9.4:
P-value
When a test statistic is calculated from the sample statistic, such as sample proportion, it can be located in a probability distribution.
This value of the test statistic demarcates an area under the curve from the rest of the area.
This area at the tail of the distribution is the P-value, where P stands for probability.
Assuming that the null hypothesis is true, there is always a chance of observing the calculated test statistic, or a value higher than that, in the critical region of the given distribution.
A P-value provides the probability of getting that test statistic value in the critical region just by chance alone.
So, when the P-value is observed to be smaller than a predetermined value—such as 0.05—we reject the null hypothesis, as it indicates that the observed outcome is highly unlikely and the evidence against the null hypothesis is stronger.
The P-value can be calculated at the right tail, left tail, or both the tails depending on the hypothesis or the value of the test statistic.
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.