# T.DIST Function in Excel

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

syntax
```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.

ABCDE
1ValueDegrees of FreedomCumulativeFormulaResult
2601TRUE`=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

ABCDE
1ValueDegrees of FreedomCumulativeFormulaResult
283FALSE`=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.

ABCDE
1ValueDegrees of FreedomCumulativeFormulaResult
2102TRUE`=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.

ABCDE
1ValueDegrees of FreedomCumulativeFormulaResult
254FALSE`=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.

ABCDE
1ValueDegrees of FreedomCumulativeFormulaResult
275TRUE`=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

1. 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.
2. The T.DIST function can be used instead of a table of critical values for the t-distribution.
3. 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.
4. If any argument is non-numeric, T.DIST returns the #VALUE! Error value. Always ensure that your arguments are numeric.
5. The T.DIST function is helpful in the hypothesis testing of small sample data sets.