How to find Z Alpha/2 (za/2)

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

This tutorial explains the following:

• How to find z_α/2 using a z table.
• How to find z_α/2 using a calculator.
• The most common values for z_α/2.

Let’s jump in!

How to find z_α/2 using a z table

Suppose we want to find z_α/2 for some test that is using a 90% confidence level.

In this case, α would be 1 – 0.9 = 0.1. Thus, α/2 = 0.1/2 = 0.05.

To find the corresponding z critical value, we would simply look for 0.05 in a z table:

Notice that the exact value of 0.05 doesn’t appear in the table, but it would be directly between the values .0505 and .0495. The corresponding z critical values on the outside of the table are -1.64 and -1.65.

By splitting the difference, we see that the z critical value would be -1.645. And typically when we use z_α/2 we take the absolute value. Thus, z_.01/2 = 1.645.

How to find z_α/2 using a calculator

We can also use a Critical Z Value Calculator to find z_α/2 for some test.

For example, for some test that is using a 90% confidence level we can simply enter 0.1 as the significance level and the calculator will automatically return the value of 1.645 as the corresponding critical z value:

Common Values for z_α/2

The following table displays the most common critical values for different values of α:

The way to interpret this table is as follows:

• For a test using a 90% confidence level (e.g. α = 0.1), the z critical value is 1.645.
• For a test using a 95% confidence level (e.g. α = 0.05), the z critical value is 1.96.
• For a test using a 99% confidence level (e.g. α = 0.01), the z critical value is 5.576.

And so on.

How to use the Z Table (With Examples)
How to Find the Z Critical Value on a TI-84 Calculator