Whenever you come across the term zα/2 in statistics, it is simply referring to thez critical valuefrom the z table that corresponds to α/2.

This tutorial explains the following:

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

Let's jump in!

How to find zα/2 using a z table

Suppose we want to find zα/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:

za/2 in z table

Notice that the exact value of 0.05doesn't appear in the table, but it would be directly between the values.0505and.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 zα/2 we take the absolute value. Thus, z.01/2 = 1.645.

How to find zα/2 using a calculator

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

For example, for some test that is using a 90% confidence level we can simply enter 0.1as the significance level and the calculator will automatically return the value of1.645 as the corresponding critical z value:

Z critical value calculator

Common Values for zα/2

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

Common za/2 values

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 is1.645.
  • 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.

Additional Resources

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