T.INV
TheT.INV
function returns the inverse of the Student's tdistribution for the provided probability and degrees of freedom. This function is commonly used to calculate a critical value from the tdistribution when working with small sample sizes.
 How to use
T.INV
formula?  Examples of using
T.INV
formula T.INV
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T.INV
Usage
Use the T.INV
formula with the syntax shown below, it has 2 required parameters:
 probability (required):
The probability associated with the twotailed Student's tdistribution.  degrees_freedom (required):
The degrees of freedom for the Student's tdistribution.
Examples
Here are a few example use cases that explain how to use theT.INV
formula in Google Sheets.
Calculating a Confidence Interval for a Small Sample
When working with a small sample size, the tdistribution 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 twosample ttest. 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.
Related Formulas
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 tdistribution 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 ttest. 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 twotailed probability of the Student's tdistribution. 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 righttailed Student's tdistribution 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.
Learn More
You can learn more about the T.INV
Google Sheets function on Google Support.