# T.INV Function in Excel

Part 1: Introduction

Definition, The T.INV function in Microsoft Excel returns the left-tailed inverse of the Student’s t-distribution.

Purpose The function is used to find the t-value given a certain probability and degrees of freedom. This is particularly useful in hypothesis testing and confidence interval construction.

Syntax & Arguments

syntax
`T.INV(probability, deg_freedom) `

The T.INV function syntax has the following arguments:

• probability: Required. The chance associated with the Student’s t-distribution.
• deg_freedom: Required. The number of degrees of freedom with which to characterize the distribution.

Return value The T.INV function returns the left-tailed inverse of the Student’s t-distribution.

Remarks

• If either argument is non-numeric, T.INV returns the #VALUE! Error value.
• If probability <= 0 or if probability > 1, T.INV returns the #NUM! Error value.
• If deg_freedom is not an integer, it is truncated.
• If deg_freedom < 1, T.INV returns the #NUM! Error value.

Part 2: Examples

Example 1

Purpose of Example: To calculate the left-tailed inverse of the Student’s t-distribution for a given probability and degrees of freedom.

ABCD
1ProbabilityDegrees of FreedomFormulaResult
20.752`=T.INV(A2, B2)`0.8165

Explanation: In this example, we use the T.INV function to calculate the left-tailed inverse of the Student’s t-distribution for a probability of 0.75 and 2 degrees of freedom.

Example 2

Purpose of Example: To calculate the left-tailed inverse of the Student’s t-distribution for a different probability and degrees of freedom.

ABCD
1ProbabilityDegrees of FreedomFormulaResult
20.803`=T.INV(A2, B2)`0.9785

Explanation: In this example, we use the T.INV function to calculate the left-tailed inverse of the Student’s t-distribution for a probability of 0.80 and 3 degrees of freedom.

Example 3

Purpose of Example: To calculate the left-tailed inverse of the Student’s t-distribution for a different probability and degrees of freedom.

ABCD
1ProbabilityDegrees of FreedomFormulaResult
20.854`=T.INV(A2, B2)`1.0639

Explanation: In this example, we use the T.INV function to calculate the left-tailed inverse of the Student’s t-distribution for a probability of 0.85 and 4 degrees of freedom.

Example 4

Purpose of Example: To calculate the left-tailed inverse of the Student’s t-distribution for a different probability and degrees of freedom.

ABCD
1ProbabilityDegrees of FreedomFormulaResult
20.905`=T.INV(A2, B2)`1.4759

Explanation: In this example, we use the T.INV function to calculate the left-tailed inverse of the Student’s t-distribution for a probability of 0.90 and 5 degrees of freedom.

Example 5

Purpose of Example: To calculate the left-tailed inverse of the Student’s t-distribution for a different probability and degrees of freedom.

ABCD
1ProbabilityDegrees of FreedomFormulaResult
20.956`=T.INV(A2, B2)`1.9432

Explanation: In this example, we use the T.INV function to calculate the left-tailed inverse of the Student’s t-distribution for a probability of 0.95 and 6 degrees of freedom.

Example 6

Purpose of Example: To calculate the left-tailed inverse of the Student’s t-distribution for a different probability and degrees of freedom.

ABCD
1ProbabilityDegrees of FreedomFormulaResult
20.997`=T.INV(A2, B2)`2.9979

Explanation: In this example, we use the T.INV function to calculate the left-tailed inverse of the Student’s t-distribution for a probability of 0.99 and 7 degrees of freedom.

Example 7

Purpose of Example: To calculate the left-tailed inverse of the Student’s t-distribution for a different probability and degrees of freedom.

ABCD
1ProbabilityDegrees of FreedomFormulaResult
20.9958`=T.INV(A2, B2)`3.4995

Explanation: In this example, we use the T.INV function to calculate the left-tailed inverse of the Student’s t-distribution for a probability of 0.995 and 8 degrees of freedom.

Part 3: Tips and Tricks

1. Always ensure that the degree of freedom is at least 1. If it’s less than 1, the T.INV function will return an error.
2. The T.INV function can be used instead of a table of critical values for the t-distribution.
3. If probability <= 0 or if probability > 1, T.INV returns the #NUM! Error value.
4. If any argument is non-numeric, T.INV returns the #VALUE! Error value. Always ensure that your arguments are numeric.
5. The T.INV function is helpful in hypothesis testing small sample data sets and constructing confidence intervals.