Classification
Contents
Definition
P-value is one of most used statistical term, it is a quick method for detecting statistical significance where if the P-value<(signifiance level) then the result is significant. signifiance level or alpha is a pre-defined threshold value small value 0.05 or 0.1. Looking at Wikipedia,
A p-value is defined as the probability of obtaining as extreme or a more extreme result than found in observed data, where the probability is computed under a null hypothesis H0 (under the assumption that the null hypothesis is correct). It demonstrates typically as a useful measure of evidence against a null hypothesis or a probability quantifying the strength of the evidence against the null hypothesis in favor of the alternative, hence large value of it suggests the rejection of null hypothesis in favour of the alternative hypothesis. When the P-value is equal to or greater than the significance level, we conclude that there is insufficient evidence to reject the null hypothesis. We do not reject the null hypothesis, and we say that the results are not significant at the significance level
If T is a test statistic for which the extreme values suggest rejection of H0, then the p-value for the data observation Y is
-
p= P(T ≥ T(Y ) H0 ) for a one-sided right-tail test, -
p= P(T ≤ T(Y ) H0 ) or a one-sided left-tail test, -
p= 2min(P(T ≥ T(Y ) H0 ), P(T ≤ T(Y ) H0 ) )
It shows p-value provides a diatance measure; it shows how far out is the test statistic under holding the null hypothesis. The further out the test statistic in the tail, we get smaller the P-value, and the stronger the evidence against the null hypothesis in favor of the alternative.
Usage
Reporting the p-value might not enough, so we can add sentence, the following table might help to choose our sentence in our report
| Range | Sentence |
|---|---|
| P-value> 0.1 | No evidence against the null hypothesis. The data appear to be consistent with the null hypothesis. |
| 0.05 < P < 0.10 | Weak evidence against the null hypothesis in favor of the alternative |
| 0.01 < P < 0.05 | Moderate evidence against the null hypothesis in favor of the alternative. |
| 0.001 < P < 0.01 | Strong evidence against the null hypothesis in favor of the alternative. |
| P < 0.001 | Very strong evidence against the null hypothesis in favor of the alternative. |
Misusage
Sometime the P-value is incorrectly intrepted the probability that the null hypothesis is true. It does not make sense, because the randomness come from the observed data and it can measure thw one’s believe of the null hypothesis. Also it is suggested to use other measure of evidence, such as confidence interval, likelihood ratio.
References
- [1] https://en.wikipedia.org/wiki/P-value
License
Copyright (c) 2020 Saeid Amiri
