Calculate sample proportion, confidence intervals, one-proportion z-tests, and required sample size from successes, sample size, and expected proportion.

Inference assumes a representative random sample of independent binary outcomes. Approximate methods do not correct selection bias or dependence.

P-Hat Formula

The following formula is used to calculate p-hat (p^).

p = X / n

  • Where p^ is the sample proportion, an estimate of the population proportion
  • X is the number of occurrences of an event
  • n is the sample size

To calculate p-hat (p^), divide the number of occurrences of an event by the sample size.

P-Hat Definition

P-hat (p^) is the sample proportion: the number of successes divided by the sample size. It estimates the population proportion.

Generalizing this estimate to the population requires an appropriate sampling design. Confidence intervals and z-tests also require their stated statistical assumptions.

P-hat is most often used in the field of statistics, but statistics are used in nearly all STEM fields, so you can say that the p-hat sees important use in many fields. A formula and example of how it's used are shown below the calculator.

P-hat Example

How to calculate p-hat?

  1. First, determine the sample size.

    Determine the size of the sample you wish to analyze. For this example, we will say this is a sample size of 100.

  2. Next, determine the number of occurrences in the sample.

    Measure how many occurrences of an event or parameter are found in the sample. For this example, we will say this is 10.

  3. Finally, calculate p-hat.

    Calculate p^ using the formula. We find p^=10/100 = .10.

FAQ

What is p-hat?

P-hat, also denoted p^, is the sample proportion x/n. It estimates the population proportion p from the observed successes and sample size; the estimate is not the known population probability.