Pfalse

Pfalse is a non-standard, context-dependent symbol used in statistics and data analysis to denote the probability that a given claim, hypothesis, or detected effect is false. Because it is not universally defined, its exact meaning varies by author, field, and application. In practice, pfalse can refer to different quantities in different settings, so it is important to consult the defining source.

In Bayesian contexts, pfalse is sometimes used to denote the posterior probability that the null hypothesis is false (i.e., that the alternative is true) after observing data. This interpretation depends on the chosen prior distribution over hypotheses and the likelihood function. In decision-theoretic or frequentist framing, pfalse may be described as the probability that a decision rule leads to a false conclusion, such as a false positive, under the specified model or threshold.

In multiple testing and discovery contexts, some authors use pfalse to indicate the probability that a reported finding is a false positive. However, this usage is not standardized; the more common terms are false discovery probability or false discovery rate, which have their own formal definitions and methods.

Relation to other statistics: pfalse is distinct from a p-value, which measures the compatibility of observed data with the null hypothesis under the null model rather than the truth status of the hypothesis itself. Because definitions of pfalse differ, readers should verify the exact meaning in any given source.

See also: p-value, false positive rate, false discovery rate, Bayesian hypothesis testing, posterior probability.