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
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.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Probability | Degrees of Freedom | Formula | Result |
| 2 | 0.75 | 2 | =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.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Probability | Degrees of Freedom | Formula | Result |
| 2 | 0.80 | 3 | =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.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Probability | Degrees of Freedom | Formula | Result |
| 2 | 0.85 | 4 | =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.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Probability | Degrees of Freedom | Formula | Result |
| 2 | 0.90 | 5 | =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.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Probability | Degrees of Freedom | Formula | Result |
| 2 | 0.95 | 6 | =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.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Probability | Degrees of Freedom | Formula | Result |
| 2 | 0.99 | 7 | =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.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Probability | Degrees of Freedom | Formula | Result |
| 2 | 0.995 | 8 | =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
- 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.
- The T.INV function can be used instead of a table of critical values for the t-distribution.
- If probability <= 0 or if probability > 1, T.INV returns the #NUM! Error value.
- If any argument is non-numeric, T.INV returns the #VALUE! Error value. Always ensure that your arguments are numeric.
- The T.INV function is helpful in hypothesis testing small sample data sets and constructing confidence intervals.