# 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.

## Usage

Use the `T.INV` formula with the syntax shown below, it has 2 required parameters:

Parameters:
1. probability (required):
The probability associated with the two-tailed Student's t-distribution.
2. degrees_freedom (required):
The degrees of freedom for the Student's t-distribution.

## Examples

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

### Calculating a Confidence Interval for a Small Sample

When working with a small sample size, the t-distribution is commonly used to calculate a confidence interval. The `T.INV` function can be used to calculate the critical value needed for this calculation.

### Testing for a Significant Difference between Two Sample Means

The `T.INV` function can be used to calculate the critical value needed for a two-sample t-test. This test is commonly used to determine if there is a significant difference between the means of two populations.

### Calculating a Confidence Interval for the Difference between Two Sample Means

Similar to the first use case, the `T.INV` function can be used to calculate the critical value needed to calculate a confidence interval for the difference between two sample means.

## Common Mistakes

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

### Not providing required arguments

Make sure to provide both the probability and degrees of freedom arguments to the `T.INV` function.

### Providing invalid arguments

The probability argument must be between 0 and 1 and the degrees of freedom must be greater than 0.

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

• `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.

• `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.

• `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.

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