# T.INV.2T Function

Calculates the two-tailed Student's T-Distribution

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## What is the T.INV.2T Function?

The T.INV.2T Function[1] is categorized under Excel Statistical functions. It will calculate the two-tailed Student’s T-Distribution. The Student’s T-Distribution is a continuous probability distribution that is frequently used for testing hypotheses on small sample data sets.

In financial analysis, T.INV.2T is often used in examining the risk-return relationship of a portfolio. The T.INV.2T function is the updated version of the TINV function.

### Formula

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

The T.INV.2T function uses the following arguments:

1. Probability (required argument) – This is the probability associated with the Student’s T Distribution. It should be between 0 and 1.
2. Deg_freedom (required argument) – The number of degrees of freedom with which to characterize the distribution.

### How to use the T.INV.2T Function in Excel?

To understand the uses of the T.INV.2T function, let’s consider a few examples:

#### Example 1

Suppose we are given the following data:

If we want to calculate the value of the function for a probability of 0.5, the formula to use will be:

We get the result below:

So, the T-value of the Student’s T-distribution for the data above is 0.727.

#### Example 2

We wish to calculate a one-tailed t-value that will be returned by replacing probability with 2*probability. Suppose we are given the following data:

For a probability of 0.8 and a degree of freedom of 10, the two-tailed value is calculated using the formula below:

We get the result below:

The above value is a two-tailed value. The one-tailed value for the same probability and degrees of freedom can be calculated as shown below:

We get the following result:

### Things to remember about the T.INV.2T Function

1. #NUM! error – Occurs when:
• The given probability is less than zero or the probability is equal to zero or is greater than one.
• The given degree of freedom is less than 1.
2. #VALUE! error – Occurs when one or both of the supplied arguments are non-numeric.
3. If the deg_freedom argument is not an integer, it is truncated.