# T.INV Excel

## What Is T.INV Excel?

T.INV in Excel is a function primarily used in statistics and hypothesis testing, allowing users to find the value of t-critical or inverse cumulative distribution for a specified probability and degrees of freedom. The function helps calculate the inverse of a student’s t-distribution, which is nothing but a bell-shaped graph.

This function comes under the umbrella of inverse t-distribution, a key concept in inferential statistics. It is beneficial when conducting hypothesis tests or constructing confidence intervals where sample sizes are small or the population standard deviation is unknown.

To utilize the T.INV Excel function fully effectively, let’s delve into an example.

First, we must enter the formula. The complete formula, which will be input in cell C2, is as follows: =T.INV(0.68, 2). As you enter each value, the resulting value appears in cell C2.

### Syntax

The T.INV Excel function utilizes the following arguments:

Probability – This is a required argument. It represents the probability associated with the Student’s T Distribution.

Deg_freedom – This is a required argument. It denotes the number of degrees of freedom used to characterize the distribution.

###### Key Takeaways
• The T.INV function calculates the inverse value of the student’s T-distribution function. It helps find the T-score for any degrees of freedom and any sample size.
• The T.INV function is particularly useful for decision-making processes that involve estimating population parameters based on limited data or determining if a hypothesis can be accepted or rejected within a specified confidence level.
• The T.INV function of Excel provides professionals with a reliable statistical tool for making informed decisions and analyzing data accurately within their work environments.

### How To Use T.INV Function in Excel?

Step 1: Choose the empty cell which will contain the result. Go to the “Formulas” tab and click it.

Step 2: Select the “More Functions” option from the menu.

Step 3: Select the “Statistical” option from the drop-down list. Select “T.INV” from the drop-down menu.

Step 4: A window called “Function Arguments” appears. Enter the value in the “Probability” and “Deg_freedom.”  Select OK.

#### 2. Enter the worksheet manually

Step 1: Select an empty cell for the output. Type “=T.INV()” in the selected cell. Alternatively, type “=T” and double-click the T.INV function from the list of suggestions shown by Excel.

Step 2: Press the “Enter” key to get the result.

### Examples

#### Example #1

To better understand and apply the concept of the T.INV Excel function, let’s consider the following example. In the table provided, the data is organized as follows:

To calculate the desired output in cell D2, follow these steps.

Step 1: Select the cell where you want to enter the formula and calculate the result. For this demonstration, let’s choose cell D2. Enter the formula. The complete formula to be entered is:

=T.INV(B2, B3).

Step 2: After entering each of the values, press the Enter key. The resulting value will be displayed in cell D2, as shown in the image.

The left-tailed inverse of the t-distribution, with 80% probability and 5 degrees of freedom, is 0.920.

#### Example #2 – T.INV Function with Data from Cells

Let’s look at an example with the table before us. The data is organized as follows:

• Column A encompasses the Probability.
• Column B encompasses the Degree of Freedom.
• Column C encompasses the T.INV Excel Result.

Now, let’s calculate the desired output in cell C2.

Step 1: Choose the column C to get the output. First, let us proceed to cell C2. The complete formula to be entered in cell C2 is:

=T.INV(A3, B3)

Step 2: Press Enter. You get the result for Row 3. Using the Autofill handle, the formula can be applied from cells C4 to C8.

The right-tailed inverse of the t-distribution is displayed in Column C.

#### Example #3

The following example aims to help you understand the #NUM! Error when using the T.INV Excel function. Let’s consider the following scenario:

There are two tables. Table 1 has a probability value of 0 and a degree of freedom value of 2, whereas Table 2 has a probability value of 0.5 and a degree of freedom value of -2.

Now, let’s check what happens when we use the T.INV formula. First, to calculate the desired output in cell D2, follow these steps:

Step 1: Select the cell where you want to enter the formula and calculate the result. For this demonstration, let’s choose cells D2 & D6. Enter the formula.

The complete formula to be entered in cells D2 & D6 is:

in cell D2 =T.INV(B2, B3)

in cell D6 =T.INV(B6, B7).

Step 2: After entering the formulas in the respective cells, press the Enter key. The resulting value will be displayed in cells D2 & D6, as shown in the provided image.

By following these simple steps, you can effectively understand the T.INV Excel function and avoid encountering the #NUM! Error. For the first table, we get a #NUM error since the probability is less than zero.

For the second table, the #NUM! Error is obtained as the degree of freedom is less than one.

#NUM! error

• Degree of freedom is < 1
• If Probability <=0 or > 1

#### Example #4

The following example aims to help you understand the #VALUE! error that can occur when using the T.INV Excel function. Let’s consider the following scenario:

In the table provided, the data is organized as follows:

The table has a probability value of “a” and a degree of freedom value of 4.

Now, let’s look at what happens when this condition is present in our table. To calculate the desired output in cell D2, follow these steps:

Step 1: Select the cell where you want to enter the formula and calculate the result. For this demonstration, let’s choose cell D2. Enter the formula:

= T.INV(B2, B3)

Step 2: Press the Enter key. The resulting value will be displayed in cell D2, as shown below.

Here, we get the #VALUE! ERROR as the probability is a non-numeric value. By following these steps, you can understand the T.INV function in Excel and avoid encountering the #VALUE! Error.

### Important Things To Note

• #NUM! Error – This error occurs.
• when the given probability is less than or equal to zero or greater than one.
• when the given deg_freedom is less than 1.
• #VALUE! Error – This error occurs.
• when one or both supplied arguments are non-numeric.
• Or if deg_freedom is not an integer, it will be truncated.

1. What is the purpose of the use of the T.INV Function in Excel?

The purpose of using the T.INV Excel function is to calculate the inverse of the student’s t-distribution. This distribution is widely used in hypothesis testing and constructing confidence intervals when the population standard deviation is unknown, and the sample size is small.
For example, in the table below, the data is organized as follows. For example, in the table below, the data is organized as follows.

Choose the cell where you want to input the formula; let’s go with cell D2. The complete formula to be typed in cell D2 is:
=T.INV(B2, B3).
Once you’ve entered each value in the previous step, hit the Enter key. The resulting value will pop up in cell D2, just like in the image provided.

2. Are there any limitations or restrictions when using the T.INV function in Excel?

When using the T.INV function in Excel, it is essential to be mindful of its limitations and restrictions.
• Firstly, the T.INV Excel function assumes that the input data follows a t-distribution, which might only sometimes be the case in real-world situations where other statistical distributions may be more appropriate.
• Additionally, the T.INV function requires a degree of freedom parameter, which represents the sample size minus one for calculating critical values. However, it does not provide an automatic adjustment for small sample sizes.

3. Where is the T.INV Function in Excel?

One can activate the T.INV function in Excel using the following steps:
• Choose the empty cell for the result.
Go to the “Formulas” tab and select the “Statistical” group.
• Select “T.INV” from the drop-down menu.
• A window called “Function Arguments” appears.
• Enter required values in the “probability” and “deg_freedom.” Select OK.