pvalue

A p-value is a measure used in statistical hypothesis testing to quantify the compatibility of observed data with a null hypothesis. Formally, it is the probability of obtaining a result at least as extreme as the one observed, assuming that the null hypothesis is true and that the statistical model being used is correct. The exact calculation depends on the chosen test and its sampling distribution under the null.

In practice, researchers compare the p-value to a predetermined significance level, often denoted alpha. If the p-value is at or below alpha, the null hypothesis is rejected as statistically unlikely given the data; if it is above alpha, the null is not rejected. The choice of a one-sided or two-sided test affects the interpretation of the p-value, with two-sided tests considering extreme outcomes in both directions.

P-values are frequently misunderstood. A small p-value does not prove that the null is false, nor does it measure the probability that the observed effect is true or practically important. They are also sensitive to sample size and model assumptions; larger samples can yield small p-values for trivial effects, while small samples can produce large p-values even for meaningful effects. Misuse includes p-hacking and selective reporting, especially in the presence of multiple comparisons, where adjustments to the significance level or p-values are necessary.

Related concepts include confidence intervals and Bayesian alternatives such as Bayes factors. Proper interpretation emphasizes the role of the p-value as one piece of evidence about the null hypothesis, not a definitive verdict on the truth of any hypothesis.