Whenever you come across the term **t _{α/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 t
_{α/2}using a z table. - How to find t
_{α/2}using a calculator. - How to use t
_{α/2}values.

Let’s jump in!

**How to find t**_{α/2} using a t table

_{α/2}using a t table

Suppose we want to find t_{α/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**:

**How to find t**_{α/2} using a calculator

_{α/2}using a calculator

We can also use the Inverse t Distribution Calculator to find t_{α/2} for some test.

For example, suppose we once again want to find t_{α/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 t**_{α/2} Values

_{α/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 (t_{α/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