# T.DIST

The `T.DIST` function returns the probability of a Student's t-distribution with a specified degrees of freedom. This function is usually used in hypothesis testing to determine the probability that a sample mean is within a specified range of values.

## Usage

Use the `T.DIST` formula with the syntax shown below, it has 3 required parameters:

Parameters:
1. x (required):
The numeric value at which to evaluate the distribution.
2. degrees_freedom (required):
An integer indicating the number of degrees of freedom.
3. cumulative (required):
A boolean value that indicates whether to return the cumulative distribution function or the probability density function. Enter TRUE for the cumulative distribution function (CDF) and FALSE for the probability density function (PDF).

## Examples

Here are a few example use cases that explain how to use the `T.DIST` formula in Google Sheets.

### Calculating the probability of a t-distribution

Suppose you have a sample of 10 observations and you want to know the probability of observing a mean of 5 or less. You can use the `T.DIST` function to calculate this probability.

### Testing a hypothesis

You can use the `T.DIST` function to test a hypothesis about the mean of a population. For example, you may want to test whether the mean weight of apples in a sample is significantly different from the mean weight of oranges in a sample.

### Finding confidence intervals

The `T.DIST` function can be used to find confidence intervals for the mean of a population. For example, you may want to find a 95% confidence interval for the mean height of people in a certain age group.

## Common Mistakes

`T.DIST` not working? Here are some common mistakes people make when using the `T.DIST` Google Sheets Formula:

### Forgetting to convert the degrees of freedom to an integer

The degrees of freedom must be a positive integer. If you provide a non-integer value, the function will return a #NUM! error. Make sure to use the INT function to convert the degrees of freedom to an integer if necessary.

### Using the wrong value for the cumulative parameter

The cumulative parameter has a default value of TRUE. If you want to return the probability density function instead, make sure to set the cumulative parameter to FALSE.

The following functions are similar to `T.DIST` or are often used with it in a formula:

• `T.DIST.2T`

The `T.DIST.2T` function returns the two-tailed probability of the Student's t-distribution. This function is commonly used in hypothesis testing to determine if two sets of data have different means. It is also used in confidence interval estimation, where it calculates the probability that the difference between two population means falls within a specified range.

• `T.DIST.RT`

The `T.DIST.RT` function returns the right-tailed Student's t-distribution of a given value, given the degrees of freedom. It is commonly used in hypothesis testing to determine the probability of observing a value as extreme or more extreme than a test statistic under the null hypothesis.

• `T.INV`

The `T.INV` function returns the inverse of the Student's t-distribution for the provided probability and degrees of freedom. This function is commonly used to calculate a critical value from the t-distribution when working with small sample sizes.

• `T.INV.2T`

The `T.INV.2T` function returns the two-tailed inverse of the t-distribution. This is commonly used in hypothesis testing to determine the critical value of t for a given level of significance and degrees of freedom.

• `T.TEST`

The `T.TEST` function calculates the probability associated with a Student's t-test. This function is commonly used in statistics to determine whether two samples are likely to have come from the same two underlying populations that have the same mean. It returns the probability that the two samples are different. The function assumes that the two samples are independent of each other and have equal variances.

## Learn More

You can learn more about the `T.DIST` Google Sheets function on Google Support.