What is a 'P-Test'

A statistical method used to test one or more hypotheses within a population or a proportion within a population. When testing a hypothesis about a population proportion (p) within a large population (one in which the sample size, "n", is not greater than 5% of the overall population), the formula is:

x = (m/n-P) / SqRt[P(1-P)/n]
m= "yes" response
n = random sample size
p = proportion
P = population

This formula is used to test three hypotheses:

  1. p ≤ P
  2. p ≥ P
  3. p = P

The p-test statistic typically follows a standard normal distribution when large sample sizes are used, and researchers use Z-tests to determine whether a hypothesis passes based on a specific significance level will be rejected. The larger the p-value in the p-test, the more likely the hypothesis is true.


For example, a polling group contacted a group of investors and asked if they felt that the economy would fall into a recession. Of the 1000 people contacted, 700 said that they thought that the economy was heading toward recession. The researchers then applied the P-Test to determine if p ≤ 0.60, p ≥ 0.60, or p = 0.60; basically, what percentage of the population believe that the economy will fall into a recession.

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