How to Find the Z Critical Value in Excel


Whenever you conduct a hypothesis test, you will get a test statistic as a result. To determine if the results of the hypothesis test are statistically significant, you can compare the test statistic to a Z critical value. If the absolute value of the test statistic is greater than the Z critical value, then the results of the test are statistically significant.

Fortunately, Excel makes it easy to find Z critical values using the following function:

NORM.S.DIST(probability)

where:

  • probability: The significance level to use.

This function returns a Z critical value, based on the significance level you chose.

This tutorial provides three examples of how to use this function to find Z critical values.

Example 1: Two-Tailed Test

Find the Z critical value for a two-tailed test, using α = 0.10.

For a two-tailed test, there will be two critical values:

  • NORM.S.INV(α/2)
  • NORM.S.INV(1-α/2)

We can use the following functions in Excel to calculate these critical values:

Z critical value calculation for two-sided test in Excel

Thus, the two critical values for this test are -1.645 and 1.645. This means if the test statistic is less than -1.645 or greater than 1.645, then the results of the hypothesis test are statistically significant.

Example 2: Right-Tailed Test

Find the Z critical value for a right-tailed test, using α = 0.05.

For a right-tailed test, there will be one critical value: NORM.S.INV(1-α)

We can use the following function in Excel to calculate this critical value:

Z critical value calculation for right-sided test in Excel

Thus, the critical value for this test is 1.645. This means if the test statistic is greater than 1.645, then the results of the hypothesis test are statistically significant.

Example 3: Left-Tailed Test

Find the Z critical value for a left-tailed test, using α = 0.01.

For a left-tailed test, there will be one critical value: NORM.S.INV(α)

We can use the following function in Excel to calculate this critical value:

Z critical value for left-tailed test in Excel

Thus, the critical value for this test is -2.326. This means if the test statistic is less than -2.326, then the results of the hypothesis test are statistically significant.

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