Table of Contents
To find the Alpha/2 values, you need to use a statistical table or calculator to determine the two-tailed critical value for a given level of significance (usually 0.05). The Alpha/2 values are the two probability values from either side of the mean that represent the level of significance. For example, if you have a 0.05 level of significance, the Alpha/2 values would be 0.025 from either side of the mean. These values will then be used to calculate the confidence intervals for the data.
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:
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
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.