*20*

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** TÂ 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 aÂ t distribution table 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:Â How to Find the Z Critical Value in Excel**

**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**Â T.INV.()** function, which uses the following syntax:

**T.INV**(probability, deg_freedom)

**probability:Â**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**Â T.INV.2T()** function, which uses the following syntax:

**T.INV.2T**(probability, deg_freedom)

**probability:Â**The significance level to use**deg_freedom**: The degrees of freedom

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

**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,Â we can type the following formula into Excel: **T.INV(0.05, 11)**

This returns the valueÂ **-1.79588**. This is the critical valueÂ 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,Â we can type the following formula into Excel: **ABS(****T.INV(0.05, 11))**

This returns the valueÂ **1.79588**. This is the critical valueÂ 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,Â we can type the following formula into Excel: **T.INV.2T(0.05, 11)**

This returns the valueÂ **2.200985**. This is the critical valueÂ 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 t distribution table withÂ Î± = 0.05 for two tails and DFÂ *(degrees of freedom)* = 11.

**Cautions on Finding the T Critical Value in Excel**

Note that both theÂ **T.INV****()** and **T.INV.2T()Â **functions in Excel will throw an error if any of the following occur:

- If any argument is non-numeric.
- If the value forÂ
*probabilityÂ*is less than zero or greater than 1. - If the value forÂ
*deg_freedom**Â*is less than 1.

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