How to Find t Alpha/2 Values


Whenever you come across the term tα/2 in statistics, it is simply referring to the t critical value from the t-distribution table that corresponds to α/2.

This tutorial explains the following:

  • How to find tα/2 using a z table.
  • How to find tα/2 using a calculator.
  • How to use tα/2 values.

Let’s jump in!

How to find tα/2 using a t table

Suppose we want to find tα/2 for some test that is using the following values:

  • Alpha Level: 0.10
  • Types of test: Two-tailed
  • Degrees of freedom: 20

Using a t-distribution table, we can find that the t critical value is 1.725:

t alpha/2 value in t-table

How to find tα/2 using a calculator

We can also use the Inverse t Distribution Calculator to find tα/2 for some test.

For example, suppose we once again want to find tα/2 for some test that is using the following values:

  • Alpha Level: 0.10
  • Types of test: Two-tailed
  • Degrees of freedom: 20

We can enter the following values into the calculator and find that the t critical value is 1.7247:

This matches the t critical value that we found in the t distribution table.

How to Use tα/2 Values

In practice, t critical values are used in hypothesis tests to determine whether or not the results of a test are statistically significant.

The basic process for doing so is as follows:

Step 1: Calculate the test statistic using raw data.

Step 2: Compare the test statistic to the t critical value (tα/2).

Step 3: Reject or fail to reject the null hypothesis of the test.

If the absolute value of the t test statistic is greater than the t critical value, then we can reject the null hypothesis of the test.

Otherwise, if the absolute value of the t test statistic is less than the t critical value, then we fail to reject the null hypothesis.

Additional Resources

How to Read the t-Distribution Table
How to Find t Critical Values in Excel
How to Find t Critical Values in R

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