Sample proportion (p̂)

How to read it

Penn State’s STAT 500 course notes set the pair side by side: “p is the population proportion. It is a fixed value. p̂ is the sample proportion. It varies based on the sample.” The hat marks an estimate: p̂ is calculated from the data and estimates p, which is usually unknown. OpenStax’s Introductory Statistics describes the calculation as the number of successes, X, divided by n, the number of trials or the sample size. Unicode gives “hat” as another name for the combining circumflex accent, U+0302, and there is no single character for p̂: it is p followed by that mark.

Also searched as: p̂, p hat, p hat symbol, proportion symbol, sample proportion symbol.

p′ in OpenStax

OpenStax’s Introductory Statistics writes the sample proportion p′, read “P prime”, with q′ for the proportion of failures, and notes that the same quantity is sometimes written P̂, read “P hat”. p′ and p̂ mean the same thing.

A Latin letter for the population

The proportion is an exception to the habit of Greek letters for the population. Penn State’s notes give the population mean μ and the population proportion p as their two examples of population parameters, and x̄ and p̂ as the matching sample statistics. For a proportion it is the hat, not the alphabet, that tells the sample from the population.

Look-alikes

The p of a proportion is a different p from the one in a P-value (p), a probability from a hypothesis test, though both appear in the same textbook chapters: one of OpenStax’s tests has H₀: p ≤ 0.066 for a population proportion. The hat is the same mark as on the predicted value ŷ; the keyboard’s caret ^ is a separate character, U+005E, which Unicode cross-refers to the combining hat.