P-Value Calculator

What Is a P-Value?

A p-value is a statistical measure that tells you how likely it is to get a test statistic as extreme as the one observed, assuming the null hypothesis is true.

In most statistical tests, a p-value helps you determine whether there is sufficient evidence against the null hypothesis. Specifically, we reject the null hypothesis (H0) if the p-value is less than the significance level (α). Otherwise, we fail to reject the null hypothesis.

Note. A p-value does not prove that the null hypothesis is false. It only tells you whether there is sufficient evidence against the null hypothesis.

How to Use This P-Value Calculator

This calculator is organized into several sections to allow you to compute the correct p-value based on your test statistic. To calculate the p-value, follow these steps:

1. Select the correct tool based on your test statistic. A quick guide is:
   • Use the P-value from Z if you have a z-statistic
   • Use a P-value from t if you have a t statistic and degrees of freedom
   • Use a P-value from Chi-square if you have a chi-square statistic and degrees of freedom
   • Use a P-value from F if you have the computed F-statistic, numerator degrees of freedom (df₁), and the denominator degrees of freedom (df₂)
   • Use the P-value from correlation (r) if you have the computed Pearson’s correlation, and the sample size (n)
2. Enter the required parameters
3. Click Calculate

Each of the tools will instantly return the correct p-value for your test and tell you whether to reject or fail to reject the null hypothesis at the 5% significance level. However, if your study uses a different significance level, you should manually compare the p-value with your significance level and make the decisions as follows:

• If p ≤ α, reject the null hypothesis.
• If p > α, fail to reject the null hypothesis.

Still struggling to identify the right tool for your test? The table below provides a quick summary of each of the p-value calculators and when to use them.

P-Value from Z Score Calculator

Use the p-value from z score calculator when your test statistic follows the standard normal distribution. This is common in z tests, large-sample hypothesis tests, and tests involving proportions.

To use this tool, follow these steps:

1. Enter the z statistic (z-score)
2. Select the correct type of test (Right, Left, or Two-Tailed)
3. Click Calculate

Example

A researcher wants to test whether a new teaching method improves average test scores. The test gives a z-statistic value of 2.10. Find the correct p-value for this test.

Solution

Since the researcher is testing for an improvement, this is a right-tailed test.

Using the calculator:

1. Go to the P-Value from Z Score section.
2. Enter 2.10 as the z score.
3. Choose Right-tailed.
4. Click Calculate.

The calculator gives a p-value of 0.017864

Since 0.017864 < 0.05, the result is statistically significant at the 5% level. Therefore, the researcher would reject the null hypothesis and conclude that the new teaching method improves average test scores.

P-Value from T Statistic Calculator

Use the p-value from t calculator when you have a t value and degrees of freedom. This is common for one-sample t tests, paired t tests, and independent samples t tests.

Therefore, to find the p-value from t using the calculator, follow these steps:

1. Enter the t statistic
2. Enter the degrees of freedom
3. Select the correct type of test (Right, Left, or Two-tailed test)

Note. The degrees of freedom are important because the shape of the t distribution changes depending on the df value. A t statistic with 8 degrees of freedom does not produce the same p-value as the same t statistic with 80 degrees of freedom.

Example

A researcher conducts a t-test to determine whether the average sleep time of students differs from 8 hours. The results are:

• t = 2.35
• df = 18

Find the correct p-value for this test.

Solution

Since the test aims to determine whether there is a significant difference, the test is two-tailed.

To find the correct p-value for this test using the calculator, follow these steps:

1. Go to the P-Value from T Statistic section.
2. Enter 2.35 as the t statistic.
3. Enter 18 as the degrees of freedom.
4. Choose Two-tailed.
5. Click Calculate.

The calculator gives a p-value of 0.03038.

Since 0.0303 < 0.05, the result is statistically significant. Therefore, the researcher would reject the null hypothesis and conclude that the average sleep time differs from 8 hours.

P-Value from Chi-Square Statistic Calculator

Use the p-value from chi-square statistic calculator when your test statistic follows a chi-square distribution. This is common in chi-square goodness-of-fit tests and chi-square tests of independence.

