Part 1: Introduction
Definition, The T.DIST function in Microsoft Excel returns the Student’s left-tailed t-distribution.
Purpose The t-distribution is used in the hypothesis testing of small sample data sets. This function is used in place of a table of critical values for the t-distribution.
Syntax & Arguments
T.DIST(x, deg_freedom, cumulative) The T.DIST function syntax has the following arguments:
- x: Required. The numeric value at which to evaluate the distribution.
- deg_freedom: Required. An integer indicates the number of degrees of freedom.
- cumulative: Required. A logical value that determines the form of the function. If cumulative is TRUE, T.DIST returns the cumulative distribution function; if FALSE, it returns the probability density function.
Return value The T.DIST function returns the Student’s left-tailed t-distribution.
Remarks
- If any argument is non-numeric, T.DIST returns the #VALUE! Error value.
- If deg_freedom < 1, T.DIST returns an error value. Deg_freedom needs to be at least 1.
Part 2: Examples
Example 1
Purpose of Example: Calculate the Student’s left-tailed t-distribution for a given value using 1 degree of freedom.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Value | Degrees of Freedom | Cumulative | Formula | Result |
| 2 | 60 | 1 | TRUE | =T.DIST(A2, B2, C2) | 0.9947 |
Result: The result of the formula would be the Student’s left-tailed t-distribution for the given value, returned as the cumulative distribution function.
Explanation: In this example, we use the T.DIST function to calculate the Student’s left-tailed t-distribution for a value of 60, using 1 degree of freedom. The cumulative parameter is set to TRUE, so the function returns the cumulative distribution function.
Example 2
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Value | Degrees of Freedom | Cumulative | Formula | Result |
| 2 | 8 | 3 | FALSE | =T.DIST(A2, B2, C2) | 0.0007 |
Result: The result of the formula would be the Student’s left-tailed t-distribution for the given value, returned as the probability density function.
Explanation: In this example, we use the T.DIST function to calculate the Student’s left-tailed t-distribution for a value of 8, using 3 degrees of freedom. The cumulative parameter is set to FALSE, so the function returns the probability density function.
Example 3
Purpose of Example: To calculate the Student’s left-tailed t-distribution for a given value using 2 degrees of freedom.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Value | Degrees of Freedom | Cumulative | Formula | Result |
| 2 | 10 | 2 | TRUE | =T.DIST(A2, B2, C2) | 0.9933 |
Result: The result of the formula would be the Student’s left-tailed t-distribution for the given value, returned as the cumulative distribution function.
Explanation: In this example, we use the T.DIST function to calculate the Student’s left-tailed t-distribution for a value of 10, using 2 degrees of freedom. The cumulative parameter is set to TRUE, so the function returns the cumulative distribution function.
Example 4
Purpose of Example: To calculate the Student’s left-tailed t-distribution for a given value, using 4 degrees of freedom.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Value | Degrees of Freedom | Cumulative | Formula | Result |
| 2 | 5 | 4 | FALSE | =T.DIST(A2, B2, C2) | 0.0146 |
Result: The result of the formula would be the Student’s left-tailed t-distribution for the given value, returned as the probability density function.
Explanation: In this example, we use the T.DIST function to calculate the Student’s left-tailed t-distribution for a value of 5, using 4 degrees of freedom. The cumulative parameter is set to FALSE, so the function returns the probability density function.
Example 5
Purpose of Example: To calculate the Student’s left-tailed t-distribution for a given value using 5 degrees of freedom.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Value | Degrees of Freedom | Cumulative | Formula | Result |
| 2 | 7 | 5 | TRUE | =T.DIST(A2, B2, C2) | 0.9918 |
Result: The result of the formula would be the Student’s left-tailed t-distribution for the given value, returned as the cumulative distribution function.
Explanation: In this example, we use the T.DIST function to calculate the Student’s left-tailed t-distribution for a value of 7, using 5 degrees of freedom. The cumulative parameter is set to TRUE, so the function returns the cumulative distribution function.
Part 3: Tips and Tricks
- Always ensure that the degree of freedom is at least 1. If it’s less than 1, the T.DIST function will return an error.
- The T.DIST function can be used instead of a table of critical values for the t-distribution.
- The cumulative parameter determines the form of the function. If it’s TRUE, T.DIST returns the cumulative distribution function; if it’s FALSE, it returns the probability density function.
- If any argument is non-numeric, T.DIST returns the #VALUE! Error value. Always ensure that your arguments are numeric.
- The T.DIST function is helpful in the hypothesis testing of small sample data sets.