ was true. So, the more your estimate differs from $H_0$, the lower is the p-value. The p-value simply tells you the probability to make an error when rejecting $H_0$ because even if an estimate differs strongly from $H_0$, there is still a low probability to observe it under $H_0$. Hence, people try to make this error probability very low and use usually as max for p 5%. – random_guy Dec 19 '14 at 20:50