###
9.4: *P*-value

*P*-value is one of the most crucial concepts in statistics.

*P*-value stands for the probability value. *P*-value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample.

A large *P*-value calculated from the data indicates to not reject the null hypothesis. But a higher *P*-value does not mean that the null hypothesis is true. The smaller the *P*-value, the more unlikely the outcome and the stronger the evidence is against the null hypothesis. The null hypothesis is rejected if the evidence is strongly against it. Generally, *P*-value < 0.05 is considered statistically significant, where 0.05 is the pre-decided significance level.

*P*-value is not a probability of rejecting the null hypothesis. It is neither a permissible statistical error nor a sampling error that may occur while conducting an experiment or collecting data. It is also not an error rate. *P*-value also does not mean that there is a 95% chance (at a pre-decided 95% significance level) that the observed difference or the outcome is real. *P*-value does not convey any information about the truth of null or alternative hypotheses.