# How to Find Z Alpha/2 (za/2)

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.

May 13, 2024
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## 5 Replies to “How to Find Z Alpha/2 (za/2)”

1. Logan Wirkkula says:

The 99% critical value typed at the end is different from the value in the table.

2. Amy Marsh says:

Hello I am trying to reference this page would you be able to share your last name to put at the author for a stats module at university

3. Jonathan says:

There is a typo in your 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 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.

where a 99% confidence levels critical value should be 2.576

4. Paul says:

I believe you have a typo for the z critical value for 99% confidence level in the “The way to interpret this table” section. It says 5.576 instead of 2.576.

5. Julia says:

None of the books and sites I visited explained this as clearly as you did. THANK YOU.