In frequentist statistics, the p-value is a function of the observed sample results (a test statistic) relative to a statistical model, which measures how extreme the observation is.

Statistical hypothesis testing making use of p-values are commonly used in many fields of science and social sciences, 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.

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.

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.

For instance, if the null hypothesis is assumed to be a standard normal distribution N(0,1), the rejection of this null hypothesis can either mean (i) the mean is not zero, or (ii) the variance is not unity, or (iii) the distribution is not normal, depending on the type of test performed.

However, supposing we manage to reject the zero mean hypothesis, even if we know the distribution is normal and variance is unity, the null hypothesis test does not tell us which non-zero value we should adopt as the new mean.In statistics, a statistical hypothesis refers to a probability distribution that is assumed to govern the observed data.Thus, this naive definition is inadequate and needs to be changed so as to accommodate the continuous random variables.The American Statistical Association, in a statement on the use of p-values, affirmed the usefulness of properly interpreted p-values, but cautioned that p-values are "commonly misused and misinterpreted." The use of bright-line rules as cutoffs, such as p ≤ 0.05, without other supporting statistical evidence, was particularly criticized: The widespread use of “statistical significance” (generally interpreted as “p ≤ 0.05”) as a license for making a claim of a scientific finding (or implied truth) leads to considerable distortion of the scientific process.Null hypothesis testing is a reductio ad absurdum argument adapted to statistics.In essence, a claim is shown to be valid by demonstrating the improbability of the consequence that results from assuming the counter-claim to be true.

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