# TINV

The `TINV` function returns the inverse of the Student's t-distribution for a given probability and degrees of freedom. This function is commonly used in statistical analysis to determine the value of t for a given probability and degrees of freedom.

## Usage

Use the `TINV` 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 number of degrees of freedom for the distribution.

## Examples

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

### Calculating critical values

The `TINV` function can be used to calculate critical values for the Student's t-distribution. For example, if you are conducting a two-tailed t-test with a 95% confidence level and 10 degrees of freedom, you would use `=TINV(0.025, 10)` to find the critical value.

### Calculating confidence intervals

The `TINV` function can be used to calculate confidence intervals for a population mean when the population standard deviation is unknown. For example, if you have a sample of 25 observations with a mean of 10 and a sample standard deviation of 2, you could use `=TINV(0.025, 24)*2/SQRT(25)` to calculate a 95% confidence interval for the population mean.

### Calculating p-values

The `TINV` function can be used to calculate p-values for t-tests. For example, if you have a t-statistic of 2.5 with 10 degrees of freedom, you could use `=TINV(0.05, 10)` to find the critical value and then use the `TDIST` function to calculate the p-value.

## Common Mistakes

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

### Using a probability value outside the valid range

The probability value used in the `TINV` function must be between 0 and 1 (inclusive). If you use a value outside this range, the function will return an error.

### Using an incorrect degrees of freedom value

The `TINV` function requires the correct number of degrees of freedom for the distribution. If you use an incorrect value, the function will return an incorrect result.

### Using the wrong type of t-distribution

The `TINV` function is used to find the inverse of the Student's t-distribution. If you use the function to find the inverse of another type of t-distribution, the function will return an error or an incorrect result.

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

• `TDIST`

The `TDIST` function calculates the probability associated with a Student's t-Test. It returns the probability that the difference between two data sets is greater than or equal to a certain value. This function is commonly used in hypothesis testing.

• `TTEST`

The `TTEST` formula is a statistical formula used to determine the probability of two sample means being equal. It is commonly used in hypothesis testing to determine if there is a significant difference between two sets of data. The formula returns the probability value associated with a t-test, which can be used to determine if the null hypothesis should be rejected or not.

• `CONFIDENCE`

The `CONFIDENCE` function calculates the confidence value for a population mean. This is often used in statistical analysis to determine the range in which a population mean is likely to fall. The function takes three parameters: the significance level (alpha), the standard deviation of the population (standard_deviation), and the size of the population (pop_size).

• `STDEV`

The `STDEV` function calculates the standard deviation of a set of numbers. It measures the amount of variation or dispersion of a set of values from the average (mean) value. It is commonly used in statistics to determine the spread of a data set. The values can be supplied as individual cells, ranges, or constants.

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