Whenever you come across the term zα/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 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:
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 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 0.1 as the significance level and the calculator will automatically return the value of 1.645 as the corresponding critical z value:
Common Values for zα/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.