P-value

In statistics, the p-value is the probability that, using a given statistical model, the statistical summary (such as the sample mean difference between two compared groups) would be the same as or more extreme than the actual observed results.Statistical hypothesis testing making use of p-values is commonly used in many fields of research such as economics, finance, political science, psychology,biology, criminal justice, criminology, and sociology. Their misuse has been a matter of considerable controversy.

The p-value is defined as the probability of obtaining a result equal to or "more extreme" than what was actually observed, when the null hypothesis is true.

In frequentist inference, the p-value is widely used in statistical hypothesis testing, specifically in null hypothesis significance testing. In this method, as part of experimental design, before performing the experiment, one first chooses a model (the null hypothesis) and a threshold value for p, called the significance level of the test, traditionally 5% or 1% and denoted as α. If the p-value is less than or equal to the chosen significance level (α), the test suggests that the observed data is inconsistent with the null hypothesis, so the null hypothesis must be rejected. However, that does not prove that the tested hypothesis is true. When the p-value is calculated correctly, this test guarantees that the Type I error rate is at most α. For typical analysis, using the standard α = 0.05 cutoff, the null hypothesis is rejected when p < .05 and not rejected when p > .05. The p-value does not, in itself, support reasoning about the probabilities of hypotheses but is only a tool for deciding whether to reject the null hypothesis.

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