P-Value

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In statistical hypothesis testing, the p-value or probability value is the probability for a given statistical model that, when the null hypothesis is true, the statistical summary (such as the sample mean difference between two compared groups) would be the same as or of greater magnitude than the actual observed results.[1] The use of p-values in statistical hypothesis testing is common in many fields of research[2] such as economics, finance, political science, psychology,[3] biology, criminal justice, criminology, and sociology.[4] Their misuse has been a matter of considerable controversy.

The p-value is used in the context of null hypothesis testing in order to quantify the idea of statistical significance of evidence.[a] 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.

As such, the only hypothesis that needs to be specified in this test and which embodies the counter-claim is referred to as the null hypothesis (that is, the hypothesis to be nullified). A result is said to be statistically significant if it allows us to reject the null hypothesis. That is, as per the reductio ad absurdum reasoning, the statistically significant result should be highly improbable if the null hypothesis is assumed to be true. The rejection of the null hypothesis implies that the correct hypothesis lies in the logical complement of the null hypothesis. However, unless there is a single alternative to the null hypothesis, the rejection of null hypothesis does not tell us which of the alternatives might be the correct one.

As a general example, if a null hypothesis is assumed to follow the standard normal distribution N(0,1), then 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.