**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.