# The P-Value – Definition & Examples

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A p-value, also known as a probability value, is a digit that defines how probable you are to find a certain set of outcomes if the formulated null hypothesis is true. It is usually derived from a statistical test.

## P-value – In a Nutshell

• The probability value is the plausibility of getting results at a minimum as extreme as the observed outcomes of a statistical hypothesis if the null hypothesis is true.1
• It is a statistical measurement derived from a statistical test and used to validate a hypothesis against observed data. It also helps decide whether to reject or retain a null hypothesis.
• The p-value determines the statistical significance of the observed difference.1
• The probability value is usually found in p-value tables or statistical software.2

## Definition: P-value

In statistics, the probability value refers to the likelihood of obtaining results at a minimum as extreme or significant as the experimental results of a statistical hypothesis test, assuming that the null hypothesis is true.

The p-value offers the minor significance level at which the null hypothesis would be vetoed as an alternative to refusal points. You can calculate the p-value using statistical programs or software.

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## The null hypothesis for the p-value

In statistical tests, the null hypothesis usually states that there isn’t a correlation between the interest variables or no difference among groups. Therefore, a null hypothesis predicts no statistical significance between the observed results and the data sets to which they belong.3

In contrast, the alternative hypothesis predicts that there is a variance between the group or a relationship between the variables.1

Example: Formulating the null and alternative hypothesis

You want to determine if there is a disparity in lifespan between two groups of rabbits fed on different diets.

• You can label the two diets as X and Y.
• Using a two-tailed statistic test, you can test the difference between diets X and Y.

## What precisely is a p-value?

The probability value explains or determines how probable your observed data could have befallen under your formulated null hypothesis.

Therefore, the probability rate (value) tells you how recurrently you would anticipate seeing a test statistic as extreme or beyond the one derived by your statistical test, assuming that the H0(null hypothesis) was correct.1

It is also worth noting that the p-value is a percentage or proportion. Therefore, a probability value of 0.05 implies that 5 percent of the time, you would identify a test statistic as extreme as that found if your null hypothesis was correct.2

Example:

If the rabbits in your test live longer on either diet, then your test statistic from your test will meticulously match the null hypothesis’ test statistic. Therefore, the subsequent p-value will be near 1 (not exactly one).

In contrast, if there is a variance in the lifespan between the two groups, your test statistic will be more distant from the predicted null hypothesis value. Therefore, the p-value will be smaller.

However, the probability value will never be zero because even in extreme cases, there is a plausibility that the series of observations in your observed data could have occurred coincidentally.

## Calculating the p-value

Statistical programs and software like R and SPSS exist for automatically calculating p-values. Also, several tables for approximating the p-value exist online.2

The tables depend on the test statistics and freedom degrees of your test to show how frequently you would anticipate seeing a similar test statistic in the presented null hypothesis.

Note that the probability value calculation usually is contingent on the applied statistical test for hypothesis testing.3

This is because:

• Different statistical tests have varying assumptions.
• The quantity of independent variables you have in your test usually changes the size of the test statistic you need to generate the same probability value.2

The p-value usually describes the same thing, regardless of the test you use.

Example: Selecting a statistical test

• You can use a t-test with two samples to compare your groups because you will be comparing two diets.
• ANOVA tests would work for three diets.

## Statistical significance and the p-value

Researchers use probability values to tell if a specific measured pattern is statistically significant. The statistical significance measures the likelihood of the null premise of a study is correct.

• The most popular threshold is p is less than 0.05.
• This means that you would anticipate to discover a test statistic equally extreme as that mathematically devices by your test only 5 percent likely (in time).

However, your study field usually influences the threshold.

• For instance, some study fields prefer a 0.01 or 0.001 threshold.
• The threshold value is also called the alpha value.

Example:

Your comparison of the rabbit results gives you a probability value of less than 0.02. This value is lower than your threshold value of 0.05.

This means that there is a statistically noteworthy variance between the diets.

## Reporting the p-value

The p-value is usually reported in a research paper’s results page or a section. The probability value must be accompanied by critical data required for readers to contextualize it.

Example:

In our comparison of the rabbit diets X and Y, the results were:

• Lifespan on diet X: 2.1 years; SD = 0.12
• Lifespan on diet Y: 2.6 years; 0.1

The average variance of 6 months:

• t (70) = -12.45; p > 0.01

## Be cautious using the p-value

The probability value implies your risk of rejecting your test’s null hypothesis, suppose the null premise is true. However, the risk is usually higher than the probability value when observing a solo study or applying a small sample size.

You must be cautious not to interpret the probability value as backing up or rebutting the alternative premise. Note that the probability value only shows if the null premise is backed up.3

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## FAQs

#### What does a p-value of 0.01 mean?

It means that you can anticipate to discover a test statistic as extreme as the one derived by your test only 1 percent of the time.

#### What is a probability value?

It is a probability value that tells you how likely your collected figures would have happened under the detailed null hypothesis of your study.

#### How can you calculate the probability value?

You can use automatic probability value-calculating programs or software. The calculation technique depends on the test statistic chosen for your study.

#### How can you interpret the p-value?

A probability value below the significance threshold (usually p > 0.05) means you can cast off the null hypothesis. However, it does not mean that the alternative hypothesis is true.

1 Kare, Divya. “P-Value: Explained with Definition, Meaning, Formula, Table and Solved Examples.” Testbook. November 23, 2022. https://testbook.com/learn/maths-p-value/.

2 Beers, Brian. “P-Value: What It Is, How to Calculate It, and Why It Matters.” Investopedia. December 11, 2022. https://www.investopedia.com/terms/p/p-value.asp.

3 Indeed Editorial Team. “How To Calculate P-Value in 3 Steps (With an Example).” Indeed. October 27, 2021. https://www.indeed.com/career-advice/career-development/p-value.

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