What is a 'P-Test'

A p-test is a statistical method used to assess 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, meaning one in which the sample size, "n," is not greater than 5 percent 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.


A p-test can be applied in any number of scenarios. 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.

As one website explains, "for a study to be considered significant it needs to pass a statistical test called a p-test. If the p-value, resulting from this test, is less than 0.05 this means that there is less than a 5 percent chance of the results arising due to random chance. Essentially this means that the likelihood of the result being due to the reasons prescribed by the researchers is over 95 percent. This is a high level of probability and means that, if the studies were all carried out correctly, they should have been at least 95 percent repeatable."

How a P-Test Can Help with Picking Good Stocks

An article from The Motley Fool explained the value of being able to parse statistics to truly understand the inner mechanisms of how things operate. That comes especially handy when analyzing stocks, not least, as the Fool explained, those from complex spaces such as biotechnology.

"The success or failure of biotechs depends heavily on statistics used in clinical trials," the website noted. "And few statistical factors are as important as the p-test."

The simplest way to understand p-tests is their focus on probability, the site explains that "in particular, the probability that a hypothesis is true. With clinical trials of a drug, it's critical to ensure that any perceived effectiveness of the drug isn't due to chance. Trials are structured to show statistically what the probability of results being due to chance are."

For investors, a basic working knowledge of how statistics inform clinical trials can help them better understand clinical results, often enabling them to make better assessments of a biotech stock's potential returns.

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