# 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.

## Usage

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

Parameters:
1. probability (required):
The probability of the t-distribution.
2. degrees_freedom (required):
The degrees of freedom of the t-distribution. Must be a positive integer.

## Examples

Here are a few example use cases that explain how to use the `T.INV.2T` formula in Google Sheets.

### Calculating critical values for hypothesis testing

In hypothesis testing, the critical value of t is used to determine whether to reject or fail to reject a null hypothesis. The T.INV.2T function can be used to calculate this critical value for a given level of significance and degrees of freedom.

### Calculating confidence intervals

The T.INV.2T function can be used to calculate the confidence interval for a sample mean when the population standard deviation is unknown. This is done by taking the sample mean, calculating the standard error, and then using T.INV.2T to find the critical value of t for the desired level of confidence.

### Calculating sample sizes

The T.INV.2T function can be used to calculate the sample size needed to estimate the population mean with a desired level of confidence and margin of error. This is done by first calculating the standard error using the population standard deviation (if known) or the sample standard deviation (if unknown), then using T.INV.2T to find the critical value of t for the desired level of confidence, and finally solving for n.

## Common Mistakes

`T.INV.2T` not working? Here are some common mistakes people make when using the `T.INV.2T` Google Sheets Formula:

### Using incorrect degrees of freedom

Make sure to use the correct degrees of freedom for the specific hypothesis test or statistical analysis being performed. Using an incorrect value can lead to incorrect results.

### Using probability outside of range [0,1]

The probability value must be between 0 and 1, inclusive. Using a value outside of this range will result in an error.

The following functions are similar to `T.INV.2T` 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.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.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.

You can learn more about the `T.INV.2T` Google Sheets function on Google Support.