p Value - the probability of observing a test statistic that is as extreme or more extreme than currently observed assuming that the null hypothesis is true. This can be expressed as Pr(data|H0), where "Pr" is read "the probability of" and "|" is read as "given" or "conditional upon." The statistic should NOT be interpreted as the probability of H0 being true.
p Value can be used in different ways. Using a fixed-level method of hypothesis testing, we compare the p value to a predetermined a. If p < a, the null hypothesis is rejected. This provides a method of "inductive behavior" intended to restrict the number of type I errors a researcher will make in the long run. Fixed-level testing was promoted by Pearson and Neymann as a framework decision making but has been criticized as "unscientific" according to some points of view.
p Value can also be used more flexibly if we adopt Fisher's philosophy of significance testing. Using Fisher's approach the p value is as a measure of evidence from a single experiment. As a measure of evidence, the p value is meant to be combined with other sources of information. Thus, there is no set threshold for "significance" (Fisher, 1973).
The researchers should not place reliance on the p value as a means of reaching causal conclusions. The p values must be interpreted in context of other information.