The sample proportion, denoted p̂, is given by p̂=, where x is the number of individuals in the sample with the specified characteristic. The sample proportion, p̂, is a statistic that estimates the population proportion, p.

In hypothesis testing, p is the calculated p-value (defined here in Chapter 10), the probability that rejecting the null hypothesis would be a wrong decision. In tests of population proportions, p stands for population proportion and p̂ for sample proportion (see table above).

The uncertainty in a given random sample (namely that is expected that the proportion estimate, p̂, is a good, but not perfect, approximation for the true proportion p) can be summarized by saying that the estimate p̂ is normally distributed with mean p and variance p (1-p)/n.

We can equally imagine states of definite momentum, p, with p ̂ p = p p. Then α (p) = ⟨ p | α ⟩ is the wave function in position space; in this representation p ̂ is given by p and x by (i ℏ) d ∕ d p.