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

The T critical value can be found by using a  or by using statistical software.

To find the T critical value, you need to specify:

• A significance level (common choices are 0.01, 0.05, and 0.10)
• The degrees of freedom
• The type of test (one-tailed or two-tailed)

Using these three values, you can determine the T critical value to be compared with the test statistic.

Related: 

How to Find the T Critical Value in Excel

Excel offers two functions to find the T critical value.

T.INV

To find the T critical value in Excel for a one-tailed test, you can use the T.INV.() function, which uses the following syntax:

T.INV(probability, deg_freedom)

• probability: The significance level to use
• deg_freedom: The degrees of freedom

This function returns the critical value from the t distribution for a one-tailed test based on the significance level and the degrees of freedom provided.

T.INV.2T

To find the T critical value in Excel for a two-tailed test, you can use the T.INV.2T() function, which uses the following syntax:

T.INV.2T(probability, deg_freedom)

• probability: The significance level to use
• deg_freedom: The degrees of freedom

Examples of Finding the T Critical Value in Excel

The following examples illustrate how to find the T critical value for a left-tailed test, right-tailed test, and a two-tailed test.

Left-tailed test

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 Excel: T.INV(0.05, 11)

This returns the value -1.79588. This is the critical value for a left-tailed test with significance level of 0.05 and degrees of freedom = 11.

Right-tailed test

To find the T critical value for a right-tailed test with a significance level of 0.05 and degrees of freedom = 11, we can type the following formula into Excel: ABS(T.INV(0.05, 11))

This returns the value 1.79588. This is the critical value for a two-tailed test with significance level of 0.05 and degrees of freedom = 11.

Two-tailed test

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 Excel: T.INV.2T(0.05, 11)

This returns the value 2.200985. This is the critical value for a two-tailed test with significance level of 0.05 and degrees of freedom = 11.

Note that this also matches the number we would find in the with α = 0.05 for two tails and DF (degrees of freedom) = 11.

Cautions on Finding the T Critical Value in Excel

Note that both the T.INV() and T.INV.2T() functions in Excel 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.