Correlation (r) Critical Value Table

3 min read Joseph Mburu
Statistical Tables

Use this interactive correlation (r) critical value table to find the critical value for Pearson’s correlation coefficient. Select the table type (two-tailed, left-tailed or righ-tailed), choose the significance level, enter the degrees of freedom, and the correct critical value will be highlighted.

Two-tailed is the default for most correlation tests. Use a one-tailed table only when the problem gives a specific direction.
The default is α = 0.05.
For Pearson correlation, df = n − 2.

Two-Tailed Pearson Correlation r Critical Value Table

Values are critical values of Pearson’s r. Enter df and select α to highlight the matching table value.

Note: Correlation tests are usually two-tailed by default because we often test whether r is different from 0 in either direction. Use a right-tailed or left-tailed table only when the problem specifically asks you to test a direction, such as a positive correlation or a negative correlation.

What Is an r Critical Value?

An r critical value is the cutoff used to determine whether a Pearson correlation coefficient is statistically significant. In this case, we compare the calculated Pearson’s correlation coefficient r with the critical value and make decisions as follows:

  • If the absolute value of the calculated correlation coefficient is equal to or greater than the critical value, we reject the null hypothesis (H0) and conclude that the correlation is statistically significant.
  • If the absolute value of the calculated correlation coefficient is less than the critical value, we fail to reject the null hypothesis (H0) and conclude that the correlation is not statistically significant.

How to Use This Interactive R Critical Value Table

This interactive correlation critical value table makes it easy for you to look up the correct critical value within a few clicks. To use the table:

  1. Select whether you are conducting a one-tailed or two-tailed test. Most correlation tests are two-tailed unless otherwise stated.
  2. Select the significance level from the dropdown and enter the correct degrees of freedom (df)
  3. Click the “Find Critical Value” button

The table will instantly highlight the correct r critical value for you.

Recall. Use a one-tailed test when your hypothesis predicts a specific direction of the linear relationship.

How to Read the R Critical Value Table

To find the correlation critical value from the table manually, follow these steps:

  1. Identify the significance level (α)
  2. Compute the degrees of freedom (df)
  3. Find the value where the α column meets the df row. This is the r critical value.

Example

Suppose you have a sample of 20 paired observations and are conducting a two-tailed test at α = 0.05 to determine whether the number of hours spent studying is correlated with the final exam score. Find the r critical value using tables.

Solution

To find the correlation critical value using the table, follow these steps:

Step 1. Identify the significance level

From the question, α = 0.05

Step 2. Compute the degrees of freedom

By definition, the degrees of freedom formula for a correlation test is: df = n-2, where n is the number of paired observations.

Thus, df = 20-2

= 18

Want a quick way to calculate the correct degrees of freedom for your Pearson’s correlation test? Use the degrees of freedom calculator.

Step 3. Find the value where the α column meets the row.

The α = 0.05 column meets the df=18 row at 0.4438, as shown below.

Finding critical value using r-critical value table example

Therefore, the r critical value for the test is ±0.4438.

Want a quick way to find the correlation critical value without using tables? Use the r critical value calculator instead.

Now suppose your calculated Pearson correlation coefficient is: r = −0.52. In this case, we would make the decision as follows:

Since the |−0.52| is greater than the critical value (0.4438), we reject the null hypothesis and conclude that there is a statistically significant relationship between the two variables.