# T.INV Function

Calculates the left-tailed student's t-distribution

## What is the T.INV Excel Function?

The T.INV Excel Function is categorized under Statistical functions. It will calculate the left-tailed student’s t-distribution. The student’s t-distribution is a continuous probability distribution that is frequently used in testing hypotheses on small sample data sets.

As a financial analyst, the T.INV function is used in portfolio risk analysis, particularly, the risk-return relationship of a portfolio. The function is often used when the sample size is smaller, i.e., when a portfolio is comprised of only 20 stocks or 5 asset classes.

### T.INV Formula

=T.INV(probability,deg_freedom)

The T.INV function uses the following arguments:

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

### How to use the T.INV Excel Function

To understand the uses of the T.INV function, let us 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 0.20, the formula to use is: We get the result below: So, the left-tailed inverse of the student’s t-distribution with a probability of 20% and 5 degrees of freedom is -0.920.

#### Example 2

Suppose we are given the following data: If we want to calculate the value of the function for a probability of 0.80, the formula to use is: We get the result below: So, the left-tailed inverse of the student’s t-distribution with a probability of 80% and 10 degrees of freedom is 0.879.

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

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