To find the p-value using this calculator, follow these steps:

• Enter the chi-square statistic
• Enter the degrees of freedom
• Click Calculate

Note. Most chi-square tests use the right-tail area because larger chi-square values show greater disagreement between observed and expected values.

Example

A researcher wants to know whether gender and preferred learning method are associated. After running a chi-square test of independence, the results are:

• χ² = 9.84
• df = 3

Find the p-value for the test.

Solution

Using the calculator:

1. Go to the P-Value from Chi-Square Statistic section.
2. Enter 9.84 as the chi-square statistic.
3. Enter 3 as the degrees of freedom.
4. Click Calculate.

The calculator gives a p-value of 0.019976.

Since 0.019976 < 0.05, the result is statistically significant. Therefore, the researcher would reject the null hypothesis and conclude that there is evidence of an association between the two variables.

P-Value from F Statistic Calculator

Use the p-value from F statistic calculator when your test statistic follows an F distribution. This is common in ANOVA, regression model tests, and tests involving variances.

To find the p-value from F using the calculator:

1. Enter the F statistic
2. Enter the numerator degrees of freedom (df₁)
3. Enter the denominator degrees of freedom (df₂)

Note. Most F tests are right-tailed. This is because large F values usually provide stronger evidence against the null hypothesis.

Example

A researcher conducts a one-way ANOVA to compare the mean exam scores of students taught using three different methods. The ANOVA output gives:

• F = 4.62
• numerator df = 2
• denominator df = 27

Find the p-value for the test.

Solution

Using the calculator:

1. Go to the P-Value from F Statistic section.
2. Enter 4.62 as the F statistic.
3. Enter 2 as the numerator degrees of freedom.
4. Enter 27 as the denominator degrees of freedom.
5. Click Calculate.

The calculator gives a p-value of 0.018809.

Since 0.018809 < 0.05, the ANOVA result is statistically significant. The researcher would reject the null hypothesis and conclude that at least one group mean is different.

P-Value from Correlation Coefficient Calculator

Use the p-value from correlation coefficient calculator when you want to test whether a Pearson correlation coefficient is statistically significant.

To find the p-value from r using this tool, follow these steps:

1. Enter the Pearson correlation coefficient, r
2. Enter the sample size, n
3. Select the test type (Right, Left, or Two-Tailed)

The p-value from r calculator converts the correlation coefficient into a t-statistic and then calculates the p-value using the t distribution.

Note. Use a two-tailed test when you want to know whether the correlation is different from zero in either direction. However, if you anticipate the direction of the relationship between the variables before analyzing the data, you should use a one-tailed test (left-tailed for a negative relationship or right-tailed for a positive relationship).

Example

A researcher wants to test whether study time is related to exam score. A sample of 25 students gives a Pearson’s correlation coefficient, r = 0.46. Assuming no prior information is known about the direction of this relationship, calculate the p-value for the test.

Solution

Since no prior information is known about the direction of the relationship, we use a two-tailed test.

Using the calculator:

1. Go to the P-Value from Correlation Coefficient section.
2. Enter 0.46 as the correlation coefficient.
3. Enter 25 as the sample size.
4. Choose Two-tailed.
5. Click Calculate.

The calculator gives a p-value of 0.020686.

Since 0.020686 < 0.05, the correlation is statistically significant. The researcher would conclude that study time and exam score are significantly related.

How to Interpret the P-Value

After calculating the p-value, the next step is to compare it with your significance level. The table below provides a quick overview of how to make a decision about your hypothesis based on the p-value

For example, if your p-value is 0.032, you would reject the null hypothesis at the 0.05 level. However, if your p-value is 0.124, you would fail to reject the null hypothesis.

Common Mistakes When Calculating P-Values

Here are some common mistakes to avoid:

• Using the z calculator when your test statistic follows a t distribution
• Entering the wrong degrees of freedom
• Choosing the wrong tail type
• Using a one-tailed test after seeing the result
• Comparing the p-value with 0.05 when your study uses a different alpha level
• Treating the p-value as the probability that the null hypothesis is true

A good rule is simple: identify your test statistic, degrees of freedom, and tail type before calculating the p-value.

Frequently Asked Questions