Whenever you perform a hypothesis test, you will get a test statistic as a result. To determine if the results of the test are statistically significant, you can compare the test statistic to a critical value.
If the absolute value of the test statistic is greater than the critical value, then the results of the test are statistically significant.
To find a t-critical value in Google Sheets, you can use the following syntax:
- T.INV(probability, deg_freedom) – Returns t-critical value for a one-tailed t-test.
- T.INV.2T(probability, deg_freedom) – Returns t-critical value for a two-tailed t-test.
To find a z-critical value in Google sheets, you can use the following syntax:
- NORM.S.INV(probability) – Returns critical value for a one-tailed z-test.
- NORM.S.INV(probability/2) – Returns critical value for a two-tailed z-test.
The following examples show how to use each of these functions in practice.
Example 1: One-Tailed T-Test Critical Value
To find the t-critical value for a left-tailed test with a significance level of 0.05 and degrees of freedom = 11, we can type the following formula into Google Sheets:
The critical value is -1.79588.
Example 2: Two-Tailed T-Test Critical Value
To find the t-critical value for a two-tailed test with a significance level of 0.05 and degrees of freedom = 11, we can type the following formula into Google Sheets:
The critical value is 2.200985.
Example 3: One-Tailed Z-Test Critical Value
To find the z-critical value for a left-tailed test with a significance level of 0.05, we can type the following formula into Google Sheets:
The critical value is -1.64485.
Example 4: Two-Tailed Z-Test Critical Value
To find the z-critical value for a two-tailed test with a significance level of 0.05, we can type the following formula into Google Sheets:
The critical value is -1.96.
Cautions on Finding Critical Values in Google Sheets
Note that the T.INV(), T.INV.2T(), and NORM.S.INV() functions will throw an error if any of the following occur:
- If any argument is non-numeric.
- If the value for probability is less than zero or greater than 1.
- If the value for deg_freedom is less than 1.
You can find more Google Sheets tutorials on this page.